Combined Laser Gamma Experiments At Eli Np

Combined Laser Gamma Experiments at ELI-NP

Technical Design Report

RA5 – TDR

Edited by

Kensuke Homma (Hiroshima University / IZEST, chair)

Keita Seto (ELI-NP)

Ovidiu Tesileanu (ELI-NP, coordinator)

April 2015

Contributors

Yasuo Arai KEK, Japan

Sohichiroh Aogaki ELI-NP

Bertrand Boisdeffre ELI-NP

Loris D’Alessi ELI-NP

Ioan Dancus ELI-NP

Dan Filipescu ELI-NP

Masaki Hashida Kyoto University, Japan

Takashi Hasebe Hiroshima University, Japan

Kensuke Homma Hiroshima University, Japan / IZEST, France

Anton Ilderton Chalmers University, Sweden

Yoshihisa Iwashita Kyoto University, Japan

Masaki Kando JAEA, Japan

James Koga JAEA, Japan

Tetsuro Kumita Tokyo Metropolitan University

Kayo Matsuura Hiroshima University, Japan

Toseo Moritaka Osaka University, Japan (ELI-NP)

Kazuhisa Nakajima Institute for Basic Science, Korea

Yoshihide Nakamiya Kyoto University, Japan

Cristian Petcu ELI-NP

Mihai Risca ELI-NP

Syuji Sakabe Kyoto University, Japan

Keita Seto ELI-NP

Ovidiu Tesileanu ELI-NP

Hiroaki Utsunomiya Konan University, Japan

Zafar Yasin ELI-NP

Abstract

We propose experimental setups in the E7 and E4 experimental areas at ELI-NP to tackle problems of fundamental physics, taking advantage of the unique configuration and characteristics of the new research infrastructure to be constructed in Magurele, Romania. There are seven research topics (denominated RA5-RR, Pair, PPEx, VBir, Pol, DM and GG) proposed. The first chapter in the TDR is devoted to each of these topics, comprising rate estimates, simulation results, technical description, timeline and budget. The experimental setups proposed follow a gradual approach from the point of view of complexity, from the “Day 1” experiments to experiments for which the prerequisites include results from the previously performed ones. In addition, there are two generic R&D tasks proposed in this TDR, related to the development of a detection system, Gamma-Polari-Calorimeter (GPC), commonly applicable to energy measurements for electrons, positrons and gamma-rays above the 0.1 GeV energy scale and the preparatory tests for laser plasma acceleration of electrons up to necessary energies 210 MeV, 2.5 GeV and 5 GeV for the later stage experiments, respectively. Two proposed ideas for further research are presented in the Appendices.

TDR Revision History:

Glossary

Classification of experiments (code name of experiments in RA5-TDR)

RA5-PPEx Experiments of Production and Photoexcitation of isomers (Ch.1)

RA5-DM Experiments in search of the Dark Matter (Ch.2)

RA5-GPC R&D of Gamma Polari-Calorimeter (Ch.3)

RA5-RR Experiments of Radiation Reaction (Ch.4)

RA5-Pair Experiments of e-e+ Pair production in the tunneling regime (Ch.5)

RA5-Pol Experiments of Polarization properties (Ch.6)

RA5-GG Experiments in the Gamma-Gamma Collider (Ch.7)

RA5-VBir Experiments of Vacuum Birefringence (Ch.8)

AGB Asymptotic Giant Branch

ASIC Application Specific Integrated Circuit

CSok Sokolov equation/model in classical dynamics

DAQ Data AQuisition

EFT Effective Field Theory

ELI–NP Extreme Light Infrastructure – Nuclear Physics

FE Front-end Electronics
GS Gamma-ray Source

GBS Gamma Beam System

HV High voltage

IC Interaction vacuum Chamber

ID Identification

IM Intensity Monitoring part

LAD Lorentz-Abraham-Dirac equation/model

LBL Light-by-Light scattering

LL Landau-Lifshitz equation/model

LPA Laser Plasma Acceleration

LWFA Laser WakeField Acceleration

MC Monte Carlo

MOU Memorandum of Understanding

PMT PhotonMultiplier Tube

QED Quantum ElectroDynamics

QCD Quantum ChromoDynamics

QPS Quasi Parallel colliding System

QSok Sokolov equation/model in quantum dynamics

RR Radiation Reaction

SPD Single Photon Detection part

SSD Silicon Strip Detector

SZK Seto-Zhang-Koga equation/model

TDR Technical Design Report

WM Wave Mixing part

Mathematical notation:

4-dimensional affine space

3-dimensional Euclidi space

4-dimensional linear space belonging to

(the model space of )

Lorentz metric (defined on the flat spacetime)

Minkowski spacetime

Introduction

This proposal includes two main topics in physics with staged developments to gradually tackle them. The first is nuclear reactions, linked to the possibility to reach, at ELI-NP, conditions encountered in the interior of stars – the production and photoexcitation of isomers is proposed. The second topic is probing the photon-photon interactions below the MeV energy scale in general which have not been explored thoroughly to date by utilizing the laser-laser, laser-gamma and gamma-gamma collision systems. By these various combinations of photon beams, we can test sub-eV Dark Matter scenarios as well as nonlinear QED effects both in perturbative and non-perturbative regimes. It also includes the laser-electron scattering for the fundamental tests on the radiation mechanisms and pair production via the tunneling process in extremely high-intensity laser fields. The laser-electron experiment also aims at the generation of polarized gamma-rays from sub-GeV to GeV as probes for the later stage experiments to explore the vacuum birefringence under high-intensity laser fields. Considering all of the above, we define several sections for the experiments performed at E7 and E4 experimental areas (Fig. 0.0-1 and Fig.0.0-2). Two ideas for further studies possible to be pursued in RA5 (E7 experimental area) were proposed as Letters of Intent to ELI-NP and are presented in Appendices C and D.

Fig.0.0-1 The Physics cases in RA5-TDR

Fig. 0.0-2 The work space for the proposals in RA5-TDR

Fig. 0.0-3 The staged flow charts of the proposals.

We define experimental stages and the flow charts depending on the experimental areas, R&D subjects, and combinations of beam sources necessary for individual experimental proposals as shown in Fig. 0.0-3, where abbreviations L, e, γ and A correspond to laser, electron, gamma-ray beams and nucleus targets, respectively.

“Stage 1” experiments correspond to technically less difficult proposals based on available beam sources within the current ELI-NP design.

At E7, the production of isomers by irradiating MeV electrons produced with one 1PW/10PW laser line and the excitations with gamma irradiations (RA5-PPEx) from the Gamma Beam System will be measured via the observation of neutron emissions. Because the expected life times of the isomer states are larger than millisecond scale, the synchronization issue does not exist in this proposal.

At E4, search for weakly coupling sub-eV Dark Matter (RA5-DM) with 0.1PWx2 and then 1PWx2 will be performed, which is the simplest experiment to utilize only the laser beams in vacuum chambers.

The prime R&D topic necessary for the following stages 1.5, 3 and 4 is the development of the common detector, Gamma-Polari-Calorimeter (RA5-GPC), to measure momenta of e+ and e-, energies of gamma-rays above 0.1 GeV and the degree of linear polarization of gamma-rays via the conversion process to e+e-.

The second R&D subject is the generation of 210 MeV, 2.5 GeV and 5.0 GeV electron beams based on Laser Plasma Acceleration (LPA) with gas cells for experimental proposals in the stages 2, 3 and 4. Though we will perform proof-of-principle experiments at existing infrastructures prior to the operational phase of ELI-NP, we do not include specific proposals for this subject in our TDR, because other ELI-NP TDR teams also plan this kind of experiments and we will share the relevant technical information by the time of commissioning in 2018.

“Stage 1.5” proposals are fundamental tests on radiation reaction (RA5-RR), on degrees of linear polarization (RA5-Pol) and on pair production (RA5-Pair) via the tunneling process in extremely high-intensity laser fields by combining 600MeV electrons from the linac (ELI-NP Gamma Beam System) and a 10PW laser at E7. All proposed measurements are possible with the GPC.

These experiments can be an alternative proposal to the E7-stage-1 experiment (RA5-PPEx) which shares the common interaction chamber at E7. Depending on the advances of the preparatory experiments relevant to RA5-PPEx and on the decision to construct the electron transport line to E7, the staging order between L(e)++A (RA5-PPEx) and e(0.6GeV)+L(RA5-RR,Pair,Pol) may be swapped. The stage 1.5 proposals require an additional electron transport line to the E7 area in order to get the accurately controlled stable electron bunches from the linac (of the Gamma Beam System). Also an additional Compton-scattering-based calibration system to synchronize one electron bunch with a 10PW laser pulse must be in place. The electron bunches will arrive to E7 from the linac with a lower repetition rate of 1Hz instead of 100Hz, to reduce the electron current for the beam dump in E7. Therefore, it is foreseen to guide 1PW laser pulses operated at 1Hz into the E7 area (through the existing 10PW beamlines) which is synchronized with 10PW with a fixed time difference in advance. However, these additional implementations do not pose difficulties from the technical point of view.

“Stage 2” experiment is the realization of an all-optical table-top gamma-gamma collider at E4 (RA5-GG) to verify the QED-based elastic gamma-gamma scattering. This utilizes the same interaction chamber as that used for RA5-DM at E4. This proposal requires 210 MeV electrons by means of laser plasma acceleration (R&D topic).

“Stage 3” experiments essentially repeat the same measurements as those in the stage 1.5 with upgraded electron energies by means of laser plasma acceleration. Moreover, we aim at the production of linearly polarized 1GeV gamma-ray source via the nonlinear inverse Compton process with 5.0 GeV electrons for the next stage.

“Stage 4” experiment is measurement of vacuum birefringence (RA5-VBir) via the depolarization of linearly polarized incident gamma-rays due to the effect of non-perturbative QED interactions in a focused high-intensity laser field. This proposal requires the linear polarized 1 GeV gamma-ray source developed in the Stage 3.

Based on the following basic parameters for 0.1PW, 1PW and 10PW lasers and for electrons from GBS LINAC, we briefly introduce in the following sub-sections the physics cases listed above.

Table.0.0-1 Parameters of the available laser output

Table.0.0-2 Parameters of the electron beam from GBS LINAC

0.1 Stage 1

0.1.1 Production and photoexcitation of isomers at E7 (RA5-PPEx)

In this setup, we will investigate the production and photoexcitation of isomers (RA5-PPEx) in the E7 area. The interaction chamber, common for all E7 experiments, can be placed either at the crossing point between 10PW laser and gamma from GS (Fig. 0.1-1) or at the position required by Stage 1.5 experiments (the choice depends on the adopted neutron detection strategy, to be established in the preparatory experiments).

Fig.0.1-1 Experimental setup of E7-Stage 1

Nuclei in the interior of stars are considered to be in a thermal photon bath at a temperature. As a result, nuclei are thermalized in the ground state and excited states with the thermal population probability expressed by the Boltzmann factor , where is the excitation energy and the Boltzmann constant. Therefore, nuclear reactions are induced on excited states in a nucleus as well as on the ground state under the stellar condition.

For example, in the s-process nucleosynthesis [Kae11], the temperature of the photon bath can be K in the He intershell and K in the thermal pulse phase of low-mass AGB stars with M < 4M☼ (solar mass) and K in the core He burning, and K in the shell C burning of massive stars with M > M☼. It can be K in the deep O-Ne layers of massive stars exploding as type II supernovae in the p-process nucleosynthesis [Arn03,Uts06].

Nuclear reactions are induced only on the ground state in a nucleus at low temperature in nuclear laboratories on earth. We envisage an experimental setup to induce photoexcitation on an isomeric state in a nucleus in the ELI-NP’s E7 experimental area, taking full advantage of the capability of irradiating the nucleus with extremely intense radiation beams with different, controlled and highly accurate photon energies.

Figure 0.1-2 depicts a concept of the production and photoexcitation of an isomeric state in 155Gd at 121 keV with the half-life of 32 ms. The 155Gdm isomer is produced by a single shot of one arm of the 10PW laser (with full or reduced power at the repetition rate of one shot/minute) or with the 1PW laser at 1Hz repetition rate. The choice depends also on the isomer under study (the latter possibility being preferable for longer lived states). The laser pulse accelerates electrons at MeV energies, and then these hit a tungsten target in order to produce Bremsstrahlung gamma photons that consequently encounter the Gd target. The isomer is photo-excited just above the neutron threshold by a highly-monochromatic -ray beam from the GBS under the condition that photoexcitation of the ground state does not reach the neutron threshold. Thus, photoexcitation of the isomer is unambiguously verified by detecting photoneutrons.

Goal of this research:

Detecting the photoneutrons resulting from the interaction of the isomer with the gamma radiation beam from GBS.

Fig.0.1-2 Concept of production and photoexcitation of an isomer 155Gd with the half-life of 31.97 ms by synchronized irradiations of laser and -ray beams at E7.

0.1.2 Search for sub-eV Dark Matter candidates at E4 (RA5-DM)

In this proposal we search for frequency shifted photons via four-wave mixing in the vacuum caused by stimulated decay of resonantly produced DM when two color lasers are combined and focused into the vacuum as illustrated in Fig. 0.1-3. Figure 0.1-4 shows the experimental setup we propose at E4.

Fig.0.1-3 Quasiparallel colliding system(QPS) between two incident photons out of a focused laser beam with the focal length , the beam diameter , and the upper range of incident angles determined by geometric optics. The signature is produced via the four-wave mixing process, with by mixing two-color waves with different frequencies 1ω and in advance at the incidence.

Fig. 0.1-4 Arrangement of the basic components for the setup and the CAD drawing at E4 to search for sub-eV Dark Matter via four-wave mixing in the vacuum.

A large fraction of dark components in the universe motivates us to search for yet undiscovered fields to naturally interpret the relevant observations. Because we know examples of resonance states coupling to two photons at 126GeV (scalar field, Higgs) and 135MeV (pseudoscalar field, neutral pion) within only three orders of magnitude on the mass scale, there might be yet undiscovered similar types of resonance states over much wider energy ranges in nature, in particular, in the lower energy side as long as the coupling to two photons is so weak that these dark fields are not discovered by conventional methods to date. This encourages us to further search for resonance states at energy ranges below 1MeV that conventional charged particle colliders will never be able to access. There are theoretical rationales to expect sub-eV particles such as the axion (pseudoscalar boson) [Pec97] and the dilaton (scalar boson) [Fuj03] associated with breaking of fundamental symmetries in the context of particle physics and cosmology. Therefore, we are led to probe such fields via their coupling to two-photons in the sub-eV mass range. Furthermore, the advent of high-intensity laser systems and the rapid leap of the intensity encourage the approach to probe weakly coupling dark fields with optical photons by the enhanced luminosity factor [Hom12i, Taj12].

We therefore propose searches for resonantly produced dark fields with quasi-parallel two-color laser-laser collider at E4 where 100TW x 2 lasers are available and 1PW x 2 will also be available if the beam transport at the upstream is slightly reconfigured.

Goal of this research:

Even if no statistically significant four-wave mixing signal is observed, it is possible to constrain fundamentally important theoretical models for Dark Matter such as QCD axion scenarios based on the mass-coupling relation of the exchanged fields as shown in Fig.0.1-5. The accessible domains by the searches at ELI-NP are indicated by the two red lines from the top to the bottom for cases where 0.1PW with an OPA-based inducing laser and 1PW with an OPA-based inducing laser are assumed, respectively. The assumed data taking periods are commonly about 10 days. The red lines indicate that ELI-NP has the potential to test QCD axion scenarios in the mass range 1-100 meV, corresponding to a sensitivity beyond the present world record.

Fig.0.1-5 Upper limits on the coupling – mass m relation for the scalar field exchange.

As references in Fig.0.1-5, we put existing upper limits by our pilot search (Search at Hiroshima) based on this method [Hom14] and also by the other types of scalar field searches by vertically shaded areas: the ALPS experiment [Ehr10] (the sine function part of the sensitivity curve is simplified by unity for the drawing purpose) which is one of the ”Light Shining through a Wall” (LSW) experiments, searching for non-Newtonian forces based on the torsion balance techniques (Etö-wash [Abe07], Stanford1 [Chi03], Stanford2 [Smu05]) and the Casimir force measurement (Lamoreaux [Lam97]). The domains below the vertically shaded areas are all excluded. We note that if we require the proper polarization combinations between initial and final states for pseudoscalar fields [Hom12p], we will be able to test the QCD axion models in the near future. As a reference, we show the expected mass-coupling relation based on the QCD axion scenario for E/N = 0 [Ber12a] (KSVZ model [Kim79]) which is indicated by the inclining dotted line. The pink horizontal line indicates the gravitational coupling limit.

0.1.3 R&D for Gamma-Polari-Calorimeter (GPC)

Gamma Polari-Calori-meter (GPC) is the common detector system that will be employed in Stage 1.5, 3 and 4 at E7 as illustrated in Fig.0.1-6 a) conceptual drawing and b) CAD drawing.

Fig.0.1-6a) Conceptual drawing for Gamma Polari-Calori-meter (GPC). Note that the typical e+e- opening angle is around sub-mrad. The angle at the top-view is exaggerated.

Fig. 0.1-6 b) CAD drawings for GPC

GPC is designed to be able to measure incident gamma-ray energies from 0.1-5.0 GeV via the conversion process to e+e- pairs and simultaneously measures the degree of linear polarization. Therefore, a part of GPC also guarantees capability to measure momenta of e+ and e- individually without the gamma-converter.

Goal of this research:

The requirements to this detector system are :

1. momentum resolution with respect to above 100 MeV e+ and e- below 10%.

2. analyzing power to the degree of linear polarization is greater than 30%.

3. capability to measure more than ten e+e- pairs per shot.

Figure 0.1-7, 0.1-8 and 0.1-9 indicate an event display for a pair creation event simulated by GEANT4, the inclusive momentum resolution for e+ and e- above 0.2 GeV, and the analyzing power of polarimetry with respect to 1GeV gamma-rays, respectively.

Fig. 0.1-7 An event display of a gamma-ray conversion process into e+e- simulated by GEANT4.

Fig. 0.1-8 Inclusive momentum resolution of produced e+ (blue) and e- (red) above 0.2 GeV.

Fig. 0.1-9 Analyzing power of gamma-ray polarimetry corresponding to a 50% level. The amplitude as a function of rotation angles of reaction planes of e+e- pairs around the gamma-ray incident axis with respect to the polarization plane of the incident gamma-rays reaches 50% (blue circle) of that of incident 100% linear polarized gamma-rays with 1 GeV (black empty circle).

Stage 1.5

In this setup (Fig.0.2-1), we will investigate radiation reaction (RA5-RR), e-e+ pair production (RA5-Pair) and polarization (RA5-Pol) at E7. We can carry out these 3 experiments simultaneously, therefore the considered experimental setup in this stage is only one configuration (Table 0.2-1). We also investigate the same topics in Stage 3 but employing the multi-GeV electron source produced by LWFA (please see the configuration Fig. 0.4-1 in Sect.0.4).

Fig. 0.2-1 Experimental setup of E7-Stage 1.5 (see also Fig. 4.2-3)

Table 0.2-1: parameters for experiments

0.2.1 Radiation reaction (RA5-RR)

Radiation reaction (RR) is the first important effect in the interaction between the ultra-high intense laser and a high energetic electron. In the case that an electron has a high energy, it is predicted that this single electron can emit strong light by the interaction with ultra-high intense laser. When using lasers at ELI-NP (10PW – 1022 W/cm2 class), all experiments require us to consider RR [Kog04]. RR represents not only a radiation-feedback effect to an electron motion, but it describes the characteristics of an electron or how an electron interacts with an external field.

The most basic model was suggested by Dirac, as the Lorentz-Abraham-Dirac (LAD) equation (1938) [Dir38]. However it includes the energy divergence which is one of the mathematical difficulties named the run-away solution. By transformation of the LAD equation, we can find . Therefore, many theoreticians have tried to propose a lot of models for improvements. For example, the Landau-Lifshitz model is a basic-first order perturbation of LAD equation [Lan94]. I. Sokolov suggested that radiation should be described via the total cross section [Sok10]. One of the authors of this TDR, K. Seto considers the LAD model in quantum vacuum for stabilizing the LAD equation [Set14-1,2 and Set15-1,2]. Our strong interest is the changing of “the (running) coupling between an electron and high-intense fields”. The current RR models are based on this idea. We will investigate the basic evidences for establishing the theoretical model of radiation reaction in E7 by using a 10 PW-1022-23 W/cm2 laser (in Table 0.2-1) and the electron beam of 600MeV from the linac or over 4GeV from LWFA. The results obtained will push further the knowledge of nonlinear/non-perturbative QED treatments.

Goal of this research:

Observing the minimum energy of an electron and the maximum energy of radiation from an electron. The stochastic average of them is equal to the edge of radiation reaction (see Fig.0.2-2) under the condition of Table 0.2-1.

0.2.2 The e+e- pair production in the tunneling regime (RA5-Pair)

Typical consequence of quantum electrodynamics (QED) is electron-positron pair production. Especially, pair production only by photons is attractive as a conversion process between matter and vacuum. There is a long history of theoretical work on this process from the beginning of QED. However, experimental verification is not sufficient for these theories since it is difficult to realize the light source energetic enough to produce the electron-positron pairs.

There are several processes to realize the pair production in vacuum. One is the Breit-Wheeler process derived from perturbation theory of QED [Bre 34]. High energy photons interact with each other and are converted into particle pairs. The threshold is determined by the total energy of the interacting two photons. The other is spontaneous pair production in a background electromagnetic field [Sch 51]. This process should be considered in the non-perturbative regime under the action of numerous photon interactions, which is not demonstrated compared to the perturbative regime. The threshold is determined by the background field strength and is still far from the available laser intensities.

Fortunately we can approach some part of the non-perturbative regime, i.e., strong-field QED, via a combined scheme: interaction between a strong laser field and high energy photons [Sch 08]. Detailed cross sections have been obtained theoretically based on the semi-classical approach. The theory indicates that state-of-the-art intense lasers can potentially achieve the near threshold condition of pair production. Possibility of pair production experiment in ELI-NP is considered to provide a proof of the strong-field QED.

In this proposal, we consider a simple experimental configuration similar to that of the previous experiment, SLAC E-144 [bam 99]. The SLAC experiment is one of the few experimental examples on the pair production in laser fields. It is shown that SLAC and ELI-NP could approach different regimes of pair production, being complementary in the exploration of strong-field QED.

Goal of this research:

Detection of positrons assuming the laser parameters in Table 0.2-1 (see also Fig.0.2-2).

0.2.3 Polarization Properties of Emission in Strong Fields (RA5-Pol)

Recent progress of intense laser technology provides new opportunities to explore the physics of light. One of the most fundamental processes of light is photon emission from a moving electron. There are two physical pictures on this. One is based on classical electrodynamics. Electrons accelerating under the action of a background electromagnetic field radiate electromagnetic waves. The other is based on quantum electrodynamics. The photon and electron interact with each other and are scattered with the resulting energies. In extremely strong fields, these two pictures are unified. The quantum emission process becomes nonlinear under the action of strong background field and electromagnetic waves in classical radiation are quantized. Theoretical estimations indicate that we could approach the transition of physical regime from classical to quantum by means of the laser and electron beam facilities in ELI-NP. In this proposal we focus on the polarization properties of photon emission in strong fields. While radiated electromagnetic field in classical regime is highly polarized, the quantum radiation cross section indicate the emitted photons are depolarized under the influence of spin effects.

Goal of this research:

Observing the degree of polarization under the parameters in Table 0.2-1 (see Fig.0.2-1).

Fig. 0.2-2 Key prediction: the interaction between an initial 600MeV electron and 1×1022W/cm2 laser. We observe (1) the scattered electron by RA5-RR experiment, (2) pair production by RA5-Pair experiment and (3) polarization of electron’s radiation by RA5-Pol experiment, in this Stage 1.5.

Stage 2

0.3.1 All optical table-top  collider at MeV at E4 (RA5-GG)

The proposal RA5-GG aims at observation of real photon – real photon elastic scattering event for the first time in history as illustrated in Fig. 0.3-1. The experiment will be performed at where the cross section is maximized. For this experiment we need 210 MeV electron beam based on LPA R&D. This collider can be completely set-up in the interaction chamber used for the DM search in Fig.0.1-4.

Fig. 0.3-1 An all-optical table-top () collider: a) top-view including two LPAs and the detector system to capture the scattering, b) collision geometry around the interaction point, IP, where -rays are produced at each Compton scattering point (CP) in head-on collisions and is the distance between IP and CP.

Goal of this research:

We verify the QED-based  scattering cross section by observing large angle scattering events showing clear back-to-back correlated gamma rays with 0.5-1.0 MeV as shown in the event display in Fig. 0.3-1. A three-month data taking period with 0.1PWx2 lasers operated at 10Hz would be necessary to claim the five sigma statistical significance of such back-to-back events. Once we confirm it, we will shift our focus to search for dark field resonances around that energy range in general by changing . The variable of gamma-gamma collisions by combining laser-plasma accelerated electrons and the seed laser for Compton scattering to produce gamma rays is the unique feature of ELI-NP. For this general search, we will use both 0.1PWx2 and then 1PWx2 lasers at E4. The series of measurements in the stage 1 and 2 at E4 are considered to be a general investigation on photon-photon interactions over the wide energy range from a few MeV down to sub-eV range.

Stage 3

In this stage, we repeat the same measurements as those in the stage 1.5, RA5-RR/Pair/Pol by upgrading electron energy with laser plasma wakefield accelerator. Therefore, 10PW lasers will be used and collision geometry will change from that of the stage 1.5 (Fig.0.4-1). We consider this stage also as the preparatory experiments for Stage 4 experiment, namely RR5-VBir – vacuum birefringence. To achieve this in Stage 4, we also aim at the generation of linearly polarized gamma-rays around 1 GeV in E7 area. Prerequisites for this experiment are the results of the demonstrations of LWFA and RR and the generation of radiation from the interaction between photons and high energy electrons of 0.6GeV, 2.5GeV and 5GeV, respectively.

Table 0.4-1: parameters for observations

Fig. 0.4-1 Experimental setup of E7 – Stages 3 and 4. (see also Fig. 4.2-5)

Goal of this research:

Observing the minimum energy of an electron and the maximum energy of radiation from an electron. The stochastic average of them is equal to the edge of radiation reaction (RA5-RR)

Detection of positrons (RA5-Pair)

Observing the degree of polarization (RA5-Pol) assuming the laser parameters in Table 0.4-1.

Fig. 0.4-2 Key prediction: the interaction between an initial 5.0GeV electron and 2×1023W/cm2 laser. We observe (1) the scattered electron by RA5-RR experiment, (2) pair productions by RA5-Pair experiment and (3) polarization of electron’s radiation by RA5-Pol experiment, in this Stage 3.

Stage 4

0.5.1 Test of QED-induced birefringence (RA5-VBir)

High energy photons passing through an intense laser field may change helicity/polarization state due to light by light scattering (“LBL”) [Hal34]. If we consider a probe, e.g. an X-ray laser pulse, then some portion of photons in the probe can flip state, and this appears macroscopically as a small ellipticity in the polarization of the probe beam. This is “vacuum birefringence” due to the intense field [Tol52, Hei06].

Fig.0.5-1 Photons are emitted in a small cone around the direction, from electrons moving in the plane. is the half-opening angle in the spectrum. is the azimuthal angle around the (primary) beam direction.

At ELI-NP [ELI] as shown in Fig.0.4-1, we plan to study LBL using radiation as the probe. The radiation itself is generated by electrons interacting with an intense optical laser. The radiation then passes through a second intense 10 PW beam, and the parallel and perpendicular polarized parts of the spectrum will mix due to LBL as depicted in Fig.0.5-1. Hence we estimate here the impact of LBL on the radiation spectrum. Note that photons also scatter due to LBL, see e.g. [Kin12, Gie13], but this can be neglected – when the probe frequency is much higher than the background frequency (in this case, optical), the scattering becomes “eikonal” and effectively forward [Din14a]. Two experimental setups are proposed, for the use of both 10PW beams or splitting all necessary beam inputs from only one 10PW beam, with the parameters in Table 0.5-1 and 0.5-2, respectively.

Table 0.5-1 Parameters of laser in the case of double 10 PW system

Table.0.5-2 Parameters of laser in the case of a single 10 PW system

Goal of this research:

We test the depolarization effect or birefringence under the focused high-intensity laser field. Given a target laser field of 2×1023 W/cm2 probed by 1 GeV 100% linearly polarized gamma-rays whose polarization planes are rotated by 45% with respect to the polarization plane of the target laser, we anticipate the flip probability reaches a 30% level. For the actual incident probe gamma-rays with 80% linear polarization, we thus expect that the degree of polarization from the initial value is reduced to 24%. Figure 0.5-2 shows the simulated results on the angular distribution of produced e+e- pairs reconstructed by GPC around the incident gamma-ray direction with the expected number of shot statistics of 103 accumulated over 20 hours with 10PW at 1/60Hz. The evaluated analyzing power of GPC is 50%. Though the modulating amplitude is reduced from 80% to 24%, we still can observe the depolarization behavior with a good statistical significance.

Fig. 0.5-2 Depolarization effects or birefringence of incident 1GeV 80% linearly polarized gamma-rays measured by GPC. The black fit curve is when no target laser field exists, while blue fit curve is when there is a target field of 2×1023 W/cm2 with the expected number of shot statistics of 103 accumulated over 20 hours with 1/60Hz.

0.6 Total Budget

RA5-E7 1142 k€

(common interaction chamber, beam dumps and beam transport in E7, computing infrastructure – detailed in Sub-section 1.5, Budget of RA5-PPEx)

RA5-PPEx 100 k€

RA5-DM 1450 k€

RA5-RR 1600 k€

(400 k€ general equipment for Stage 1.5 experiments +1200 k€ general equipment for laser beam delivery in E7 for Stage 1.5-3-4 experiments)

RA5-Pair 50 k€

RA5-Pol included in RA5-RR/Pair/VBir

RA5-GG 905 k€

RA5-VBir 515 k€

Gamma-Polari-Calorimeter 326 k€

Computation resources – cluster 110 k€, included in RA5-E7 above

0.7 Timelines

Timelines of RA5-TDR are shown in Fig.0.7-1 below.

Fig.0.7-1 Timeline of RA5-TDR

RA5-TDR

Stage 1

Experiments of

RA5-PPEx production and photoexcitation of isomers (Ch.1)

RA5-DM Dark matter (Ch.2)

R&D of

RA5-GPC Gamma-Polari Calori-Meter (Ch.3)

1. Production and Photoexcitation of Isomers (RA5-PPEx)

1.1 Physics Case

1.1.1 Photoneutron reactions on nuclei in the ground state

In nuclear astrophysics [Moh00,Uts06], the reaction rate (), the number of reactions taking place per unit time, for a photoreaction induced on a ground-state nucleus leading to the emission of a neutron is given by

, (1.1.1)

where c is the speed of light, the photoneutron cross sections, and the number of photons per unit volume and energy . In a stellar interior at a temperature , is remarkably close to a black-body or Plank distribution:

. (1.1.2)

When Eq. (1.1.2) is substituted for in Eq. (1.1.1), the rate becomes a function of parameter . It is then possible to define the photon energy range which is the most relevant for determining at the temperature of astrophysical interest. This results from the properties of the integrand of Eq. (1.1.1), the product of the photoneutron cross section and the Planck distribution . The integrand differs significantly from zero only in a relatively small energy range defined immediately above neutron threshold. We call this range the Gamow window for photoneutron reactions. Figure 1.1-1 illustrates this Gamow window.

Figure 1.1-1 The Gamow window for photoneutron reactions defined immediately above neutron threshold Sn. A narrow energy window is defined as the product of the photoneutron cross section and the Planck distribution.

1.1.2 Stellar photoneutron reactions

In stellar environments, nuclear excited states are thermally populated. Figure 1.1-2 depicts photoexcitation on a thermally populated excited state. At high temperatures, thermalization may enhance the photoreaction rates by several orders of magnitudes.

Figure 1.1-2 Photoexcitation on the excited state lated statee

The right-hand side of Eq. (1.1.1), which corresponds to photodisintegration from the ground state only, must be replaced by a sum of the rates for photodisintegration from all (ground and excited) states , each term being weighted by the appropriate Boltzmann factor. Thus, the astrophysical reaction rate is defined by

, (1.1.3)

where

(1.1.4)

is the temperature-dependent partition function of the target nucleus. Note that in , is replaced by the cross section for photodisintegration from state . Photoexcitation strength function is determined by the photoabsorption cross section summed over all possible spins of the final states [Cap09]:

(1.1.5)

Here, X represents the electric (E) or magnetic (M) excitation mode and L the multipolarity.

Although nuclear reactions naturally take place not only on the ground state but also on excited states thermally populated in the interior of stars, closed nuclear systems at high temperatures and densities formed by the gravitational force, they are induced only on the ground state in experimental laboratories on Earth. As a result, there is no experimental information on , , and for any excited state . Note that , where is the neutron transmission coefficient and the sum of all particle and radiative transmission coefficients. Above neutron threshold (E > Sn: neutron separation energy), is generally dominated by which becomes zero at Sn. Due to a lack of the experimental information, the Hauser-Feshbach statistical model is used to calculate , , , and , assuming that the gamma-ray strength function is the same as the one for the ground state.

Thus, it is indispensable to experimentally investigate stellar photoreactions in the laboratory.

1.1.3 Inducing and detecting stellar photoreactions at E7

The ELI-NP may become the first research laboratory where stellar photoreactions are induced and detected. We propose an experiment to induce stellar photoreaction at E7 by producing isomers with the high power lasers and photo-exciting isomers with the intense gamma-ray beam.

The experiments of producing the isomers may be performed either by multiple laser shots (Type I) or a single laser shot (Type II) of the 10PW lasers. An isomer is produced in the inelastic electron scattering or in a photoabsorption reaction, leaving a nucleus in either bound states or unbound states; The bound states decay to the isomeric state via -transition [Bel99], while the unbound states undergo neutron emission followed by γ-transition to the isomeric state [Gok06]. Laser-accelerated electrons with kinetic energies of the order of MeV (or the subsequent Bremsstrahlung radiation) most effectively produce isomers. Therefore, a key technology is to produce a vast number of MeV electrons by laser acceleration suited to the production of isomers, by optimizing the operation condition of the laser with the pulse width of fs.

The Type I experiment is applicable to long-lived isomers with half-lives sufficiently longer than the frequency (1/60 Hz) of the 10PW laser. The production of a large number of long-lived isomers is required in the first step followed by subsequent irradiations with a -ray beam in the second step to photo-excite the isomers. In contrast, the Type II experiment is applicable to all isomers irrespective of their half-lives because isomers are produced by a single laser shot and simultaneously irradiated with a -ray beam that is synchronized to the laser shot. Since the laser shot and the -ray irradiation are synchronized in a time interval of the order of ps, the Type II experiment is also applicable to excited state with half-lives comparable to the synchronization time. The signal-to-noise ratio, limited by the fact that a relatively small number of isomers are produced by a single laser shot is greatly improved by applying a short time gate for the synchronized irradiation of laser and -ray beams. A Type II experiment for an isomer 155Gdm with a half-life of 32 ms is depicted in Fig.0.3-1.

Table 1.1-1 lists isomers of research interest.

Photoexcitation of isomers is verified by detecting photoneutrons. The 155Gdm isomers with the spin-parity of 11/2- and the excitation energy 121 keV are photo-excited just above the neutron threshold at 6635 keV by a highly monochromatic -ray beam with an energy spread 0.5% (33 keV) in FWHM at energies between 6314 and 6635 keV. Thus, photoneutron emission occurs on 155Gd not in the ground state but in the isomeric state. The neutron detection is carried out in collaboration with the research group “Gamma above Neutron Threshold”.

Table 1.1-1 Isomers of research interest

1.2 Technical Proposal

The proposed experiment of the production and photoexcitation of isomers requires the following preparatory R&D:

A preparatory investigation of laser acceleration of electrons with the 1PW laser at the CETAL facility in Magurele. The peak power (1PW) and pulse width of the laser need to be modified and optimized to accelerate electrons in the MeV region at high fluxes. A gas or solid target will be employed for this purpose (this will be defined in a common ELI-NP – CETAL research project).

Test for the production of isomers with the 1PW laser at the CETAL facility. Production reactions of the inelastic electron scattering, (e,e’) and (e,e’n), as well as photoabsorption of the Bremsstrahlung gamma ray photons, need to be investigated with emphasis on the production efficiency of isomers.

The fundamental technology developed by the preparatory investigation will be applied to the proposed experiment with the 10PW laser and the gamma beam at the ELI-NP facility. In the E7 experimental area there will be possible to use also the 1PW laser beam at 1Hz repetition rate, transported through the 10PW beamline(s). A long focal-length parabolic focusing mirror, housed in a turning box located in the E1/E6 experimental area, will allow for the use of the long focus (9.5m) at 1PW and 10PW. This is beneficial for electron acceleration in a gas target, and specifically for this experiment we do not need very tight focus, a long focal being desirable.

The electrons accelerated with the help of the high-power laser will hit a first target, of W, to produce Bremsstrahlung radiation in the gamma domain. Then, at a distance that depending on the isomer to be studied and on the geometry of the electron acceleration and Bremsstrahlung setup may vary from a few mm to a few cm, there is the second target, containing the nucleus of interest. By irradiation with the Bremsstrahlung gamma rays, part of the nuclei in this target will reach (directly or indirectly) the isomeric state to be investigated.

At a next moment (after a delay depending on the lifetime of the isomeric state), the target is irradiated with the gamma beam from GBS with an energy tuned in such a way as to be slightly above the neutron threshold from the isomeric state (but not also from the ground state) and the photoneutrons are detected.

At ELI-NP there is foreseen a 4π array for neutron detection, which is described in the “Gamma above Neutron Threshold” TDR (Figure 1.2-1). The procedures for the purchase of the 3He detectors for this array already started. Depending on the results of the preparatory experiments, the detectors will be placed around the secondary (isomer) target, or a fast transport system will be installed to transport the target to the 4π array after the irradiation with the Bremsstrahlung gamma photons. In either case, the neutron detectors array will be placed on the gamma radiation beam from GBS (and the photoexcitation of the isomers created in the target shall occur when the target is in the detectors array).

Figure 1.2-1 Schematic image of the 4π neutron detector structure, proposed in the ELI-NP TDR “Gamma Above Neutron Threshold”.

1.3 Estimation of Count Rates/Feasibility of Proposed Devices

There are several considerations that support the idea of performing this experiment at ELI-NP. One of them is the availability of an intense, narrow-bandwidth gamma radiation beam. Another one is the possibility to use high power lasers for accelerating electrons and put the nuclei in the isomeric states of interest.

The signal to noise ratio for detection is greatly enhanced by the fact that only a small fraction of the time is covered by the gamma radiation pulses, the macrobunches occupying only 50μs each second.

Due to the fact that the production of isomeric states is expected to be more efficient with the help of gamma photons with respect to electron scattering, there is envisaged the use of a Bremsstrahlung target placed immediately after the electron acceleration site (laser beam focus). In Figure 1.3-1 below there are displayed the results of the Geant4 simulation of the Bremsstrahlung spectra originating from a W target on which 106 laser-accelerated electrons arrive with an energy of 40MeV and an energy spread of 1%.

Figure 1.3-1 Spectrum and histogram of the number of Bremsstrahlung gamma radiation photons exiting the primary W target, function of the angle and energy.

The number of electrons accelerated with the help of 1PW or 10PW lasers can be estimated/extrapolated from previous experiments at existing, lower power lasers [Esa09]. Thus, a number of 1010 electrons accelerated in the 50MeV range can be expected from a 1PW laser pulse, while for 10PW this figure may be one order of magnitude higher.

Considering only the photons exiting the W target at small angles in the direction of the incident electrons, and imposing an energy threshold above which photons produce the transfer of nuclei on the isomeric state, one can estimate the number of isomers produced per laser shot.

Taking as an example the 176Lum case, due to the quite large lifetime of the isomeric state, several 1PW laser shots can be used in order to excite the target. For a 1 hour laser functioning, meaning the delivery of 3600 shots at 1PW on target, and assuming a secondary 176Lu target of 1 mm diameter on which consequently the 8×108 ph/s (within the bandwidth) gamma beam hits, a count rate of about 0.3 neutron/second is expected in the 4π detector. By using a gate of equal duration with the time needed for neutron moderation in the polyethylene for each gamma macro-bunch, the signal to noise ratio is greatly increased (by a factor of more than 103).

For the short-lived isomers, such as 155Gdm (32ms), they can be produced by one shot of the 10PW laser, then photo-excited by synchronized irradiations with a single-shot of gamma micro-bunch followed by neutron detection with fast Li glass scintillation detectors with a time gate 100ns.

The preparatory experiments of laser acceleration of electrons aim to improve these numbers by increasing the electron yield and optimizing the geometry of the setup.

1.4 Timeline of implementation and milestones

The timeline of RA5-PPEx is shown as Fig.1.4.1.

Fig.1.4.1 Timeline of RA5-PPEx

1.5 Estimated Budget

Specific for the RA5-PPEx experiment

Table 1.5-1 Costs for the experimental items specific for the RA5-PPEx proposal

Common for all experiments

Table 1.5-2 Costs for the interaction chamber, electron acceleration setup and computational resources (common also to other proposals in this TDR)

2. Dark Matter Search (RA5-DM)

2.1 Physics Case

There are theoretical rationales to expect sub-eV particles such as the axion (pseudoscalar boson) [Pec97] and the dilaton (scalar boson) [Fuj03] associated with breaking of fundamental symmetries in the context of particle physics and cosmology. Therefore, we are led to probe such fields via their coupling to two-photons in the sub-eV mass range. Furthermore, the advent of high-intensity laser systems and the rapid leap of the intensity encourage the approach to probe weakly coupling dark fields with optical photons by the enhanced luminosity factor [Hom12i, Taj12].

We advocate the concept of the quasi-parallel laser collider to produce a resonance state of a hypothetical boson in the sub-eV mass range and simultaneously induce the decay in the background of a coherent laser field [Fuj11, Hom12a, Hom12p]. The exchange of such a low-mass field is interpreted as the four-wave mixing process in the vacuum. Figure 2.1-1 illustrates the four-wave mixing process where two photons with the degenerate energy ω are used for the resonance production and the inducing laser field has the energy with , and a photon with the energy is created as the signature of the interaction. This four-wave mixing process is well-known in quantum optics [Dru6.1, Yar97], where atomic dynamics governs the phenomenon instead of the exchange of the hypothetical resonance state, and the application to test the higher-order QED effect can also be found in Ref.[Mou99]. We identify this wave mixing system as a special kind of photon-photon colliders, whose significant advantage is that the interaction rate has cubic dependence on the laser intensity, while the conventional particle colliders have quadratic dependence on the number of charged particles per colliding bunch [Hom12p]. The cubic dependence of the interaction rate highly motivates us to extend the method to much higher pulse energy and higher-intensity laser systems.

The proposed method can in principle distinguish whether the exchanged boson is scalar or pseudoscalar based on combinations of polarization states in the initial and final state photons [Hom12p]. Therefore, the method has impacts on searches for axion-like particles as well as the fifth force [Fuj6.1].

Here we summarize formulae necessary to obtain the coupling-mass relation from experimental parameters. The formulae are basically from Ref.[Hom12p], however, we reevaluate the relations to apply to the realistic experimental conditions in the pilot search. We thus provide the details of the corrections in Appendix A and B compared with those in Ref.[Fuj11, Hom12p].

The effective interaction Lagrangian between two photons and a hypothetical low-mass scalar field has the generic form expressed as

(2.1.1)

4 where has the dimension of energy while being a dimensionless constant.

Fig.2.1-1 Quasiparallel colliding system(QPS) between two incident photons out of a focused laser beam with the focal length , the beam diameter , and the upper range of incident angles determined by geometric optics. The signature is produced via the four-wave mixing process, with by mixing two-color waves with different frequencies 1ω and in advance at the incidence.

Fig.2.1-2 Definitions of kinematic variables [Fuj11].

In the case of the scalar field exchange, the possible linear polarization states in the four-wave mixing process when all wave vectors are on the same plane as illustrated in Fig.2.1-2 are expressed as follows:

, (2.1.2)

Where photon energies from the initial to the final state are denoted by the linear polarization states {1} and {2} which are orthogonal to each other. In this pilot experiment, we pursuit the second case of Eq.(2.1.2).

We then introduce notations to describe kinematics of four photons as illustrated in Fig.2.1-2, where the incident angle ϑ is assumed to be symmetric around the z-axis in the average sense, because we focus lasers symmetrically by a lens element. We introduce an arbitrary number u with to re-define momenta of the final state photons as

and , (2.1.3)

where we require . We consider to measure ω3 with the specific polarization states as the signature of the interaction. With these definitions, energy-momentum conservation is expressed as [Hom12p]

, (2.1.4)

(2.1.5)

(2.1.6)

(2.1.7)

Given a set of physical parameters of the scalar field exchange: mass m, coupling to two photons g/M, and the polarization dependent factor FS with a specified set of linear polarizations S as explained below, the yield is parameterized as

, (2.1.8)

which is quoted from Eq.(56) in Appendix A, where the subscripts and denote creation and inducing lasers, respectively, wavelength, pulse duration, a common focal length, a common beam diameter, and upper and lower values on determined by the spectrum width of , respectively, is the combinatorial factor originating from the consideration on multimode frequency states [Hom12p], the average numbers of photons in coherent states, the numerical factor relevant to the integral of the weighted resonance function defined by Eq.(43) in Appendix A, and we partially apply natural units to parameters specified with [eV].

We have discussed the effect of the spectrum width in the case that the spectrum width of the creation laser is negligibly small compared to that of the inducing laser in Ref.[Hom12p]. However, this is not always the case. For example, this pilot experiment is actually performed with the condition that both widths are nearly equal as we explain in the next section. We provide the treatment on the effective choice of u and u applicable to the most general case in Appendix B in detail.

In the case of as specified by the second of Eq.(2.5.2) applied to the scalar field exchange (SC), the polarization dependent factor is estimated as [Hom12p]

(2.1.9)

with for a given via in Eq.(2.5.7). This factor originates from a degree of freedom on the azimuthal rotation of the plane including and around the z-axis in Fig.2.1-1 with respect to that defined by and . The other polarization combinations can also be calculated based on Appendix of Ref.[Hom12p].

From Eq.(2.1.8) we express the coupling parameter to discuss the sensitivity as a function of for a given set of experimental parameters via the following equation

(2.1.10)

under the condition , because the pulse energy of the creation laser is more important to enhance the signal yield due to the quadratic dependence on the energy.

We note that above formulation is also applied to pseudoscalar fields in general with slightly different coefficient from that of scalar fields [Hom12p].

2.2 Technical Proposal

2.2-A. Conceptual design for this experiment

Figure 2.2-1 illustrates the conceptual view of the experimental setup. The setup consists of the wave mixing part (WM), the interaction vacuum chamber (IC), the intensity monitoring part (IM) and the single photon detection part (SPD).

WM combines a pulse laser to create a resonance state with another pulse laser with different wavelength which induces the decay with specified linear polarization states. For the purpose of the calibration, a laser beam containing the signal energy is also combined. The wave mixing can be achieved by a set of dichroic mirrors.

The creation laser is the linearly polarized 0.1PW(2.2J/22fs) / 10PW(22J/22fs) laser pulse with the wavelength 820 nm. The inducing laser in NIR is the linearly polarized laser produced via optical parametric amplification (OPA) with a seed. Given wave lengths for creation laser and inducing laser beams which result in , the corresponding wavelength of four-wave mixing is expected to be

. (2.2.1)

The linear polarization state {1} is defined by the incident creation laser, while the state {2} is for the inducing laser which is adjusted so that the planes of the linear polarizations become orthogonal to each other.

After wave mixing with specified polarization states, the combined laser beams share the common optical axis, and they are guided into the interaction chamber (IC) maintained. After focusing the combined beams inside IC, the divergent beams are parallelized by a set of achromatic parabola mirrors. The beam focusing parameter is important, because this gives the upper limit of the sensitive mass range by the possible range of the incident angle ϑ via Eqs.(39) -(41) in Appendix A. The resonance production is enhanced when is satisfied, that is, when a CMS-energy between two incident photons coincides with the exchanged mass. If an angular coverage is too small compared to a mass we are interested in, the resonance condition is never satisfied. Therefore, the focusing parameter can adjust the sensitive mass range via the upper limit on the incident angles.

The absolute beam intensities are monitored by the beam profile monitor. The non-interacting creation and inducing laser fields are kicked out by individual dichroic mirrors and the reflected waves are measured by the photo diodes PD1 and PD2 for creation and inducing laser pulses, respectively. These amplitude information are used to monitor the relative intensity variation on the shot-by-shot basis.

Fig.2.2-1 Conceptual view of the experimental setup to measure the four-wave mixing process in the vacuum. This figure is quoted from [Hom14]

The signal wave is further guided to a group of grating (this part is conceptually expressed as a prism) and refracted to the detection system, while the residual non-interacting creation and inducing beams are refracted to different directions. These non-interacting waves are further reflected by mirrors and a small fraction of that laser photons are used for spatial alignment between creation and inducing lasers.

For instance, in the scalar field search, we require the initial and final state photon energies with their linear polarization states as follows:

(2.2.2)

where {1} and {2} specifies the orthogonal linear polarization states for photons in the creation beam and in the inducing beam, respectively. As a reference polarization combination, we also measure the following case simultaneously

, (2.2.3)

which is not allowed when all wave vectors in Fig.2.1-2 are on the same plane. Due to a degree of freedom on the relative rotation angle between and planes around the z-axis, however, there is a finite probability to accept this polarization combination. In order to measure the both cases on the shot-by-shot basis, we introduced the polarization beam splitter (PBS) whose polarization directions are aligned to the incident laser polarizations {1} and {2} in advance, respectively (see the enlarged view of the SPD part in Fig.2.2-1). For the two polarization paths behind the PBS, two plastic optical fibers whose transmittance are independent of the incident linear polarization states are attached with different lengths by introducing a relative time delay . These two optical fibers are attached to a common photomultiplier tube (PMT) through lenses so that we can count the number of photons in the two different time domains T{1}and T{2}separated by that time difference on the digitized wave form of the analog output from the common PMT.

In order to shutout residual non-interacting creation and inducing laser photons, short pass filters(SPF) with the nominal OD∼ 4 for each to accept only signal wavelength are placed inside the tube in front of the PBS. The detection efficiency to the signal wavelength is evaluated in advance of the pilot measurement with the two same-type PMT’s with the beam splitter(BS) in Fig.2.2-1.

The readout of the analog signal from the photomultiplier is performed by 4-ch waveform digitizer (10-bit cPCI High-Speed Digitizers, Acqiris DC26.2 type U1065A provided by Agilent Technologies) without any electronics for amplification to avoid adding noise sources. The measured maximum rate of the readout by requiring simple online preselections is ∼ 10 kHz. The digitizer is similar to the digital oscilloscope, however, the readout speed is three orders of magnitude higher. Thus online selections based on an algorithm are applicable before waveforms are actually stored.

Fig.2.2-3 Single shot example of a digitized waveform with peaks within the 50 ns time window.

Trigger signals are created by discriminating pulse heights of analog signals on PD1 and the digitizer is synchronized with these trigger signals. By denoting the existence or absence of green (representing ) and red (representing ) lasers as and or and , respectively, we can consider following four wave-mixing patterns: , , , and representing cases including signal (S), dark currents or pedestal (P), residual of creation laser photons (C), and residual of inducing laser photons (I), respectively. Monitoring the green and red laser amplitudes at individual triggers allows to identify the four patterns of wave-mixing S, P, C and I based on the offline analysis on the recorded digitized waveform. Waveforms are recorded with 500 sampling points during the 250 ns time window corresponding to 0.5 ns/division which is consistent with the time resolution on the leading edge of the used photomultiplier (PMT) for the single photon detection.

As the online level trigger, we require that at least one signal-like signature below 1.00 mV threshold after online pedestal subtraction is found in either T{1} or T{2} time domain within the two 15 ns windows (see green bands in Fig.2.2-3), and only waveforms containing such a signature are recorded on the disk for the offline analysis.

2.2-A. Data analysis strategy

In order to test statistical significance of four-wave mixing signals, the quantities we discuss are which are acceptance-uncorrected numbers of photons found in the time domains T{i} with the linear polarization states i = 1, 2 in the case of the signal pattern (S). For the following paragraphs, we abbreviate the symbols of the time domains with specified polarization states, unless confusion is expected.

First, the four patterns: signal (S), pedestal (P), residual of green laser photons (C) and residual of red laser photons (I) are identified by looking at amplitudes of photodiodes recorded in the waveform data, and the number of events of individual patterns: WS, WP , WC and WI , respectively, are counted. These numbers are used as the weights to evaluate the number of photons in the signal pattern by subtracting those in the other patterns. Since there is no complete wave filters, we must expect non-zero numbers of residual photons in the three patterns except the pedestal pattern where the dominant background is the thermal noise from the photomultiplier. We, therefore, interpret the observed raw numbers of photons n in the four patterns specified with individual subscripts as

(2.2.4)

where we assume that the observed pedestal counts include thermal noises from the photodevice and ambient noises such as cosmic rays, hence, the pedestal counts should be commonly included in the other three patterns in the average sense. By considering the event weights of the four trigger patterns, we then deduce the true number of photons in the signal pattern as follows

(2.2.5)

We note that, exactly speaking, the physical meaning of is different from the number of photons, because the dominant pedestal charges are produced by thermal noises of the photodevice. As long as observed charges are expressed in units of single-photon equivalent charge, however, this treatment is justified.

The analysis steps to obtain observed raw numbers nij with trigger patterns and linear polarization states j = 1, 2 are as follows. Figure 2.2-3 shows a single shot example of the digitized waveform within a 50 ns time window. The two time domains within a 3.5 ns interval subtended by two solid vertical lines, respectively, are equally defined which are separated by the known time difference of 23.6.5 ns due to the different optical fiber lengths. The shorter (earlier time domain) and longer (later time domain) fibers correspond to the linear polarization states {1} and {2}, respectively.

Photon-like signals or thermal noise signals are identified by the negative peak finding. After finding a time bin with the largest amplitude in the negative direction, a global pedestal amplitude is determined by averaging over the 250 ns window excluding the peak region as shown by the horizontal line in Fig.2.2-3. We then find the falling edge and define the signal arrival time t0 at the detector as the time bin at the half value of the peak amplitude after subtracting the pedestal value, which is indicated by the dotted vertical line. We require that a peak structure is identified by a pair of falling and rising edges around the peak position tp. By defining time intervals from the falling edge to the peak and the peak to the rising edge as and , respectively, the time window of a signal, , is defined as which are indicated by solid vertical lines. The charge sum in that time window is evaluated in units of single-photon equivalent charge.

We then choose the waveforms satisfying the condition that at least one peak above 0.6 photon equivalent charge is contained for counting the number of photons in the four patterns.

2.2-B. Handling of results

We take two steps to discuss the existence of signal photons from the four-wave mixing process. First, we investigate whether the acceptance-uncorrected and indicate deviations from zero beyond the inclusive errors in individual polarization paths. We then set upper limits on the coupling-mass relation, if there is no statistically significant number of four-wave mixing signals. Otherwise, we discuss the polarization dependence of the observed finite numbers of four-wave mixing signals.

The acceptance-uncorrected numbers of photon-like signals and with signal triggers (S) after subtraction between four patterns of triggers can be obtained based on the relation in Eq.(3.2.5).

In order to evaluate the acceptance-corrected photon numbers and , we need to correct the bias due to the difference of detection efficiencies in the two optical fibers in Fig.2.2-2 for selecting {1} and {2} states, respectively. We thus parameterize the overall efficiencies, for {1} and {2} states, respectively, as

(2.2.6)

where express optical collection efficiencies by the combination of the polarization beam splitter and optical fibers equipped with two lenses, and is the pure detection efficiency of the photomultiplier not including the optical paths (see the enlarged SPD part in Fig.2.2-1). What we directly measure experimentally is a branching ratio between two paths containing exactly the same optical components and the detector as those used for the pilot measurement, which corresponds to the ratio of these two efficiencies

(2.2.7)

This quantity is determined by taking the ratio between the numbers of photons in T{1} and T{2}. With the acceptance uncorrected photon numbers are expressed as

(2.2.8)

where the second of Eq.(2.2.6) is substituted, and is known by the other measurement in advance.

As the second step, we evaluate the upper limit on the coupling-mass relation, where we regard the acceptance-uncorrected uncertainty in the polarization state {2} as the one standard deviation σ in the following Gaussian type of distribution with the mean value

(2.2.9)

where the estimator corresponds to in our case, and the confidence level is given by [Ber12s]. As the upper limit estimate, we apply with to give a confidence level of 95% in this analysis.

We then require that the expectation value of coincides with to obtain the upper limit at the 95% confidence level. In order to relate the upper limit on with the upper limit on the coupling-mass relation directly, we further need to deduce corresponding to the unbiased number of signal photons immediately after the focal point via the second of Eq.(2.2.8)

(2.2.10)

2.3 Background study in preparatory experiments

We have been performing preparatory experiments in Kyoto university in Japan to understand the background sources involved in this search method in the realistic environment. The dominant background photons can be produced via the four-wave mixing process in residual atoms around the focal spot in the vacuum chamber. In order to estimate the expected number of background photons, we can measure the pressure dependence of the number of four-wave mixing photons in the residual gas. Figure 2.3-1 shows arrival time distributions of observed photons at close to the atomospheric pressure among four trigger patterns. Clear two peak structures appear only at S-pattern. We count the number of photons within a time domain T{1} (71-75 ns) with {1}-polarized state and T{2} (94-98 ns) with {2}-polarized state. This result guarantees that our experimental technique is surely sensitive to the real four-wave mixing phenomenon. Moreover, this background process can be actively used to calibrate the space-time overlab between creation and inducing laser pulses.

Fig. 2.3-1 The arrival time distributions of observed photons per event (efficiency-uncorrected) at close to the atmospheric pressure. The left and right bands bounded by neighboring two red lines in each panel indicate the time domains T{1} and T{2} where {1} and {2}-polarized photons are expected to be observed, respectively.

We can evaluate the expected number of background photons in the actual experimental setup as a function of residual gas pressures. The observed quadratic pressure dependence of the number of four-wave mixing photons per event are shown in Fig. 2.3-2.

Fig. 2.3-2 The pressure dependence of the number of four-wave mixing photons in the residual gas per event. The red and black lines shows the quadratic dependence on pressures both for {1} and {2}-polarized states.

2.4 Experimental setup at E4

Based on the conceptual design and preparatory studies above, we plan to perform experiments in the E4 area. As the first step, we search for four-wave mixing signals with 0.1PW at 10Hz with inducing laser fields produced by optical parametric amplification (OPA) seeded by one of the two 0.1PW laser lines with combinations of small area KTP and large area KDP crystals. The second step is to perform the same experiment with 1PW at 1Hz. Therefore, the setup is designed to be able to house larger optical components for 1PW from the first step. Figure 2.4-1 shows vacuum chambers for the OPA part to produce inducing laser fields and the interaction chamber, and how they are actually arranged. The interaction chamber contains a differential pumping system around the focal spot to maintain a better vacuum state locally. The spectrum analysis part will be located outside the interaction chamber. In the event of high noise level, we can introduce longer optical fibers so that we can bring the PMT attached to the fiber-ends outside the E4 area in the worst scenario.

Fig. 2.4-1 Arrangement of the basic components for the setup and the CAD drawing at E4 to search for sub-eV Dark Matter via four-wave mixing in the vacuum.

2.5 Expected physics result with ELI-NP parameters

When statistically no significant four-wave mixing signal is observed, we can put constraints on the mass-coupling relations for exchanged fields based on the generic interaction Lagrangian coupling to two photons independent of theoretical models on the detailed coupling structure. Figure 2.5-1 shows the expected upper limit on the coupling-mass relation at the 95% confidence level which is calculated by requiring

(2.5.1)

in Eq.(2.1.10) with the realistic experimental parameters for 0.1PW and 1PW setups.

The two red lines from the top to the bottom for cases indicate the accessible domains by the searches at ELI-NP where 0.1PW with an OPA-based inducing laser and 1PW with an OPA-based inducing laser are assumed, respectively. The excluded region by the preparatory search at Hiroshima based on this four-wave mixing (FWM) in QPS [Hom14] is indicated by the slantly shaded area. As references, we put existing upper limits by the other types of scalar field searches by vertically shaded areas: the ALPS experiment [Ehr10] (the sine function part of the sensitivity curve is simplified by unity for the drawing purpose) which is one of the ”Light Shining through a Wall” (LSW) experiments, searching for non-Newtonian forces based on the torsion balance techniques (Etö-wash [Abe07], Stanford1 [Chi03], Stanford2 [Smu05]) and the Casimir force measurement (Lamoreaux [Lam97]). The domains below the vertically shaded areas are all excluded. We note that if we require the proper polarization combinations between initial and final states for pseudoscalar fields [Hom12p], we are able to test the QCD axion models in the near future. As a reference, we show the expected mass-coupling relation based on the QCD axion scenario for E/N = 0 [Ber12a] (KSVZ model [Kim79]) which is indicated by the inclining dotted line. The pink horizontal line indicates the gravitational coupling limit.

Fig.2.5-1 Upper limits on the coupling – mass m relation for the scalar field exchange. The two red lines from the top to the bottom for cases indicate the accessible domains by the searches at ELI-NP where 0.1PW with an OPA-based inducing laser and 1PW with an OPA-based inducing laser are assumed, respectively. The excluded region by the preparatory search at Hiroshima based on four-wave mixing (FWM) in QPS [Hom14] is indicated by the slantly shaded area. The vertically shaded areas show the excluded regions by the other scalar field searches: the ALPS experiment [Ehr10] (the sine function part of the sensitivity curve is simplified by unity for the drawing purpose) which is one of the ”Light Shining through a Wall” (LSW) experiments, searching for non-Newtonian forces based on the torsion balance techniques (Etö-wash [Abe07], Stanford1 [Chi03], Stanford2 [Smu05]) and the Casimir force measurement (Lamoreaux [Lam97]). As a reference for the future pseudoscalar searches, we also put the expected mass-coupling relation based on the QCD axion scenario for E/N = 0 [Ber12a] (KSVZ model [Kim79]) indicated by the inclining dotted line. The pink horizontal line indicates the gravitational coupling limit.

2.6 Timeline of implementation and milestones

The timeline of RA5-DM is Fig.2.6-1.

Fig.2.6-1 Timetable of RA5-DM

2.7 Estimated Budget

Figure 2.7-1 summarizes necessary experimental items and the costs for the RA5-DM proposal.

Fig.2.7-1 Table of experimental items and the costs for the RA5-DM proposal.

3. Gamma-Polari Calori-meter (GPC)

3.1 Role of GPC

Gamma-Polari Calori-meter (GPC) is the common detector system applied to RA5-RR, RA5-Pair and RA5-VBir subjects in both E7-stage 1.5/3 and 4. GPC is designed to be able to measure incident gamma-ray energies from 100MeV-2.0GeV via the conversion process to e+e- pairs and simultaneously measures the degree of linear polarization.

3.2 Brief technical description

Figure 3.2-1 shows the conceptual design of GPC, which consists of a thin converter, a permanent-magnet-based dipole (PMD) and two detector branches made of 3 layers of silicon pixel sensors. At the both ends of the two branches, fast scintillators are placed. In the three subjects above, we commonly focus on the higher gamma-ray energies above ~100MeV. In this case emitted gamma-rays are confined within an emission angle defined by the inverse of the Lorentz factor of incident electrons or gamma-rays. This implies that conversion points on the converter are always localized, typically within radian. This special situation gives constraints on the following GPC design.

Fig.3.2-1: Conceptual drawing for Gamma-Polari Calori-meter (GPC). Note that the typical e+e- opening angle is around sub-mrad. The angle at the top-view is exaggerated.

The converter to create e+e- pairs from gamma-rays is gold thin foil with the thickness of 2m. This target is optimized to avoid smearing opening angle of the e+e- pairs at the pair-creation point and to keep reasonably high pair-creation efficiency on the order of 10-4.

A compact permanent-magnet-based dipole (PMD) is placed immediately after the converter. This dipole enables the spatial separation of e+e- pairs from the residual gamma-ray beam as well as the charge separation between e+ and e-. Because the pixel sensors can response to both charged particles and X/gamma-rays, a matter less region is necessary to make the residual gamma-rays escape through that empty space in order to avoid secondary e+e- pairs from the pixel sensors as well as the condense hits by gamma-rays on the sensors. Therefore, GPC has the two-branch structure in its basic form.

The PMD consists of permanent magnet arrays arranged in a concentric pattern. Sub-tesla of field strength can be made in the hollow region of PMD. The diameter of PMD is a few cm and the length of magnetic field region is about 10 cm. The compactness of PMD construction enables flexible use in several experiments. The uniformity of magnetic field is expected to be a few % [Rai04]. Such high uniformity has an advantage in polarization measurements. The first two layers in individual branch determine momentum vector of outgoing particles from the magnetic field region. Momentum and pair-creation angle are reconstructed by hit information on each layer. The third layer is used to guarantee track quality. It is helpful to avoid accidental coincidences among the first two layers and to identify true tracks in entering multiple pairs. Each layer is made of silicon pixels with 17m17m. The silicon pixel layers are commonly formed with the unit sensor chip. The unit sensor chip is manufactured based on monolithic pixel radiation sensor/electronics by using a SOI (Silicon-On-Insulator) technology. The KEK team has developed a system consisting of a INTPIX4 sensor chip board and a readout board as shown in Fig.3.2-2. The INTPIX4 chip size is 10mm15mm. The thickness of the sensor chip is controllable on demand. 50m thickness is assumed in this setup.

The momentum of e+ and e- is determined by curvature radius of charged track information in the magnetic field as follows.

, (3.2.1)

where p is momentum of a charged track, B is the magnetic field, R is curvature radius of a track. Figure 3.2-3 illustrates a trajectory of charged particle in the magnetic field. A track is associated by the straight line connecting with B, C and D outside the magnetic field. The variables  and  are reconstructed on a track-by-track basis. Curvature radius, R, and pair-creation angle, 0, are calculated by  and 

The degree of linear polarization of the incident gamma-ray is characterized by anisotropy of the angle of the pair-creation plane defined by a e+e- pair with respect to the polarization plane of incident gamma-ray [B.M], that is,

, (3.2.2)

where is the degree of linear polarization of incident gamma-rays, is analyzing power and is the angle between the e+e- pair-creation plane and the linear polarization plane of the incident gamma-ray which is precisely defined in Fig.3.2-4 (a) [CdJ]. The pair-creation plane is determined by projecting onto a screen via reconstructed angle 0 as shown in Fig.3.2-4 (a). Some of extreme cases are shown in Fig.3.2-4 (b), the pair-creation plane is isotropically distributed in the unpolarized case. On the other hand, the plane is anisotropically distributed in the 100% polarized case. The amplitude of modulation shows the product of the linear polarization, Pl, and the analyzing power, A. Analyzing power shows the reduction of the amplitude due to various experimental components. Mainly Coulomb multiple scatterings in the detector material and misidentification of a track are contributed to the reduction. The analyzing power of GPC is shown in the next section.

Fig.3.2-2: INTPIX4 sensor chip and the readout board. This picture is quoted from the developer’s page at KEK [INT].

Fig.3.2-3: Momentum reconstruction via the measured variables  and .

Fig.3.2-4: (a) Definitions of variables for polarimetry. (b) Angle distribution of the pair-creation plane with respect to the polarization plane of incident gamma-ray. Green, red and black points show the distribution at the degree of polarization of 0, 50, 100%, respectively.

3.3 Performance of GPC

The performance of GPC is evaluated from two aspects. One is momentum resolution, the other is analyzing power. The requirements from the proposed experiments to GPC are shown below.

Momentum resolution with respect to above 100 MeV e+ and e- below 10%.

Analyzing power to the degree of linear polarization is greater than 30%

The simulation study is performed by the GEANT4 simulation toolkit [Geant 03]. In this study, it is assumed that incident gamma-ray has the energy of 1 GeV and 100 % linear polarization. Figure 3.3-1 shows an event display of the GEANT simulation. Gamma-ray (green) is converted into e+e- pairs at the converter. Produced e+ and e- trace a history of a red line and a blue one in the display, respectively.

Figure 3.3-2 shows momentum resolution, , of electron and positron above the momentum range of 0.2 GeV/c. is defined by

, (3.3.1)

where is reconstructed momentum, is true momentum. Momentum resolution of GPC is about 7% for both electrons and positrons.

Figure 3.3-3 shows the pair emission as a function of the angle of the pair-creation plane with respect to the polarization plane of incident gamma-ray. Open circles show the angle at the conversion point, which is equivalent to the case that the overall detection system has the ideal analyzing power (i.e. A=1.0). Blue points show realistic analyzing power of GPC. The position resolution originating from finite pixel segment is taken into account in this study. The red points, which is the extreme case the pixel size is infinitely small, are compared to the blue ones. In conclusion, the analyzing power reaches about 50%.

Feasibility of simultaneous detection of multiple pairs is also studied. As a result, GPC is capable of measuring more than ten e+e- pairs per shot at the same time without reducing analyzing power.

In summary, GPC has the momentum resolution of 7% for e+ and e-, it would be enough to clarify energy spectrum of incident gamma-ray at the high-energy end point and to distinguish or constraint theoretical models. The measurement of vacuum birefringence is the most difficult from viewpoints of polarization measurement, because the degree of linear polarization of gamma-ray after passing through the birefringent vacuum is expected to be 27%. The analyzing power of 50% is acceptable to observe small modulation with the amplitude of 10% level. The physical design of GPC is shown in Fig.3.3-4. GPC must be stored inside vacuum chamber to avoid multiple scatterings of created e+e- pairs through material or air and also water condensation on the sensor chip. Therefore whole parts of GPC can be enclosed in the chamber with the size of 38cm 74cm 50cm.

Fig.3.3-1: An event display of GEANT4 simulation.

Fig.3.3-2: Inclusive momentum resolution of produced e+ (blue) and e- (red) above 0.2 GeV.

Fig.3.3-3: Analyzing power of gamma-ray polarimetry corresponding to a 50% level. The amplitude as a function of rotation angles of reaction planes of e+e- pairs around the gamma-ray incident axis reaches 50% (blue circle) of that of incident 100% linear polarized gamma-rays with 1 GeV (black empty circle).

Fig.3.3-4: Three dimensional setup of GPC is designed by AutoCAD Mechanical 2013 software.

3.4 Cost estimation for the construction of GPC

Cost estimation for the construction of GPC is summarized in Table 3.4-1.

Table 3.4-1 Cost estimation for the construction of GPC

3.5 Timeline of implementation and milestones

Timeline of GPC is shown as Fig.3.5-1.

Fig.3.5-1 Timeline of GPC

RA5-TDR

Stage 1.5 / 3

Experiments of

RA5-RR radiation reaction (Ch.4)

RA5-Pair pair production (Ch.5)

RA5-E4 Polarization (Ch.6)

4. Radiation Reaction (RA5-RR)

4.1 Physics Cases

The following descriptions are entirely based on the recent publication [Set14-2] of the author of this section. This paper was intended to propose very briefly an experiment proposal for ELI-NP including the theoretical explanations.

4.1.1 The Original Model “Lorentz-Abraham-Dirac Model”

Ultrahigh intense lasers are being planned and constructed [Mou12] including ELI-NP [Hab11]. What kind of physical processes can we observe in the regime of these laser intensities? We often discuss QED effects like pair creation/annihilation by extreme intensities of 1024~W/cm2 [Hab11]. It has been predicted that these lasers will produce new high-field physics. Before reaching this physical process, we need to pass through the region of 1021~22W/cm2. In this regime, it is predicted that an electron will emit significant energy as light. Therefore, the motion of the electron needs to be corrected by the radiation feedback [Kog04, Zhi01]. This is a basic physical process, named ‘radiation reaction (RR)’. This effect will be appear in the regime of this laser intensities. All materials have electrons in atoms, and part of these will be freed from the potential of atoms, emitting then strong light via the interaction with the laser photons. Therefore, the RR process becomes very important for all experiments with ultra-intense lasers at intensities over 1022W/cm2.

Although many may indeed argue that this is very obvious and basic physics, the RR remains one of the difficult problems in physics. This is due to the insolvability of the equation of motion – the standard theory was formulated by Lorentz [Lor06], Abraham [Abr05] and Dirac [Dir38]. Therefore, the equation of motion with RR is named the Lorentz-Abraham-Dirac (LAD) equation. The easiest way to derive this equation is, from the radiation energy loss formula (Larmor’s formula [Lar97]) in the non-relativistic regime [Jac98, Pan61].

(4.1.1)

Where, is the electron’s rest mass, is the velocity of the electron ( is a 3-dimensional Euclidian space). is denoted as the speed of light, . Therefore, the energy change of the electron is as follows ( is an external field.):

(4.1.2)

From this equation, we can obtain the equation of motion named the Lorentz-Abraham (LA) equation.

, (4.1.3)

. (4.1.4)

Fig.4.1-1 The progress of laser intensities and research fields (Mourou chart) [Mor12]. In this proposal, the target intensity is O(1022-23)W/cm2.

Here, our dynamics is in , periodic conditions in which

, (4.1.5)

are required. Eq. (4.1.4) is the effect of RR, named the RR force. Equation (4.1.3) with (4.1.4) was converted to the relativistic regime by Dirac without any mathematical condition. This is the LAD equation.

(4.1.6)

(4.1.7)

Where, all of vectors in this equation belong to the 4-dimensional linear vector space joining in Minkowski spacetime which is the mathematical set of the 4-dimensional affine space and the Lorentz metric with the signature of . An affine space is a vector space that is has no set origin. For the theory of relativity, this method is suitable. The force of is the effect of the radiation feedback, denoted the RR force. However, Eq. (4.1.6) doesn’t have stable solutions, every solution goes to infinity (run-away; see Eq(4.1.10)) [Dir38, Jac98, Pan61 and Lan94]. At first, the LAD theory is derived as the electron’s model in classical physics. In 1938, Dirac considered how to avoid the infinity in QED. After that it was solved via renormalization [Tom46, Sch48 and Fey49], but he tried to apply the Lorentz model (1906) [lor06]. A part of an electron with the spherical charge distribution interacts with other parts of itself. But, the field at the center of this charge becomes a singular point (since , ). We need to keep in mind that the electron is treated as a point charge in classical physics. This dependence is taken over the electromagnetic mass,

. (4.1.8)

In the Lorentz’s theory, RR is derived from only the retarded field [Lié98 and Wie01]. The equation of electron’s motion (Eq.(4.1.3) with Eq.(4.1.4)) becomes

. (4.1.9)

Dirac considered that the infinity of QED is equivalent to the infinity of the electromagnetic mass [Far09]. In Dirac’s method, he treated not only the retarded field, but also the advanced field [Dir38]. Then, the equation which he obtained is the LAD equation (4.1.6) with Eq. (4.1.7). However, these equations have a mathematical difficulty which is named “run-away”. For instance, we consider the case without any external fields. In this case,

. (4.1.10)

Here, is a very small value, the solution grows up to infinity since is significant when is finite. This is the run-away solution which we need to avoid. The same problem is in the LAD equation, too. RR has involved the history of the electron model on how to avoid the run-away and the concrete problem of treating ultraintense laser-high energy electron interactions.

4.1.2 MODERN MODEL OF RADIATION REACTION

4.1.2-A Eliezer-Ford-O’Connel model and Landau-Lifshitz model

For avoidance of run-away solution, many methods have been proposed and used for simulations like PIC. The standard method for the avoidance of run-away was suggested by Eliezer, Ford-O’Connel and Landau-Lifshitz. They considered the term of the RR force was higher order corrections. Therefore, the RR force term is treated by the first order of perturbations. By replacing with in Eq.(4.1.7),

, (4.1.11)

derived by Eliezer [Eli48] and Ford-O’Connel [For93]. For PIC simulations, the external fields is the function of spacetime, . Using the chain rule of derivative in Eq.(4.1.11), we can obtain the force of Landau-Lifshitz [Lan94]:

(4.1.12)

Of course, is an external force defined by . Since this method doesn’t have a run-away, it is useful for the reference of simulations. A scheme similar to this was obtained by Rohrlich [Roh01].

4.1.2-B Sokolov model

Another method which is often used is Sokolov equation. This is similar to Landau-Lifshitz equation (4.1.12), but it is the stochastic model by using the radiation spectrum.

(4.1.13)

(4.1.14)

Here, and is recognized as mass renormalization [Sok09]. Then,

(4.1.15)

, (4.1.16)

which is passing from classical radiation to QED radiation [Sok10]. Characteristic to this model is the fact that the equations satisfy the relation but don’t satisfy .

4.1.2-C Seto-Zhang-Koga/Seto II model

One of the TDR authors, Seto has also suggested a series of new models, based on the propagation of field in quantum vacuum of Heisenberg-Euler. By correcting radiation from electron via quantum vacuum (photon-photon scatterings), we derived namely the SZK equation,

, (4.1.17)

(4.1.18)

( and ) [Set14-1, Set14-2]. Recently, this equation was upgraded to the “Seto I” model as follows [Set15-1]:

(4.1.19)

(4.1.20)

and it includes radiation-external field interactions via and . In addition, it proceeded the more general model (Seto II model):

(4.1.21)

(4.1.22)

(4.1.23)

and the definition of the homogeneous field . When , this set of equations behaves dynamically similar to Eqs.(4.1.15-16) [Set15-2]. These models demonstrated the stability of their solutions, and became good references. If we can find new dynamics, the anisotropic charge and the field will be modified via the function .

ELI-NP has the potential for carrying out relevant experiments of RR, with the help of the two 10PW – over 1022W/cm2 class lasers and the GS-LINAC. Moreover, RR has to be taken into account in all high intensity laser experiments. The recent models using QED modification show us the running coupling between an electron and radiation field in high-intense field. Therefore, this proposal is not only about the investigation of the energy loss of a radiating electron, but we may also observe the running coupling of an electron by high-fields. The experiments of RR will give us a chance to consider the physics involved by single electron with extreme-high intense fields, including both the laser fields and radiation from the electron.

We propose the head-on collision between a 10PW laser beam and 600MeV/2.5GeV/5.0GeV electrons. Figure 4.1-2 is one of the setups for RA5-RR, combining the electrons from the GBS LINAC (on a new transport line to E7) and 10PW laser beam, in Stage 1.5. We will discuss the technical details in Sect.4.3. This experiment is based on the observation of two parameters: the minimum energy of scattered electron/shot and the maximum value of the photon energy. By the correlation of these two values, one can understand the dynamics of RR.

Fig.4.1-2 Conceptual layout of RA5-RR in Stage 1.5.

4.2 Technical Proposal

From the simulation results in Section 4.3, we will classify the models of radiation reaction (RR) by using a head-on laser-electron interaction. This is common configuration with RA5-Pair (Ch.5) and RA5-Pol (Ch.6) experiments. We need to observe the minimum energy of the scattered electrons and the maximum energy of the emitted photons from the electrons. The sketch of this experiment is Fig.1.2-1/4.2-1. For this setup, a basic requirement is the synchronization between the 600MeV electron bunches from the GS-LINAC and the 10 PW laser pulses, at the sub-ps level. These are also important in the alignments of setup. In the development contracts for the 2 x 10 PW laser system and the Gamma Beam System at ELI-NP, there is already foreseen the possibility of synchronization at the 100fs level.

In addition, we propose these experiments in E7-Stage 3 (Fig. 4.2-3) employing LWFA for 2.5/5.0GeV electron beams, to enter another regime of highly intense field physics.

In the following we present the elements that form a functional experimental setup for this physics case (also for the LWFA case). These elements are also common equipment for other physics cases proposed in the TDR.

A) Single 10PW laser + GS-LINAC system

In this case, the experiments will be carried out by 600MeV electron beam from GS-LINAC.

4.2.A-1 Single 10PW-LASER BEAM

Required laser pulse parameters and control:

Aiming the peak intensity – long focal length with the [Ion13].

Moreover, the peak intensity – long focal length with the .

The laser wavelength , pulse duration and spot size by and by .

The entering laser reflected by the flat mirror on the laser pickup point in E6 hall

Traveling 180 degree against the electron beam from GS-LINAC (head-on collision)

Polarization control is required. It is also important for the experiments of RA5-Pol.

Ultrahigh intense-super Gaussian spatial shape (also as the function of time ideally). The field should be Gaussian shape.

Temporal shaping and control of rising edge of the laser pulse

Spatial shaping and control of focal spot distribution.

Laser beam transport / relay to the appropriate target areas.

The clean interaction chamber. We also plan the experiments of photon polarization flipping as QED vacuum via RR (RA5-VBir in Ch.5). The contamination becomes a critical problem in the investigation of quantum vacuum.

Fig.4.2-1 3D layout of RA5-RR/Pair/Pol experiments in Stage 1.5

Fig. 4.2-2 Relation between laser intensities and f number [Ion14]

Table.4.2.1 Parameters of 10PW laser

4.2.A-2 LASER BEAM DIAGONOSTICS

Intensity-temporal contrast measurement, especially on the rising edge of the laser pulse; FROG – frequency resolved optical gating diagnostic;

Measurement of the laser focal spot energy distribution and the phase front;

Near and Far field monitoring of the laser beams.

4.2.A-3 ELECTRON BEAM FROM LINAC

The path from LINAC to E7. An electron macro-bunch train is kicked by M27 magnet at 1Hz (see also Sect. 4.2.A-4).

Quadrupole magnetic lens are required for transportation from M27 to the E7 chamber and focusing the electron beam just before interactions.

Dipole magnets for the energy separation after scattering

The initial energy of an injected electron into the chamber is 600MeV.

1010-11 electrons/bunch is required in statistics.

The time-synchronization with 10PW-long focal laser: the electrons need to reach the laser focus-interaction point.

Table.4.2-2 Electron beam from GBS LINAC in the main experiments

4.2.A-4 Synchronization between 10PW laser and GS-LINAC

For the synchronization, we lead the laser pulse of 1PW at 1Hz operation (25J of energy with the pulse duration of 25 fsec) through the 10PW East beamline in E7.

By separating the 1PW laser beam in E7 in two beams, one of them is the time calibration laser between 10PW laser and GS-LINAC. The electron beam interacts with this laser via 90 degree scatterings.

The dimension of one micro bunch is and the 1PW seed laser pulse has the length of .

We kick only one micro bunch in the macro bunch train. Observing this scattering, we can tune the coincidence between 10PW laser and GS-LINAC.

Another path of separated 1PW-seed laser is the profile scanning laser of the electron beam from GS-LINAC.

The alignment mirror on the controllable/automatic slider table for the electron beam diagnostics.

The separated laser and electron beam interact via head on collision.

Fig. 4.2-3 Alignments and synchronization between 10PW laser and GS-LINAC

Table.4.4.3 Parameters of 1PW seed laser

4.2.A-5 Lab-Space and target chamber requirements

Single 10PW laser – 600Mev electron from LINAC experiments.

The target chamber should be as small volume as possible.

The part of the target chamber from the entrance to electron focusing point should be a pipe of the radius of O(1cm). The magnets (electron optics) should be set around this pipe.

The target chamber should be made of aluminum to reduce activation

The place of the installation of the focusing mirror in the chamber, the dimension is , depending on the laser beam diameter.

B) Double 10PW lasers + LWFA system (without GS-LINAC)

In this case, the electron beam of 2.5/5GeV is produced by LWFA.

4.4.B-1 Single 10PW-LASER BEAM

Required laser pulse parameters and control:

Aiming the peak intensity – long focal length with the .

Moreover, the peak intensity – short focal length with the .

The laser wavelength , pulse duration and spot size by and by .

Polarization control is required.

Ultrahigh intense-super Gaussian spatial shape (also as the function of time ideally). The field should be Gaussian shape.

Temporal shaping and control of rising edge of the laser pulse.

Spatial shaping and control of focal spot distribution.

Laser beam transport / relay to the appropriate target areas.

4.2.B-2 LASER BEAM DIAGONOSTICS

Intensity-temporal contrast measurement, especially on the rising edge of the laser pulse; FROG – frequency resolved optical gating diagnostic;

Measurement of the laser focal spot energy distribution and the phase front;

Near and Far field monitoring of the laser beams.

Table.4.4.4 Parameters of 10PW laser

Fig.4.2-4 3D layout of RA5-RR/Pair/Pol experiments in Stage 1.5 and 3

Fig. 4.2-5 Configuration in 2.5/5GeV electrons experiments RR/Pair/VBir

4.2.B-3 ELECTRON BEAM FROM LWFA

Generation in the North part of chamber (towards E1/E6).

Quadrupole magnetic lens are required for electron transport and focusing the electron beam just before interaction.

Energy of the generated electron is 2.5/5GeV.

The synchronization with lasers are required (see Sect. 4.2.B-4).

Energy spectrometer (GPC meter in Ch.9)

Beam profile (see Sect. 4.2.B-4)

Emittance measuring system – series of screens and focusing elements

Beam transport system

Coherent transition radiation electron bunch measuring system

Table 4.2-5 Parameters of laser for LWFA

4.2.B-4 Synchronization between 10PW laser and LWFA electron beam

For the synchronization, we lead the 1PW-seed laser at 1Hz operation (25J of energy with the pulse duration of 25 fsec) to E7 through the existing 10PW beamline (East 10PW arm).

By separating 1PW-seed laser in two beams, one of them is used for the time calibration between 10PW laser and LWFA electron beam. The electron beam interacts with this laser via 90 degree scatterings.

The dimension of one micro bunch is and the 1PW seed laser has the pulse length of .

We kick only one micro bunch in the macro bunch train. Observing this scattering, we can do the time alignment between 10PW laser and LWFA.

Another path of separated 1PW-seed laser is the profile scanning laser of the electron beam by LWFA.

The alignment mirror on the controllable/automatic slider table for the electron beam diagnostics.

The separated laser and electron beam interact via head on collision.

Fig. 4.2-6 Alignments and synchronization between double 10PW lasers and LWFA

4.2.5 ELECTRON BEAM DIAGONOSTICS

Energy spectrometer

Beam profile

Charge – Faraday cup, ICT and calibrated image plates

Emittance measuring system – series of screens and focusing element

Beam transport system

Coherent transition radiation electron bunch measuring system

4.2.6 DETECTORS

High resolution Gamma Polari-Calorimeter (GPC, see Ch.9)

4.2.7 Lab-Space and target chamber requirements

Single 10PW laser – 600Mev electron from LINAC experiments.

The target chamber should be as small volume as possible.

The part of the target chamber from the entrance to electron focusing point should be a pipe of the radius of O(1cm). The magnets (electron optics) should be set around this pipe.

The target chamber should be made of aluminum to reduce activation

The place of the installation of the focusing mirror in the chamber, the dimension is , depending on the laser beam diameter.

4.3 Estimation of Count Rates/Feasibility of Proposed Devices

4.3.1 Models and setup of calculations

In RA5-RR, the most interesting point is the choice of appropriate RR model. Table.4.3-1 is the list of models which we consider in the present phase, where symbols LL, CSok, QSok, SZK and Seto II stand for Landau-Lifshitz [Lan94], Sokolov (classical) [Sok09], Sokolov (quantum) [Sok10], Seto-Zhang-Koga models [Set14-1] and the Seto II model [Set15-2] respectively. We have performed numerical simulations of radiating electron orbit and resulting emission spectrum in order to evaluate the model dependency of laser-beam interaction. In the spectrum estimation, the quantum emission spectrum [Nik64] is employed for SQ model while the classical emission spectrum [Jac98] is used for the other models. We consider two laser conditions. (1) peak intensity by spot size and (2) by with pulse duration , wavelength . Incident electron energies are . Figure 4.3-1 is a diagram illustrating the configuration of electron scattering along with the definition of relevant angles: electron incident angle , electron scattering angle , and photon detection angle .

Fig.4.3-1 Configuration of electron scattering by pulse laser

Table.4.3-1 Models of RR

Fig.4.3-2 Conceptual design of head-on collision (LINAC 600MeV electron case)

Especially, the head-on collision is important for RA5-Pair/Pol/VBir experiments and R&D of GPC. Scatted electrons, positrons and emitted radiation can be observed by only using this GPC (about GPC, see Ch.3).

In Stage 1.5 with GS LINAC

In this section, we consider the electron energy of 600MeV by using the GS LINAC line.

4.3.2-1 Calculation results – 1×1022W/cm2 ( f # =7 ) laser + 600MeV electron case

Figure 4.3-3 shows (A) electron orbits and (B) time evolution of electron energy calculated based on SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models. Here, the case of the head-on collision, i.e., , is considered. As shown in Fig.4.3-3(A), the incident electron starts to oscillate under the action of laser electromagnetic field as it approaches the pulse laser. The electron tends to decelerate toward the direction of laser propagation ( direction) during the oscillation by light pressure. Electron eventually exhibits different dynamics according to the employed RR model and passes away into the distance with a certain scattering angle. As shown in Fig.4.3-3(B), the electron energy decreases drastically due to RR during the oscillation phase. The asymptotic value of electron energy considerably depends on the employed RR models. Scattered electron energy is estimated for various beam incident angles . We recognize two model groups from the final energies of an electron. The three models of LL, CSok and SZK are overlapped each other. And also QSok and Seto II are overlapped.

Figure 4.3-4 (A) shows the scattered electron energy as a function of incident electron angle for each RR model. Electron energy decreases considerably from the initial beam energy, 600 [MeV], due to radiation damping in any incident angles. Typical electron energy loss ranges from ~ 300 [MeV] for QSok and Seto II model to ~ 400 [MeV] for LL model. Therefore evidence of RR could be observed from the scattered electron energy. In addition, dependency of scattered electron energy on RR model becomes obvious as the incident angle becomes large.

(B)

Fig.4.3-3 (A) Trajectory of an electron counter propagating to the laser beam (head-on collision). (B) Time evolution of electron energy in the case of a 600 MeV electron. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models.

(B)

Fig.4.3-4 (A) Scattered electron energy vs. laser incident angle , (B) Electron scattering angle vs. laser incident angle . Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models.

Fig.4.3-5 Angular distributions of emitted photon energy. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models in the case of the 1×1022W/cm2 laser and a 600MeV electron. The calculational resolution of the detection angle is, .

Figure 4.3-4(B) shows electron scattering angle estimated for various incident angles. Incident electron energy in the present case is large enough so that the electrons pass through the pulse laser without significant deflections.

Returning to the topic of the head-on collision case , Fig.4.3-5 shows angle distribution of photon energy per one incident beam electron. This calculation was carried out by using the angular resolution. Emitted photon energy is confined to small angles around the beam front direction, because parallel emission is dominant for high-energy electron [the spread angle of radiation is , strong directivity]. The emission angle distribution broadens up to , which is wider than the angle distribution of scattered electron. This is because photon emission from oscillating electron directly contributes to the emission angle distribution. Thus, the emission spectrum measurement might provide an excellent indication for the model dependency of RR. Figure4.3-6 shows the prediction of the radiation spectrum and degree of polarization limited by the opening angle of 1/10γ ~ 0.02∘ as the design of the GPC foresees (Ch.3). This derivation was based on the textbook of A. A. Sokolov and I. M. Ternov [Sok86]. The polarized and depolarized radiation spectrums are described as follows:

(4.3.1)

(4.3.2)

We use the limit of the head-on case for simplification, as it is also compatible with the GPC design which limits the emission spread angle to 1/10γ. The component of “DEPOL” means the spin-magnetic dipole radiation, that it is not included in the ordinary Larmor’s radiation formula. We converted these values to number of photons , made the ratio named the degree of polarization (DoP).

. (4.3.3)

Actually, the Seto II and QSok model are the only models to which we can apply this scheme, we use Seto II model for drawing, since both models can draw the same spectrum.

Fig.4.3-6 Radiation spectrum in the case of 1×1022W/cm2 laser and a 600MeV electron. The blue and red lines means linear polarized radiation and the spin-depolarized radiation. The green line is the degree of polarization, these line were derived from Seto II model.

Hereafter, we list the various cases of laser-electron “head-on” collision.

4.3.2-2 Calculation results – 2×1023W/cm2 ( f # =2 ) laser + 600MeV electron case

In the case of 2×1023W/cm2 and 600MeV electron, the dynamics of the electron is changed with respect to the 1×1022W/cm2 case. The 20 times larger field drives the electron stronger.

Figure 4.3-7 (A) is the trajectory of the electron. The difference from 1×1022W/cm2 case is the 8-figure motion of an electron. We can find the energy oscillation with O(100MeV) in Fig.4.3-7(B), it corresponds to the 8-figure motion. The laser of 2×1023W/cm2 drives this electron forward direction of the laser propagation. The difference between two groups (SZK/LL/CSok and QSok/Seto II) depends on whether the coupling runs or not. However, it seems difficult to find it out from the final state of the electron.

This motion influences the radiation pattern (Fig.4.3-8). This has a strong spike in the initial direction of the electron, however, it emits in all directions.

(B)

Fig.4.3-7 (A) Trajectory of an electron counter propagating to the laser propagation (head-on collision). (B) Time evolution of electron energy in the case of a 600 MeV electron, initially. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models.

Fig.4.3-8 Angular distributions of emitted photon energy. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models in the case of the 2×1023W/cm2 laser and a 600MeV electron.

Fig.4.3-9 Radiation spectrum in the case of 2×1023W/cm2 laser and a 600MeV electron. The blue and red lines means linear polarized radiation and the spin-depolarized radiation. The green line is the degree of polarization. These line were derived from Seto II model.

Figure 4.3-9 shows radiation energy spectrum and the degree of polarization. This takes also in consideration the limited photon entry area into GPC detector (opening angle) corresponding to the angle in Fig.4.3-8. We can obtain 90% polarization at the photon energy of 200MeV for the secondary radiation source. The comparison of the spectrum between Fig.4.3-6 and this Fig.4.3-9, the entering photons into GPC are generated in the time duration in the results of Fig.4.3-3(B)/ 4.3-7(B).

In Stage 3 with LWFA

In this section we consider the electron energy of 2.5GeV generated by LWFA technique in Stage 3.

4.3.2-3 Calculation results – 1×1022W/cm2 ( f # =7 ) laser + 2.5GeV electron case

In the case of a 2.5GeV electron in E7-Stage 3 setup (see Fig.4.2-5), Fig.4.3-10 shows the trajectory of an electron and the time evolution of an electron’s energy in the head-on collision with the laser. Though the initial energy is different from 600MeV case, the tendencies are the same. From the asymptotic final energies, we can observe the high-intense field correction is easier to observe as in the 600MeV case.

(B)

Fig.4.3-10 (A) Orbit of normal incident beam electron (B) Time evolution of electron energy in the case of a 2.5GeV electron. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models.

Fig.4.3-11 Angle distributions of emitted photon energy. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models in the case of the 1×1022W/cm2 laser and a 2.5GeV electron.

Fig.4.3-12 Radiation spectrum in the case of 2×1023W/cm2 laser and a 600MeV electron. The blue and red lines mean linear polarized radiation and the spin-depolarized radiation. The green line is the degree of polarization. These line were derived from Seto II model.

Figure 4.2-11 is the emission spread pattern from an electron. The relativistic factor is four times larger, the emission angle is of in 600MeV case. The electrons keep their propagating directions with , the geometry of the experiments is the same of the 600MeV case. Figure 4.3-12 represents the radiation spectrum from 2.5GeV electron. In this case, we can observe 500MeV photon with >90% degree of polarization by using GPC.

4.3.2-4 Calculation results –2×1023W/cm2 ( f # =2 ) laser + 2.5GeV electron case

Fig.4.3-13 shows the trajectory of an electron and the time evolution of an electron’s energy in the head-on collision between the laser and the electron. We can find the strong RR effect (an electron’s energy drop) at first, then it is pushed by the ponderomotive force of the high-intense laser.

Fig.4.2-14 is the emission spread pattern from an electron. Radiation is mainly emitted in the original direction of an 2.5GeV electron, but also observed at all angles due to the electron’s 8-figure motion. Fig.4.2-15 represents the energy spectrum of radiation.

(B)

Fig.4.3-13 (A) Orbit of normal incident beam electron (B) Time evolution of electron energy in the case of a 2500 MeV initial energy electron. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models.

Fig.4.3-14 Angle distributions of emitted photon energy. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models in the case of the 2×1023W/cm2 laser and a 2.5GeV electron.

Fig.4.3-15 Radiation spectrum in the case of 2×1023W/cm2 laser and a 2.5GeV electron. The blue, red and green lines represent the linear polarized, the spin-depolarized radiation and the degree of polarization derived from “Seto II”.

4.3.2-5 Calculation results –1×1022W/cm2 ( f # =7 ) laser + 5.0GeV electron case

Figure 4.3-16 shows trajectory of an electron and the time evolution of then electron energy in the head-on collision between the laser and the electron. The radiation from the electron is emitted forward int the initial direction of the electron’s motion. From Fig.4.3-12, we can obtain a very high degree of polarization at 1GeV photon energy.

The emission has a very narrow pattern in the initial direction of the electron, it exceeded the limit of the angular resolution of our calculation . Therefore, the opening angle of this radiation is smaller than this value. Figure 4.3-17 is the radiation spectrum in this case. Concerning the emission angle of radiation, we will be able to observe the 1GeV photon with >90% degree of polarization in the front direction of the electron propagation.

(B)

Fig.4.3-16 (A) Orbit of normal incident beam electron (B) Time evolution of electron energy in the case of a 5.0GeV electron. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models.

Fig.4.3-17 Radiation spectrum in the case of 1×1022W/cm2 laser and a 5.0GeV electron. The blue and red lines represent linear polarized radiation and the spin-depolarized radiation. The green line is the degree of polarization. These line were derived from Seto II model.

4.3.2-6 Calculation results –2×1023W/cm2 ( f # =2 ) laser + 5.0GeV electron case

Fig.4.3-18 shows the trajectory of the electron and the time evolution of its energy in the head-on collision with the laser. Fig.4.2-19 is the emission spread pattern from an electron. Both figures are basically equivalent to the ones in Sect.4.3.2-4 (the case of 2×1023W/cm2 laser + 2.5GeV electron) excluding the initial energy of an electron and the radiated energy by light.

(B)

Fig.4.3-18 (A) Orbit of normal incident beam electron (B) Time evolution of electron energy in the case of a 5.0GeV electron, initially. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models.

Fig.4.3-18 Angle distributions of emitted photon energy. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models in the case of the 2×1023W/cm2 laser and a 5.0GeV electron.

Fig.4.3-19 Radiation spectrum in the case of 1×1022W/cm2 laser and a 5.0GeV electron. The blue and red lines represent linear polarized radiation and the spin-depolarized radiation. These line were derived from the “Seto II” model.

In Stage 4 with LWFA

In this section we consider the case of low intensity (1021W/cm2) laser and the electron energy of 5.0GeV by LWFA for RA5-VBir in Stage 4.

4.3.2-7 Calculation results – 1×1021W/cm2 ( f # =2 ) laser + 5.0GeV electron case

For the high energy photon generation, Fig.4.3-20 shows the trajectory of an electron and the time evolution of an electron’s energy in the head-on collision with the laser. Though the initial energy is different from 600MeV case, the tendencies are the same. From the asymptotic final energies, we can observe the high-intense field correction easier than in the 600MeV case. It depends on the coupling between the electron and radiated field from the electron.

The emission has a very narrow pattern in the initial direction of an electron, it exceeded the limit of the angular resolution of our calculation . Therefore, the opening angle of this radiation is smaller than this value. Fig.4.2-21 is the energy spectrum of emitted light entering into the GPC (1/10γ). We can obtain 95% polarization.

(B)

Fig.4.3-20 (A) Orbit of normal incident beam electron (B) Time evolution of electron energy in the case of a 2.5GeV electron. Line colors indicate employed RR models: SZK (black), LL(red), CSok(green), QSok(pink) and Seto II (blue) models.

Fig.4.3-21 Radiation spectrum in the case of 1×1021W/cm2 laser and a 5.0GeV electron. The blue and red lines mean linear polarized radiation and the spin-depolarized radiation. The green line is the degree of polarization,

DoP = (#POL-#DEPOL)/(#POL+#DEPOL).

It was derived from Seto II model.

4.3.3 Predictions

We employ four computational models for predictions.

(a) Monte-Carlo simulation with quantum cross section of radiation

(b) Orbit simulation with radiation reaction model with quantum cross section (QSok)

(c) Monte-Carlo simulation with classical cross section of radiation

(d) Orbit simulation with classical radiation reaction model (LL)

In the Monte-Carlo simulations, (a) and (c), photon emission events are generated based on the total cross section and emitted photon energy is chosen randomly according to the differential cross section. Assuming parallel emission, the electron loses its energy to conserve the total energy of the electron and the emitted photon. In the orbit simulations, (b) and (d), electron loses its energy continuously based on the equations of motion with radiation reaction terms. Thus electrons behave in a deterministic way according to the total cross section of emission.

Quantum effects of radiation in strong electromagnetic fields provide two features of electron scattering and photon emission. One is stochastic photon emission and electron recoil [She 72]. This effect is expected to dominate when quantized photons are emitted with energies comparable to the emitting electron energy. The other is the quantum corrections of radiation cross section. The quantum corrections are expected to be significant when quantum invariant parameter, , is comparable to or larger than unity (this parameter is explained in the section of RA5-POL). Required conditions of these two features are equivalent and we can investigate them using the experimental setup at ELI-NP.

These quantum effects are both included in model (a). Models (b) and (c) take into account either of them, quantum correction of emission spectrum and stochastic photon emission, respectively. Model (d) is the standard model of radiating electron dynamics in the classical regime. On the other hand, the minor terms of the equations of motion with radiation reaction are excluded in the Monte-Carlo simulations. Their contributions are characterized by a power of , thus they would play a limited rule in the highly relativistic case, where denotes gamma factor of electron. As explained before, the predictions of the other radiation reaction models (SZK and CSok models) can be identical to that of model (d), i.e., LL model, in the present physical condition.

Considered physical conditions correspond to the experimental setup in ELI-NP as follows. For pulse laser, laser peak intensity, pulse duration and spot size are 1022[W/cm2], 22[fs] and 5[μm], respectively. Laser wavelength is 820[nm]. For the electron beam, perpendicular bunch size is 15[μm] and one beam bunch contains 109 electrons. 1.44 million sampling particles are calculated in the Monte-Carlo simulations. We consider a head-on collision between the laser pulse and the electron beam.

Fig.4.3-22 Final energy and scattering angle of electron resulting from the head-on collision of electron beam and laser pulse. Panels (A), (B), (C) and (D) indicate the predictions from models (a), (b), (c) and (d), respectively. Display areas of angle are ±6 [deg] and ±0.3 [deg] for models (a)/(c) and (b)/(d), respectively.

Characteristics of the employed models are clearly obtained in the relationship between electron final energy and electron scattering angle [Har 14]. Figure 4.3-22 shows final energy and scattering angle of electrons resulting from the models. Panels (A), (B), (C) and (D) gives the predictions from model (a), (b), (c) and (d), respectively. Horizontal and vertical axes stand for final energy and scattering angle, respectively. Color contours indicate electron number. Electrons affected by a strong laser field lose their energy and their orbits are modified largely. Thus scattering angle tends to be large for low energy range. The scattering angle shows a wide distribution without a defined edge for model (a) and (c), while electrons are distributed in quite narrow regions of scattering angle for model (b) and (d). This difference is a typical consequence of stochastic photon emission and electron recoil. On the other hand, minimum electron energy tends to be large for the models (a) and (b) with the quantum cross section. This difference comes from the suppression of cross section due to quantum correction for high-energy photon emission.

Fig.4.3-23 Energy distribution of scattered electrons per one electron bunch. Red, purple, blue and green lines indicate the prediction of models (a), (b), (c) and (d), respectively. Energy bin size is 10 [MeV].

From the measurement of scattered electrons, we can examine the validity of employed models. Figure 4.3-23 shows energy distributions of scattered electrons. Red, purple, blue and green lines stand for the energy spectrum obtained from models (a), (b), (c) and (d), respectively. The electron energy is limited to a certain minimum energy in radiation reaction models (b) and (d). The minimum energies, ~ 450[MeV] for model (b) and ~ 160[MeV] for model (d), correspond to the final energy of the electron, which enters to the center of laser pulse (see, Fig. 4.3-2). Model prediction can be distinguished clearly in ~ 50-60[MeV] energy range. Per one electron bunch, ~10-100 electrons can be detected in model (a) while > 104 electrons will be found in model (c). Here energy bin size is assumed to be 10 [MeV]. The detection angle is within ± ~5 [deg] as shown in Fig. 4.3-22. There is no electron in this range in the radiation reaction models, (b) and (d).

Figure 4.3-24 shows angle distribution of scattered electron with energies of 180-240 [MeV]. Red, purple, blue and green lines are obtained from models (a), (b), (c) and (d), respectively. Electrons are widely distributed within ± 5 [deg] in the Monte-Carlo models (a) and (c). For detection angle ~5 [deg], ~ 10-100 electrons are detected (angle bin size 0.1[deg]). In contrast, electrons are concentrated in a narrow range of ± ~ 0.2 [deg] in model (d). No electron will be detected in model (b).

Fig.4.3-24 Angle distribution of scattered electron per one electron bunch. Red, purple, blue and green lines are results of models (a), (b), (c) and (d), respectively. Electrons in the energy range 180-240 [MeV] are collected here. There is no electron in this energy range for model (b). Angle bin size is 0.1[deg].

Fig.4.3-25 Photon energy spectrum obtained from models (a): red, (b): purple, (c): blue and (d): green. Photon count is per one electron bunch and energy bin size is 10 [MeV].

The difference due to the employed cross sections is also evident in the emitted photon spectrum. Figure 4.3-25 shows the photon energy spectrum. Red, purple, blue and green lines indicate the energy spectrum obtained from models (a), (b), (c) and (d), respectively. In the radiation reaction models, (b) and (d), the energy spectrum is obtained by distributing the electron energy loss in each time step onto photon energy bins according to the differential cross section. The predictions are significantly different in high-energy range between the models employing quantum and classical cross sections. For each cross section, Monte-Carlo simulations indicate similar spectrum to that obtained from the radiation reaction model. Roughly ~104 photons are emitted in the range of ~ 300-400 [MeV] in the models employing the quantum cross section (models (a) and (b)). For the classical cross section (models (c) and (d)), ~106 photons are emitted in the same energy range.

Angle distribution of emitted photon is given in Fig. 4.3-26. Red and blue lines stand for the predictions of model (a) for high-energy range (red: > 400[MeV]) and for almost all energy range (blue: > 6[MeV]). Purple and green lines are obtained from model (b). High-energy component (> 400[MeV]) are collected in the purple line, while all photons are collected in the green line. The emission angle of high-energy photons is significantly concentrated in the beam incident direction within ±2 [deg] in both models. As indicated in purple and green lines, stochasticity of emission affects the scattering angle in the lower energy range.

Fig. 4.3-26 Photon angle distribution per one electron bunch obtained from the models (a): red/blue and (b): purple/green. Angle bin size is 1[deg] here. Only energetic photons with energies > 400 [MeV] are counted in red and purple lines. (Almost) all photons are included in blue and green lines.

Fig. 4.3-27 Energy distribution of positrons generated via 1[mm] Beryllium filter. Energy bin size is 10 [MeV]. Employed models are (b): purple and (d): green.

We also estimate the positron tracks generated by the interaction between a material filter and the generated high-energy photons. Models (b) and (d) are employed here. Figure 4.3-27 shows positron track number expected for models (b): purple and (d): green. Material filter is Beryllium with a thickness of 1 [mm]. Pair production rate in the filter is estimated by using Bethe-Heitler cross section with complete screening. A few positron tracks will be detected in the energy range 300-400 [MeV] in model (b) per one electron beam while ~100 positron tracks can be obtained in model (d). Roughly the same positron numbers are expected for Monte-Carlo models since obtained photon spectrums are similar to that obtained in the radiation reaction model in high-energy range as shown in Fig.4.3-25.

In summary, we have performed numerical simulations of laser pulse – electron beam collision for the experimental condition in ELI-NP. The simulation results indicate that the quantum effects in radiation, i.e., stochastic photon emission and corrections of radiation cross section, become evident in final electron energy, scattering angle and emitted photon spectrum. Optimal detection range of electron (photon) energies and angles have been considered based on the simulation results.

4.3.4 Predictions for an alternative electron source

The electron bunch can be generated via laser wake field acceleration using another laser pulse. Electron number and energy are 108 and 2.5 [GeV], respectively. For simplicity, the other parameters are assumed to be the same as the electron bunch from LINAC. Energy distribution of scattered electrons and emitted photon spectrum are estimated for this alternative electron source.

Figure 4.3-28 shows the energy distribution of scattered electrons. Red, purple, blue and green lines stand for the prediction from models (a), (b), (c) and (d) respectively. Electrons with scattering angles < ±1 [deg] are integrated here. Energy bin size is 10[MeV]. Electron energy is gradually extended down to ~ 50 [MeV] and ~ 0 [MeV] for Monte-Carlo model (a) and (c), respectively. On the other hand, sharp cut-offs of electron energy are found at ~ 620 [MeV] and ~ 200 [MeV] for quantum (b) and classical (d) radiation reaction models. In the energy range of 60 – 80 [MeV], we can detect 1 – 10 scattered electrons per incident bunch for QED Monte-Carlo model, (a). More than 104 electrons are observed for classical Monte-Carlo model, (c). There is no electron in this energy range for radiation reaction models, (b) and (d).

Fig. 4.3-28 Emitted photon spectrum. Emission angles are integrated. Energy bin size is 10 [MeV]. Employed models are (a): red, (b): purple, (c): blue and (d): green.

Fig. 4.3-29 shows the energy spectrum of the emitted photon. Red, purple, blue and green lines stand for the predictions from models (a), (b), (c) and (d) respectively. The photon number is integrated for all emission angles. Difference of predictions from quantum ((a) and (b)) and classical ((c) and (d)) cross sections is evident in the high-energy range > 1 [GeV]. By comparing (a) and (b), one can also see the influence of stochastic photon emission in the higher energy range > 1.5 [GeV]. Total photon numbers in the energy range 2.0-2.25 [GeV] are estimated as ~104, ~102 and ~5×105-106 for model (a), (b) and the classical models ((c) and (d)), respectively. Therefore we can distinguish these model predictions by the measurement of photon spectrum using 1 [mm] Beryllium filter as in the previous section. The difference between Monte-Carlo model (a) and radiation reaction model (b) would be explained as follows: Some electrons can penetrate into the center of laser pulse without sufficient energy loss and contribute high-energy photon emission in the Monte-Carlo mode, while electrons should lose their energy sufficiently before approaching the pulse center by contentious radiation damping in the radiation reaction model.

Fig. 4.3-29 Emitted photon spectrum. Emission angles are integrated. Energy bin size is 10 [MeV]. Employed models are (a): red, (b): purple, (c): blue and (d): green.

4.4 Timeline of implementation and milestones

Timeline of RA5-RR is shown as Fig.4.4-1.

Fig.4.4-1 Timeline of Stage 1.5 and 3 experiments

4.5 Estimated Budget

With respect to the previous topics, the following supplemental equipment is deemed necessary – and it is common also for other proposals in Stage 1.5, 3 and 4 of RA5-TDR.

Table 4.5-1 Table of experimental items and the costs for the RA5-RR proposal (common also to other proposals mentioned further in this TDR)

5. E-E+ Pair Production in the Tunneling Regime (RA5-Pair)

5.1 Physics Case

We describe several pictures of pair production in vacuum and their relevance to the present experiment in ELI-NP. Perturbation theory of QED derives pair production due to collision of two energetic photons. This is called Breit-Wheeler (BW) pair production [Bre 34]. Field energy associated with its strength also becomes an energy source of particle pair. Low frequency and strong field limit suggests spontaneous pair production from a constant but intense electromagnetic field [Sau 31, Sch 51]. In the framework of QED, this process is regarded as a pair production from numerous low energy photons interacting simultaneously. Pair production in strong field is therefore not fully explored since non-perturbative treatment is required.

The spontaneous pair production is illustrated as a tunneling process in vacuum. Particles in the negative energy region can pass through the steep potential structure of background field by tunneling effect to reach the positive energy region. Probability of the tunneling process is estimated by using a typical electric field, i.e., Schwinger field , where denotes Compton wavelength. Resulting probability, , is given as

, (5.1.1)

where stands for the strength of background electric field [Sch 51]. The exponential dependency is a consequence of tunneling effect.

Figure 5.1-1 shows typical diagrams of pair production from interacting high-energy photons. Panels (A) and (B) give single-photon and multi-photon BW processes [Rei 62], respectively. Threshold of single-photon BW process is determined by total photon energy in the center of mass system (CMS) of generated particle pair. The characteristic parameter, , is

, (5.1.2)

where and are the minimum energy required for pair production and total photon energy in CMS, respectively. and are photon energies. Head-on collision is assumed here. Threshold of single photon BW process is given by . For sub threshold case , particle pair can be generated only via multi-photon BH process. If additional photons come from a laser field, minimum number of interacting photon to produce one particle pair, , is estimated by

, (5.1.3)

where a is normalized vector potential of laser and is now laser frequency [Bam 99]. Required photon energy is quite large for single BW process in laser fields since laser frequency is small. For example, minimum photon energy is ~ 100 [GeV] for laser energy ~ 1 [eV].

Figure 5.1-1 Diagrams of typical pair production processes involving energetic photons. (A) single-photon BW process. Two photons γ1 and γ2 interact with each other. (B) multi-photon BW process. N photons γ1 … γ2 interact each other. (C) Pair production from energetic photon γh in strong field. Double lines indicate dressed particle.

Figure 5.1-1 (C) represents pair production in strong field. Double lines stand for dressed electrons (or positrons) interacting with vast number of photons in external field [Fur 51]. Although the pair production is essentially non-perturbative, semi-classical approach can be applied for pair production triggered by an energetic photon in strong-field – stimulated pair production. Contribution of external field is exactly included in the dynamics of dressed particles [Vol 35, Nik 64] and perturbative interaction is considered between the energetic photon and the dressed particles. Photon interaction in semi-classical regime is characterized by the quantum parameter ,

, (5.1.4)

where , and denote Compton wavelength, field 4-tensor and 4-momentum of photon, respectively. Pair production cross section, , is then

, (5.1.5)

where , and are fine structure and Plank constants and photon energy, respectively. denotes ratio of positron (electron) energies to photon energy, i.e., and . is defined by [Ber 81, Nik 64]. Total cross section of pair production as a function of is shown in Fig. 5.1-2 (green line) along with the radiation cross sections (see, RA5-POL). Total cross section grows exponentially for . Probability of pair production is roughly estimated as [Nar 68],

(5.1.6)

This formulation invokes the tunneling effects as in the spontaneous pair production however the probability is determined by , not .

Figure 5.1-2 Total cross sections of radiation and pair production as a function of quantum parameter. Red, blue, purple and green lines indicate total cross section of radiation , difference between classical and quantum cross sections , the spin-dependent term of quantum cross section and pair production cross section , respectively. Radiation cross sections referred here are explained in the section RA5-POL.

We consider the relevance of the above mentioned pair production processes to the experiments in ELI-NP [Ion 14] while comparing with that in SLAC E-144 [Bam 99] experiment. Experimental parameters are summarized in Table I (left three columns: electron energy, number of electron per bunch and laser intensity (normalized potential)). For ELI-NP, we consider two types of electron bunches. One is the electron bunch from LINAC with an energy of 600 [MeV]. The other is generated via laser wakefield acceleration. Considered electron energy is 2500 [MeV] [Nak 14]. Energy range of seed photon (the fourth column) is roughly estimated by the energy spectrum of the photon emitted from the incident electron bunch (Experimental data for SLAC and simulation data for ELI-NP: see, RA5-RR, RA5-POL).

We estimate three typical parameters characterizing the above-mentioned three pair production processes. Head-on collision between seed photon and laser pulse is assumed here. The first parameter E/Es on spontaneous pair production (Eq.5.1.1) is quite small ( < 10-3) even for ELI-NP as shown in the fifth column. Therefore spontaneous pair production is still negligible. The second parameter Nmin in the sixth column is required photon number in multi-photon BW process (Eq.5.1.3). Mmin is quite different between ELI-NP (~105-6) and SLAC (~5). This estimation indicates that pair production could take place only in highly non-perturbative regime in ELI-NP while multi-photon process with a few photons is dominant in SLAC.

Despite this large difference of physical regime, the quantum parameter (Eq. 5.1.4) in ELI-NP (600 MeV LINAC) has a value relatively close to that in SLAC, as shown in the seventh column. The quantum parameter is here estimated by χ ~ (E/Es)(Eϒ/mc2), where Eϒ is seed photon energy. Thus similar pair production rate is expected in strong field QED under the contribution of different number of laser photons.

Finally, generated positron number per electron bunch is given in the ninth column (Observed positron number for SLAC and simulation results for ELI-NP, see Sec. 5.3). The simulation is based on the cross section described in Eq. 5.1.5. Expected positron number for 600[MeV] electron beam is similar to the result of SLAC, as indicated in the quantum parameter. For 2.5[GeV] case, the positron number increases significantly (>104) compared to the other cases. This is a consequence of the exponential growth of pair production probability as in Eq. 5.1.6. Precise measurements of pair production rate and careful comparison with the result of SLAC experiment could provide a proof of the strong field QED.

Table 5.1-1 Experimental condition and estimation of typical parameters

5.2 Technical Proposal

The requirements and the experimental setup are identical to the ones for the experiments of radiation reaction. See the section 4.2.

5.2.1 DETECTORS

For observing the e-e+ pairs, the beryllium window (-pairs converter) has to be removed (Ch.9).

5.3 Estimation of Count Rates/Feasibility of Proposed Devices

We estimate the pair production rate in the collision between electron beam and intense laser pulse. The estimation is based on a numerical simulation employing the cross sections of radiation and pair production. The cross sections are,

, (5.5.1)

where and are the cross section of radiation (Sec. 5.1) and pair production (Sec. 5.1), respectively. , and are the quantum parameter (Eq. 5.1.4 in Sec. 5.1), ratio of emitted photon energy to incident electron energy and ratio of positron (electron) energy to incident photon energy, respectively. δ is defined as for radiation and for pair production.

The experimental configuration is the same as that in RA5-RR. The primary process is again high-energy photon emission and its back reaction of electrons. The pair production is seeded by the emitted photons. That is, the pair production takes place as a two-step process,

(5.5.2)

where , and denote high energy photon, laser photon and absorbed number of laser photon, respectively. In the present situation, particle pair is also generated via direct interaction between electron and laser field without high-energy real photon (trident pair production) [Ild 11, Hu 11, Kin 13]. Probability of this process is expected to be quite small compared to the two-step process. Thus this process is neglected in the simulation.

Multiple numerical procedures are combined to evaluate each process.

Photon spectrum is calculated by Monte-Carlo model [Ner 11, Elk 11] (for 2500 [MeV] case) or the radiation reaction model (for 600 [MeV] case) with quantum cross section (see, Sec. 4.3.3). Central region of laser pulse [±3w, ±1.5s, ±1.5s] is spatially divided into (400 x 31 x 31) grids, where w and s denote pulse length in propagating direction and spot size. The photon energy bins are prepared in each spatial grid. Bin size is one thousandth of initial electron energy.

Photon absorption rate are calculated based on the total cross section of pair production for each spatial grid. Propagation angle is assumed to be 0 [deg]. In reality this is expected to be < 1[deg] for high-energy range (see Fig. 4.3-9). Absorbed photon number is accumulated in the spatial grid. Total number of absorbed photon is distributed into positron energy bin according to the differential cross section of pair production.

Dynamics of positron in the laser field is calculated by means of the Monte-Carlo simulation (see, Sec. 4.5.3). Initial condition of sampling particles is given according to the positron energy spectrum in each spatial grid. Number of sampling particle is 1.44 or 0.60 million.

Figure 5.3-1 Energy spectrum of emitted photon (blue), absorbed photon (purple) and generated positron (red). Electron beam energy is 600 [MeV]. Energy bin size is 10 [MeV].

The physical conditions considered for the simulations are as explained in Section 5.1 and summarized in Table 5.1-1. Laser intensity, pulse duration, spot size are 1022 [W/cm2], 22 [fs] and 5[μm], respectively. Two types of electron beam will be employed. One is obtained from accelerator and typical energy is 600 [MeV]. The other is obtained by using plasma wake field acceleration and energy is 2500 [MeV]. For reference, pair production is evaluated additionally for 5000 [MeV] electron beam + 2×1023 [W/cm2] pulse laser. Quantum parameter for energetic component of emitted photon will be sufficiently lager than unity in this case. Other parameters are the same as those in the case of 2500 [MeV] electron beam.

Figure 5.3-1 shows the simulation results for 600 [MeV] electron beam. Blue, purple and red lines indicate energy spectrum of emitted photon, absorbed photon and generated positron. The photon spectrum is identical to the prediction in the section of radiation reaction (RA5-RR, Sec. 4.5.3, model (b)). In this case, the quantum parameter is not so large (< 0.25, see Sec. 5.1). Thus only small fractions of high-energy photons with energies of ~200-450 [MeV] are absorbed in the laser field, as shown in the purple line. Positron energy is roughly half of the absorbed photon energy, i.e., ~ 100-300 [MeV]. Total number of positrons per one electron bunch (109 incident electrons) is ~ 1.

Figure 5.3-2 shows final energy and scattering angle of positrons resulting from the Monte-Carlo simulation. Dynamics of generated positrons is also affected by the radiation reaction in laser field. As a result, positrons lose their energy and scattering angle becomes wide. The simulation result indicate that a few positrons can be observed mostly within the energy range ~ 100-200 [MeV] and the detection angle ±5 [deg].

Figure 5.3-2 Final energy and angle distribution of scattered positrons. Electron beam energy is 600 [MeV]. Total positron number is ~1 per electron bunch.

Figure 5.3-3 shows the energy spectrum of emitted photon (blue), absorbed photon (purple) and generated positron (red) obtained for 2500 [MeV] incident electron beam. Expected quantum parameter in this case approaches unity, about four times larger than that in the previous case. As a result, the absorbed photon number increases up to O(104) per one electron bunch. The energy of absorbed photon is widely distributed in the range of ~ 500 – 2300 [MeV]. Generated positron energy is roughly ~ 50 – 1800 [MeV]. The exponential component of pair production cross section (Eq. 5.1.6) results in this dramatic increase of positron number.

Figure 5.3-4 shows the energy spectrum of positron after passing through the laser pulse in the case of 2500 [MeV] electron beam. Positrons are integrated within detection angles < 1 [deg]. The energy spectrum is mainly determined by the differential cross section of pair production. Roughly 10-100 positrons could be detected around the minimum and maximum energies of energy spectrum, 50 – 100 [MeV] and > 1500 [MeV]. We can define the differential cross section of pair production through the positron measurement.

Figure 5.3-3 Energy spectrum of emitted photon (blue), absorbed photon (purple) and generated positron (red). Electron beam energy is 2500 [MeV].

Figure 5.3-4 Distribution of final positron energy for detection angle < 1 [deg]. Initial beam energy is 2500 [MeV].

We also evaluate a more energetic interaction case, head-on collision between 5000 [MeV] electron beam and laser pulse with an intensity of 2×1023[W/cm2]. The other characteristics of laser pulse are the same as before. Figure 5.3-5 shows energy spectrum of emitted photon (red), absorbed component of photon (purple) and generated positron (blue). Emitted photon energy is extended to ~ 4000 [MeV] and quantum parameter for this energy range is estimated χ ~ 5. As a result, almost all photons are absorbed in the laser field, as shown in the red and purple lines. Observed photon spectrum in high-energy range is limited by the photon absorption due to pair production.

Figure 5.3-6 shows positron number resulting from the conversion of emitted photon via 1[mm] Beryllium filter. Red line indicates the estimation without considering photon absorption while blue line indicates the estimation for remained photons (emitted photons – absorbed photons). One can see that influence of photon absorption can be observed in the positron number with an energy of ~ 4000 [MeV]. This measurement approaches another consequence of pair production in intense electromagnetic fields.

Figure 5.3-5 Energy spectrum of emitted photon (red), absorbed photon (purple) and generated positron (blue). Electron beam energy is 5000 [MeV] and peak intensity is 2×1023[W/cm2].

Figure 5.3-6 Energy spectrum of positron converted via 1[mm] Beryllium filter. The spectrum is estimated from emitted photon spectrum with (blue) and without (red) photon absorption due to pair production. Energy bin size is 10 [MeV]. Electron beam energy is 5000 [MeV] and peak intensity is 2×1023[W/cm2].

5.4 Timeline of implementation and milestones

Timeline of RA5-Pair is shown as Fig.5.4-1 (same as Fig. 4.4-1).

Fig.5.4-1 Timeline of Stage 1.5 and Stage 3 experiments (same as Fig. 4.4-1).

5.5 Estimated Budget

The supplemental experimental devices with respect to the previous chapter are:

Fig.5.5-1 Table of experimental items and the costs for the RA5-Pair proposal

6. Polarization Properties of Emission in Strong Fields (RA5-Pol)

This topic is an additional problem of radiation in the experiments of radiation reaction (RA5-RR: Stage1.5/3, Ch.4), e-e+ pair production (RA5-Pair : Stage1.5/3, Ch.5) and vacuum birefringence (RA5-VBir : Stage4, Ch.8). The experimental setups are included in the relevant chapters. Here, we will discuss about the classical/quantum theory of the high-intense fields of photons and predictions.

6.1 Physics Cases

Classical treatment of radiation is based on the Liénard-Wiechert potential generated by a moving charged particle. In highly relativistic cases, synchrotron radiation can be applied to radiation processes in arbitrary electromagnetic fields [Jac 99]. Resulting angle distribution and frequency spectrum are

(6.1.1)

Where and are parallel and perpendicular polarized components of emission intensity. Here , and denote gamma factor of emitting electron, frequency and angle of emitted photon, respectively. is solid angle of radiation. is MacDonald function. Characteristic frequency is given by

(6.1.2)

where denotes the Lorentz 4-force. By integrating with respect to and , radiation spectrum and total radiation intensity are obtained as,

(6.1.3)

where corresponds to the total radiation intensity. At least for low energy range, synchrotron radiation is theoretically well established and has lots of technological applications and relevance to astronomical phenomena. Hereinafter, “classical cross section” is used for the synchrotron cross section, Eqs. (6.1.1) and (6.1.3).

Radiation process can be also considered in terms of quantum electrodynamics. Standard calculation schemes using perturbation theory have successfully described particle interactions involving high-energy photon emission such as (inverse) Compton scattering. However photon emission under the action of strong background electromagnetic field is not covered by the perturbation theory since numerous low energy photons simultaneously contribute the emission process. Fortunately a semi-classical approach can be applied for photon emission from high-energy electron, and we have obtained theoretical cross sections that have a direct relevance to the synchrotron radiation.

The quantum strong-field theory and related cross sections are characterized by a covariant quantum parameter [Nik 64]. The quantum parameter is defined as

(6.1.4)

Where , and denote Compton wavelength and field 4-tensor and 4-momentum of electron, respectively. Background field strength affects the cross section via the parameter. Obtained cross section is as follows:

(6.1.5)

(6.1.6)

where and are fine structure and Plank constants, respectively [Ber 7.1]. This cross section is given as a function of the ratio of emitted photon energy to incident electron energy , where and are photon and electron energies, respectively.

The radiation cross section in quantum regime, Eqs.(6.1.5) and (6.1.6), is directly compared with that of synchrotron radiation, Eq.(6.1.3). By converting photon frequency to photon energy, , the characteristic frequency of synchrotron radiation is described by the quantum parameter such that . Then, the intensity of synchrotron radiation is given as a function of and . Resulting classical cross section, , and potential of radiated electromagnetic field, , relate to the first term of quantum cross section in Eq (6.1.5) [Sok 10],

(6.1.7)

Thus polarization of this component is evaluated from that of synchrotron radiation given in Eq.(6.1.1). On the other hand, the second term, , in Eq.(6.1.6) comes from purely quantum effect relevant to electron spin, while the first term is derived from spin-less QED [Sok 86]. We assume emitted photon associated with this term is assumed to be depolarized for incident electrons without a defined polarization.

Total cross sections of radiation are given in Fig 6.1-1 as a function of quantum parameter. Red, blue, purple and green lines indicate total cross section of classical radiation , difference of synchrotron and quantum total cross sections (), the second term of quantum cross section and pair production cross section (see RA5-Pair, Sec.5), respectively. These cross sections are normalized to , where ε denotes incident energy of electron for radiation or photon for pair production. In the lower limit of quantum parameter, , dominance of to indicates that the cross section of quantum regime is identical to that of classical radiation. Difference between synchrotron and quantum cross sections arises for roughly . This difference mainly comes from the correction term in the first term of quantum cross section, , in Eq. (6.1.7). The second term, , have a certain effect on the total cross section in the range of . Pair production cross section is negligibly small for but grows exponentially for .

For head-on collision between pulse laser and electron beam, the quantum parameter experienced by electron is roughly estimated by , where denotes peak electric field of pulse laser. For ELI-NP parameter [Ion 14], i.e., laser intensity ~ 1022-1023 [W/cm2] and electron beam energy ~1 [GeV], the quantum parameter is estimated as . Therefore the transition of radiation regime from classical to quantum strong field is suitable to be explored in ELI-NP.

Figure 6.1-1 Total cross sections of radiation and pair production as a function of quantum parameter. Red, blue, purple and green lines indicate total cross section of radiation Wcl, difference between synchrotron and quantum cross sections , the second term of quantum cross section and pair production cross section , respectively.

Figure 6.1-2 Energy spectrum for polarized and depolarized components for = (A) 0.01 and (B) 0.3. Red and blue lines indicate the first and second term of cross section. Ratio of to (green) and ratio of to (purple) are also given with respect to the right side axis.

Figure 6.1-3 Angle distribution of quantum radiation for three different photon energies ξ = (A) 0.067, (B) 0.33 and (C) 0.6, where ξ denotes ratio of emitted photon energy to electron energy. Quantum parameter χ is fixed as 0.25. Red and purple lines indicate parallel and perpendicular component of the polarized term Wpl. Blue line indicates the spin-dependent term Wde.

Quantum effects associated with the second term, , can be examined by polarization measurements. The first term, , is separated into parallel, , and perpendicular, , in the similar manner to the classical cross section in Eq (7.1.1). Figure 6.1-2 shows energy spectrum of these two components and for = (A) 0.01 and (B) 0.3. For low , as shown in panel (A), the contribution of is small and emitted photons are highly polarized in parallel direction except at the low energy region with certain value of .This result corresponds to the high polarization ratio of synchrotron radiation. On the other hand, the contribution of dominates that of at the high energy region for = 0.3 as shown in panel (B). Thus clear consequence of the second term, i.e., quantum effect associated with electron spin, can be observed in the polarization component of high energy photons.

Angle distribution of photon in quantum radiation is shown in Fig. 6.1-3. Angle distribution for three different photon energies is given here. Ratio of photon energy to electron energy is ξ = (A) 0.067, (B) 0.33 and (C) 0.6. Quantum parameter is fixed as 0.25. Red and purple lines indicate parallel and perpendicular component of the polarized term Wpl. Blue line indicates the spin-dependent term Wde. For given quantum parameter, i.e., background field strength and electron energy, low photon emission is mainly given by the polarized term Wpl, while the spin-dependent term Wde contributes dominantly to high-energy photon emission. Perpendicular component of Wpl is dominant away from the electron incident direction and suppressed in high-energy photon emission. The spin-dependent term Wde, on the other hand, localized in the electron incident direction and will contribute depolarized photon emission in high-energy range.

Contributions of and to the perpendicular component tend to be small in the middle range of energy spectrum. High energy photons with high linear polarization ratio would be obtained from this energy range by using linear polarized pulse laser and high energy electron beam. Obtained photons are useful to probe the light-by-light scattering in vacuum, which will be explained in Sec.8.

6.2 Technical Proposal

This experiment is carried out as sub-experiment of RA5-RR, RA5-Pair and RA5-VBir with the layout of Stage 1.5 (Fig.0.2-1) and Stage 3 (Fig.0.4-1). See the detail of these in sections 4.2 and 8.2.

6.3 Estimation of Count Rates/Feasibility of Proposed Devices

Energy spectrum for parallel and perpendicular polarized components is examined for head-on collision between pulse laser and accelerated electron bunch. Employed conditions are relevant to the experimental setup in ELI-NP and summarized in Table. 6.3-1. We consider two types of incident electron bunch. One is the electron beam from accelerator(LINAC). Initial energy is 600 [MeV] and 109 electrons are included per electron bunch. The other is the electron bunch generated via laser wakefield acceleration. Electron energy is assumed to be 2.5 [GeV], which is expected for the interaction between plasma gas with a density of ~1018 [1/cm3] and pulse laser with a laser energy of 30 [J] [Nak 14]. Electron number is assumed to be 108 per electron bunch. Bunch size is 15 [μm] in both cases. Pulse laser is a Gaussian pulse with pulse duration of 22 [fs] and a spot size of 5 [μm]. Considered laser intensities are 1022 [W/cm2] and 1020 [W/cm2].

Table 6.3-1 : simulation parameters

Figure 6.3-1 Energy spectrum for each component of emitted photon for 600 [MeV] electron beam. Red and purple lines stand for the emitted photons related to the parallel and perpendicular components in the first term of quantum cross section, , respectively. Blue line is emitted photons for the second term of the cross section, .

Simulation scheme is almost the same as the Monte-Carlo simulation performed in RA5-RR (see Sec.2.3.3, model (a), (c)). Incident electron orbit is calculated by relativistic equations motion. Stochastic photon emission is implemented by a Monte-Carlo event generator according to the quantum cross section (Eqs. (6.1.5) and (6.1.6)). Photon energy and emission angle are recorded to obtain photon energy spectrum and angle distribution in each emission event. In addition, we record linear polarization ratio in the first term, , (Eq. (6.1.5)) and ratio the second term, , (Eq. (6.1.6)). Former is calculated from the polarization ratio of synchrotron radiation (Eq. (6.1.1)). For comparison, we also employ an alternative cross section in which the second term has the same polarization ratio as that of the first term. Hereinafter, the first and second terms of quantum cross section are called as “polarized term” and “spin-dependent term”, respectively.

Figure 6.3-1 shows energy spectrums of each component of emitted photon resulting from the interaction of 600 [MeV] electron beam. Red and blue lines stand for parallel and perpendicular components in the polarized term, , respectively. Purple line shows photon energy spectrum related to the spin-dependent term, . The parallel component dominates the perpendicular component in the polarized term, in all energy range. On the other hand, photon number for the spin-dependent term, , increases in high-energy range. For ~ 400[MeV], significant portion of photon comes from the spin-dependent term.

Figure 6.3-2 shows degree of linear polarization, P, as a function of photon energy. The degree of linear polarization is defined by , where and stand for photon numbers of the parallel and perpendicular polarized components, respectively. Red line is obtained from quantum cross section. Photon emission associated with the spin-dependent term is assumed to be depolarized. Blue and purple lines are for classical and alternative cross sections, respectively. In the ~ 400 [MeV] energy range, one can see that the degree of linear polarization dramatically decreases from ~ 80-90% to ~30% under the quantum effect of electron spin. Total number of photon is ~ 103-4 per electron bunch, as shown in Fig. 6.1-1, and expected positron track number is ~ 1-10 for 1 [mm] Beryllium filer (see, Sec.4.3.3).

Figure 6.3-2 Ratio of linear polarization as a function of emitted photon energy. We employ quantum cross section with the depolarized component (Red), classical cross section (purple) and alternative cross section (blue).

Figure 6.1-3 Energy spectrum for each component of emitted photon for 2500 [MeV] electron beam. Red and purple lines stand for the emitted photons related to the parallel and perpendicular components in the first term of quantum cross section, , respectively. Blue line is emitted photons for the second term of the cross section, .

Figure 6.1-4 Ratio of linear polarization as a function of photon energy. Energy of electron beam is 2500 [MeV].

For the 2.5 [GeV] electron bunch, photon energy spectrum and degree of linear polarization are shown in Figs. 6.3-3 and 6.3-4. Red and purple lines indicate parallel and perpendicular components in the polarized term, , respectively. Blue line shows emitted photons related to the spin-dependent term, . Intermediate energy range with maximum degree of polarization locates at 500 – 1000 [MeV]. Photon number is ~ 104 in the energy range of ~ 600 [MeV] and expected degree of linear polarization is ~75%. We can confirm the polarization property of polarized term, , through the measurement of this relatively high degree of linear polarization. In addition, the obtained highly polarized photon beam with energies ~ 600 [MeV] would be a candidate of probe for light-by-light scattering, which is realized by using another pulse laser (see, RA5-VBir, Sec.8).

We also estimate the ratio of linear polarization for alternative electron source (case 3). Laser intensity is 1022 [W/cm2] and initial electron energy is 2.5 [GeV]. Electron number is 108 per bunch. Other parameters are identical to cases 1 and 2. This condition is the same as that considered in Sec. 4.3.4.

Figure 6.1-5 shows degree of linear polarization ratio, P, as a function of photon energy for case 3. As in Fig. 6.3-2, red, purple and blue lines denote the estimations based on the quantum cross section with the depolarized component, the classical cross section and the alternative cross section, respectively. In the energy range of 2 – 2.25 [GeV], the expected values are P ~ 0.2 for quantum cross section while P ~ 0.8 for other two models. As described in Sec. 4.3.4, total photon number is estimated to be ~ 104 in this energy range. Polarization measurement of these photons can clarify the characteristics of quantum emission.

Fig. 6.1-5 Degree of linear polarization as a function of emitted photon energy (case 3). We employ quantum cross section with the spin-dependent term (1: red), classical cross section (2: purple) and alternative cross section (3: blue).

6.4 Timeline of implementation and milestones

The timeline of RA5-Pol in “E7-Stage 1.5 and 3” is shown as Fig.6.4.1.

Fig.6.4.1 Timeline of Stage 1.5 and Stage 3 experiments in E7.

6.5 Estimated Budget

This experiment needs equipment that is already included in RA5-RR and RA5-Pair budgets.

RA5-TDR

Stage 2

Experiments of

RA5-GG Gamma-Gamma Collider (Ch.7)

7. Gamma-Gamma Collider (RA5-GG)

7.1 Physics Case

Photon-photon scattering is supposed to occur via the instantaneous vacuum polarization in the purely quantum electrodynamic (QED) process. In the context of Delbrück scattering where virtual photons are included in the external lines, there are several observations [Jar3.3]. However, pure real photon –real photon scattering has not been observed to date. At the laser energy scale, the center of mass system energy, , of two incident photons at around 1eV, head-on collisions [Mou96] and three beam collisions (four-wave mixing) [Ber00] have been performed, and the measurement at is also reported recently [Ina14]. These measurements, however, essentially sufferfrom the extremely small cross sections. For instance, the total cross section is only 10-42 barn at . This is because the cross section has the steep dependence before the imaginary part is opened as thoroughly calculated by [Tol64]. On the other hand, our proposal aims at the measurement by introducing where the elastic scattering cross section is maximized. This situation is summarized in Fig.7.1-1. Our attempt is actually feasible if head-on collisions with 0.7 MeV photon beams are realized based on the laser plasma acceleration (LPA) technique. The 0.1 PW laser system operated at 10Hz at E4 can provide a reasonable interaction rate. This measurement will provide one of the strictest tests of the perturbative QED calculation, therefore, corresponds to a milestone in the investigations of photon-photon scattering over many orders of magnitude.

Fig.7.1-1 The QED-based total cross section of real photon -real photon scattering in µb vs. [MeV]. The solid line show the unpolarized cross-section. This plot is quoted from [Mil12].

7.2 Technical Proposal

Figure 7.2-1 a) shows a table-top () collider with a realistic detector system to capture large angle scattering events. The system consists of two LPAs to generate electron beams with which two incident -beams are further produced via the inverse Compton process in head-on collisions. Initially synchronized two laser pulses are incident from the top and bottom sides of the top view, respectively. They are individually split into two drive pulses for LPA and scatter pulses for the successive inverse Compton process with electrons delivered from LPA. Figure 2 b) illustrates the collision geometry around the interaction point (IP) of scattering, which is located at the distance from the inverse Compton scattering point (CP).

Figure 7.2-1 An all-optical table-top () collider: a) top-view including two LPAs and the detector system to capture the scattering, b) collision geometry around the interaction point, IP, where -rays are produced at each Compton scattering point (CP) in head-on collisions and is the distance between IP and CP. c) a QED-based event simulated by GEANT4. d) a background event simulated by GEANT4. The blue and black trajectories in the event displays denote photons and electrons, respectively. The detector system covers the polar angle degree and the azimuthal angle degree around the beam axis consisting of 90 scintillator crystals (18 crystals in 5 layers in ) made of Ce doped Gd2SO5 (GSO:Ce). GSO:Ce is a well-balanced scintillator from the point of view on the scintillation-photon yield for a sub-MeV -ray, the time resolution and the radiation length X0. The radiation length cm is reasonably small to suppress the lateral spreads of the electromagnetic showers produced by 210 MeV electrons. The individual crystal has the depth of 10X0.

An electron beam with 210 MeV and 1.6 nC is produced from a two-stage laser wakefield accelerator21 comprising a 5-mm long gas cell filled with the mixed gas for the injector stage and a variable-length gas cell filled with pure helium for the accelerator stage. Designing parameters of the laser wakefield accelerator can be carried out by relying on the scaling law of nonlinear plasma wakefields in the bubble regime [KI04, LW07, NK14]. Provided that a laser pulse with 41 TW peak power and 85 fs duration is focused on 12 m spot radius on the entrance of the injector cell operated at plasma density of , strong nonlinear wakefields can be generated so that a 1.6 nC electron bunch could be trapped due to ionization-induced injection [PA10,CM12] and accelerated up to 40 MeV, followed by boosting its energy up to 210 MeV at the length of 2.6 cm in the accelerator cell operated at plasma density of . The relative energy spread and the normalized emittance of resultant output beams are estimated to be 4% in r.m.s. and 0.15 mm mrad, respectively.

The electron bunch is then focused via a set of permanent-magnet-based quadrupoles (PMQs) [HK80] consisting of three elements over 71.2 cm as shown in Fig.7.2-2 which displays variations of the horizontal and vertical beam envelopes simulated by TRACE3D [CK97] for the given incident parameters of the LPA configuration above.

Figure 7.2-2 A focusing system for an electron beam produced by LPA consisting of three PMQs from the ejection point (EP) of the electron beam at the gas cell for LPA to the inverse Compton scattering point (CP). The blue and red curves are traces of beam envelopes simulated by TRACE3D27 for horizontal and vertical directions, respectively.

7.3 Estimation of Count Rates/Feasibility of Proposed Devices

Figure 7.3-1 Angular definitions between the laboratory system and the electron rest frame in the inverse Compton process.

Based on these counter-propagating electron beams, we evaluate the number of incident photons produced by the inverse Compton process between a linearly polarized laser pulse and an electron bunch produced by LPA. As shown in Fig.7.3-1, the angular definitions between a laboratory frame (left) and the corresponding electron rest frame (right) distinguished by asterisks can be related via Lorentz transform with , the electron velocity in the laboratory frame relative to the velocity of light. The differential cross sections per solid angle between the two frames are related as follows:

(7.3-1)

with the Lorentz factor . We then express the partially integrated cross section over the scattered photon angle with respect to the electron beam direction in the laboratory frame as follows:

(7.3-2)

where and we adopt the Klein-Nishina formula for the unpolarized photons both in the initial and final states in the electron rest frame by multiplying a factor of two in order to apply it to the linearly polarized initial state.

The number of produced -rays, , is evaluated as with where the luminosity factor for the head-on collision case is considered and is the repetition rate of crossing between laser pulses including -photons with the beam waist of and electron bunches including -electrons with focused spot sizes and for horizontal and vertical directions, respectively. This number is then used to obtain the head-on luminosity factor for scattering via the following relation

(7.3-3)

where we assume collisions take place along the electron beam axis within the effective -beam radius at IP, . As we discuss below, effectively coincides with the beam waist of the Compton seed laser, , since two CPs are located as close as possible so that is satisfied.

Given 2 x 100TW laser operated at 10 Hz, we evaluate the QED-based scattering rate reaches . However, the driving laser for LPA of 41 TW requires 3.5 J per pulse. Therefore, whether this event rate is guaranteed or not depends on the available pulse energy for the 100TW at ELI-NP which is not well-defined based on the contract only on the peak power with THALES. If this energy is not available, we are forced to put up with 1PW laser operated at 1 Hz and the rate is reduced by one order of magnitude. Even for such a case, we may be able to claim the observation of scattering by showing the event displays, if the data taking period over several months is allowed.

The most critical design parameter is the distance . Because Compton-based -rays have the typical angular divergence of 1/e, we expect that the shorter , the larger number of produced -rays resulting in a larger luminosity factor for scattering. While we need a shorter from the point of view of the scattering yield, we simultaneously have to consider electron-electron scattering after the inverse Compton scattering, since this Møller's scattering can produce background events against the elastic scattering as shown in Fig. 2 c) and d). In order to utilize as many -rays as possible for obtaining higher luminosity, the distance should be close to zero, even though Møller's scattering events cannot be eliminated. However, as far as only large angle scattering events in the range of degree are measured, the partially integrated cross section of Møller's scattering over that solid angle is suppressed to 17.7 b for the electron energy of 210 MeV, which is evaluated by the following differential cross section with respect to solid angle

(7.3-4)

where is the incident electron energy in the center-of-mass system. On the other hand, the cross section of QED scattering is relatively enhanced over the background events in the same range. Taking the larger luminosity factor for the electron-electron scattering than that of scattering into account, the event rate for Mller's scattering reaches 0.36 Hz for and the accidental rate for the two types of scattering events to occur within the same shot can be evaluated as because the two types of scattering events occur at the same synchronized timing for all shots. This contaminated event rate corresponds to 36 % of that of the QED scattering. Therefore, even if one throws such contaminated events away without the detailed offline analysis, the statistical loss of the QED events is still acceptable. In reality, the energy deposits on the detector as well as the event topologies, whether electromagnetic showers exist or not, are very different between QED scattering and Mller's scattering as shown in Fig. 2 c) and d). Therefore, one can readily distinguish two types of scattering events at the offline analysis and possibly distinguish them even within the same contaminated event, if the two clusters are sufficiently isolated from the background electromagnetic showers.

7.4 Timeline of implementation and milestones

First, above estimates totally depend on how much ideally a table-top LPA is constructed. Realization of 210 MeV electron source is the most crucial task. Secondly, although Mller's scattering events are dominant backgrounds with respect to gamma-gamma scattering, the observation itself is a landmark where a LPA-based collider is applied to a collider for elementary particle physics for the first time. Moreover, counting the number of Mller's scattering events is indispensable to directly measure the electron-electron luminosity in the actual experimental condition. This information is essentially important to deduce the luminosity in addition to the direct measurement of the -ray flux. Therefore, it is worth constructing the detector system by aming at the observation of electron-electron scattering first.

The table-top collider in Fig.7.2-1 a) can be completely stored in the interaction chamber for the sub-eV Dark Matter search after the searches at ELI-NP have been completed. By that time, we can study on how accurately we can control LPA in the preparatory experiments at CETAL for instance.

Because we need to measure the -flux and electron-flux for luminosity measurements, we will put calorimeters before the beam dump at E4. The interaction chamber and its location for the Stage 1 RA5-DM is determined so that such detectors and beam dump materials can be accommodated for this collider setup.

The timeline of RA5-GG is presented in Fig.7.4-1.

Fig.7.4-1 Timetable of RA5-GG

7.5 Estimated Budget

Figure 7.5-1 summarizes necessary experimental items and the costs for the RA5-GG proposal.

Fig.7.5-1 Table of experimental items and the costs for the RA5-GG proposal.

RA5-TDR

Stage 4

Experiments of

RA5-VBir Vacuum Birefringence (Ch.8)

8. Test of QED-Induced Birefringence (RA5-VBir)

8.1 Physics Cases

8.1.1 Propagation of Photons in Quantum Vacuum

Quantum electrodynamics admits the scattering of photons off photons, or light by light scattering (LBL). This is a purely quantum effect, see Fig. 8.1-1. Consider LBL in the parameter regime accessible at ELI: all (invariant) field strengths will be much smaller than the Sauter-Schwinger field, , and all (invariant) energy scales will be much smaller than the electron mass. In this regime electromagnetic field interactions are governed by the perturbative expansion of the Heisenberg-Euler effective Lagrangian density [Hei35, Sch50], i.e.

(8.1.1)

where α is the fine structure constant. The Euler-Lagrange equations that follow from this effective action will clearly be nonlinear, in contrast to the classical Maxwell equations. The new nonlinear terms give an effective description of the consequences of LBL.

Consider now a high energy probe, which may be individual photons or an X-ray pulse, passing through an intense field of low energy photons such as an optical laser pulse. Due to the coherence, high intensity and low energy or the optical pulse (or rather the low energy of the large number of photons in the pulse), it may be treated as a fixed external field. In this setup, the effect of LBL on the probe can be phrased as a modification of the probe’s dispersion relation. Although one can obtain this dispersion relation by solving the modified Maxwell equations following from Eq. 8.1.1, it is simpler and more natural to use an S-Matrix approach [Din14a, Din14b].

The most obvious effect of LBL is that photons scatter, i.e. change momentum [Kin12, Gie13]. However, when the probe frequency is much higher then the background frequency (here optical), the scattering becomes “eikonal” and effectively forward, so there is no momentum change [Din14a]. There are other effects of LBL that persist even when scattering is forward, in particular the helicity/polarisation state of a photon can change. It is this effect, and specifically the probability of helicity flip, that lies behind all signals of vacuum birefringence.

Fig. 8.1-1 The lowest order (in ∝) contribution to photon-photon scattering. Solid lines denote virtual fermions. Wiggly lines denote external photons.

At ELI, we propose to measure the effects of LBL on high energy (GeV) photons radiated from electrons in relativistic motion. We describe now the experimental setup, and the relevant probabilities and spectra will be calculated below.

8.1.2 Calculation of the Flip Probability

Consider the radiation emitted by electrons in highly relativistic motion, with gamma factor . The electrons emit roughly forward in a cone of half-opening angle , with a synchrotron-like spectrum [Jac98]. At ELI, such photons will interact with a 10 PW optical beam and, due to LBL, some of the highest energy photons should flip polarization state [Din14a, Din14b]. Observing the effect of these flips in the emission spectrum would be an observation of LBL. As the photons will retain their high energy throughout, the proposed method of observation in this experiment is pair polarimetry.

In order to estimate the size of observable effects, we will below consider the standard (magnetic) synchrotron radiation spectrum of relativistic electrons as an input, and then calculate the impact of LBL on this radiation as it passes through the 10PW pulse. We begin with the synchrotron spectrum itself.

The two parameters characterizing a synchrotron spectrum are electron and the critical frequency defined by

, (8.1.2)

where is the Schwinger field and is the effective strength of the field accelerating the electron. At ELI, we expect to be able to generate electrons with energy 2 GeV, so , through interaction with a laser of energy/duration 0.2J/20fs and . Using gives . Hence characterises the synchrotron spectrum.

Let be the spectral densities of synchrotron radiation polarized, respectively, parallel and perpendicular to the plane of motion of the emitting electrons. These are plotted in Fig.8.1-2, as a function of half-opening angle (out of the plane) for the characteristic parameters above and for emission of photons – note, it is only the highest energy photons which have a high probability of changing polarization state after interaction with the 10 PW beam. The bulk of the radiation at is polarized in the plane of the electron’s motion [Duk00], while there is only a small perpendicular component. It is a mixing in these components, due to LBL, that we hope to observe in an experiment. Recall that the spectrum in Fig.8.1-2 is essentially the input for our experiment. The photons will interact with a 10PW pulse before detection, and we wish to estimate the impact of LBL on the spectrum.

Fig.8.1-2 Synchrotron emission spectrum at , with , as a function of half-opening angle .

In order to isolate the signals of interest in an experiment, the radiation will be screened so that a detector can only see photons emitted within of , as measured from a predicted emission point. This increases the purity of observable radiation, as emission at low is almost entirely polarized in the plane (of the electron’s motion). This can be seen from Fig.8.1-2 and also from the “degree of linear polarization” , defined by

. (8.1.3)

At of ( here) the degree of linear polarization is , using standard formulae for the synchrotron spectral densities.

Now let be the probability for photons to switch between “‖” and “” polarisations. This probability will depend on photon energy, its trajectory through the 10 PW field, its polarization state relative to that field, and so on. Further it is not immediately obvious how to relate the probability for polarisation changes in single photons to the redistribution of spectral densities in a continuous emission spectrum. A model for how the spectrum is affected is as follows. We will write the post-interaction densities in terms of the initial densities and the probability as (supressing arguments, see below for details)

, (8.1.4-a)

. (8.1.4-b)

The first terms on the RHS describe reduction due to polarization changes, while the second terms describe gain. Note that , so no photons are lost. The degree of linear polarization, including the effects of LBL, becomes

. (8.1.5)

It remains to find an expression for the probability . This calculation and the impact on the emission spectrum are is given below.

8.2 Technical Proposal

The QED birefringence experiment requires three laser paths. The first is used to produce high energy electrons via laser wakefield acceleration (LWFA). These electrons then interact with the second laser, generating high energy photons. Finally, these photons are collided with the third, high intensity laser, and it is here that LBL can occur.

Importantly, we require the intensity of the third laser to be O(1023~W/cm2) in order to obtain an appreciable probability for polarization flip, along with excellent synchronization between all three laser paths. There are two possible methods by which this may be achieved.

The first method is to construct three paths from a single 10 PW laser. Since all paths fork out from a single source, we can obtain the required quality of synchronization. This method limits however the energy available for the LWFA stage. We can retain enough energy for LWFA by using a double-10 PW setup, but the drawback with this second method is that the precision in synchronization is O(100psec). Thus both methods have advantages and disadvantages. We therefore propose here a combination of the two setups which allows us to choose between them, depending on the situation [Fig.1.3-1 and 8.2-1].

8.2.1 LASER BEAM

Required laser pulse parameters and control:

The 10PW laser is separated in two (the double 10PW system) or three (the single 10PW system) laser paths.

Three laser beams come into the experimental chamber (the parameters in Table 8.2-1/8.2-2).

Two methods of laser beam delivery will be available (from a single 10PW laser or a double 10PW laser beams).

Polarization control is required, including the ability to switch between linear and circular polarization.

Temporal shaping and control of rising edge of the laser pulse

Spatial shaping and control of focal spot distribution.

Laser beam transport / relay to the appropriate target areas.

Fig.8.2-1 Layout of RA-VBir experiment

(a) Double 10PW system (b) Single 10PW system

Fig. 8.2-2 The paths of laser(s). (a) the double laser system using two 10PW lasers [Tab.8.2-1]: the laser for the LWFA (blue path) is independent from others (pink paths). (b) the single 10PW system [Tab.8.2-2]: all paths are forked from the origin light.

Table 8.2-1 Parameters of laser in the case of double 10 PW system

Table.8.2-2 Parameters of laser in the case of a single 10 PW beam

8.2.2 LASER BEAM DIAGONOSTICS

Intensity-temporal contrast measurement, especially on the rising edge of the laser pulse; FROG – frequency resolved optical gating diagnostic

Measurement of the laser focal spot energy distribution and the phase front

Measurement of the degree of temporal overlap (via autocorrelation) and spatial overlap of the two 10-PW foci in the target plane

Near and Far field monitoring of the laser beams

8.2.3 ELECTRON BEAM BY LWFA

Generation in the top position of chamber.

Quadrupole magnetic lens are required for electron transport and focusing the electron beam just before interactions.

Energy of the generated electron is 2.5GeV.

The synchronization with lasers are required.

Energy spectrometer

Beam profile

Charge – Faraday cup, ICT and calibrated image plates

Emittance measuring system – series of screens and focusing elements

Beam transport system

Coherent transition radiation electron bunch measuring system

Table.8.2-3 Electron beam by LWFA

8.2.5 DETECTORS

High resolution dispersion calorimeter required for hundred MeV-GeV electrons

Energy measurements of γ-ray () .

Polarization measurements of γ-ray () .

8.2.6 Lab-Space and target chamber requirements

Laser separation modules in E6 and E7 with flat/focusing mirrors. Especially, the unit in E6 can make a switch of the options of the single/double 10 PW(s) system.

The target chamber should be lined with aluminum to reduce activation

For Observing the polarization flip, we need to prepare the long path for emitted photons from electrons. We want to extend this path the end of below in E7 hall, nearly 15m length from the radiation generated point (the focusing point of the second laser path).

8.3 Estimation of Count Rates/Feasibility of Proposed Devices

8.3.1 Estimation of the flip probability

We describe the 10PW optical laser as a Gaussian beam in the paraxial approximation, with Gaussian temporal envelope. For energy ε and FHWM duration we have the relation [Din14a]

, (8.3.1)

in which is the focal spot radius, a free parameter which describes the focusing. We take the energy to be and the pulse duration to be . A high (much greater than optical) energy photon passing through this 10PW field will not scatter, but may change polarisation state with a certain probability. In the ideal case of a photon of frequency meeting the 10PW in a head-on collision, and with polarisation angle at degrees to that of the 10PW, the probability for the photon to change polarisation state is [Din14a],

, (8.3.2)

which can be derived from an S-matrix calculation using the first-order Heisenberg-Euler effective Lagrangian in (8.1.1). This best possible case gives the highest probability. For the parameters above and taking for the spot radius of the 10PW, we have

. (8.3.3)

For GeV energy photons in idealised collisions, there is therefore a roughly 1 in 3 chance of LBL causing a polarisation change to occur. Any real experimental setup will be less than ideal and so we must now estimate the impact of experimental factors on the probability, before we can calculate the impact of LBL on a synchrotron emission spectrum.

We choose coordinates such that the 10 PW beam travels up the z–axis and reaches maximum intensity at . We assume a separation of 20cm between this focal spot and emission point of the high-energy photons that act as the probe. This separation is orders of magnitude larger than the spot size of the 10PW. This implies that, even though the typical half-opening-angle in synchrotron emission goes like , the emitted radiation will have dispersed over a wide area relative to the focal spot size by the time it reaches the interaction volume of the 10PW. (See Fig.8.3-4 in Sect. 8.3.4.) Consequently, few of the emitted photons will interact at all with the 10 PW. Again taking for the focal radius of the 10 PW, the only emission of relevance must be contained in a cone of angle where

(8.3.4)

We will confirm this below. The flip probability is then maximal for photons travelling in the -direction, emitted at the correct instant such that they cover the 20 cm separation in time to arrive at at . In this setup, the 10 PW should be linearly polarized at in the x – y plane.

Fig.8.3-1 The flip probability as a function of half-opening angle . Parameters as in the text. Doubling the beam waist () reduces the peak probability by a factor of 16. Vertical black lines mark for the two chosen beam waists, with that for leftmost.

Photons emitted from any other point at any other time, with any other polarisation, will of course have a reduced flip probability, and we must account for this. We expect the probability to fall off exponentially with practically any variable, since the 10 PW profile falls like a Gaussian in both space and time. We find, with the details given in Sect. 8.3.4, that of all the variables that influence the flip probability, the most important is the opening angle . The dependence of the probability on this variable is

. (8.3.5)

This probability is shown in Fig.8.3-2 for waist sizes of and . The probability is restricted to angles much smaller than the typical spread of the synchrotron emission; is marked in the figure. We see that increasing the spot radius by a factor of 2 gives a much broader signal. However, widening the beam at fixed energy and duration implies a loss in intensity and peak field strength. Consequently the peak amplitude is reduced by a factor of 16, consistent with Eq.(8.3.2). A tight focus is therefore required for an appreciable LBL signal.

8.3.2 Impact of LBL on the emission spectrum.

Combining the probability Eq.(8.3.5) with the model (8.1.4), we find that spectral densities of the synchrotron radiation in Fig.8.1-3 are replaced by those in Fig.8.3-2, in which we can see large LBL effects (max ) confined to a very small half-opening angle less than (as can be verified numerically) of .

The degree of linear polarisation is shown in Fig.8.3-3. For small angles there is a reduction in the degree of linear (plane) polarization due to LBL, which causes a proportion of the plane-polarized photons present to become transversely polarized.

Fig.8.3-2 Synchrotron emission spectrum as Fig.8.1-3, but including the effects of LBL. These are confined to a small opening angle , as expected. Parameters as in the text.

To calculate the total energy,, emitted onto a detector we integrate over all emitted photon frequencies and over all angles [Jac98, Duk00],

. (8.3.10)

We find, numerically,

, (8.3.11-a)

. (8.3.11-b)

We have therefore an increase of 20% in the amount of transversely polarized radiation. There is, percentage-wise, effectively no change in the amount of plane-polarized radiation reaching the detector.

Fig.8.3-3 Degree of linear polarization with and without light-by-light scattering effects, at . Typical scales shown: is the typical synchrotron angle, 40% of is the restriction to be imposed in experiment, and of is the scale below which LBL effects appear.

8.3.3 Calculational details

Fig. 8.3-4 illustrates the separation of the emission and interaction points in the experiments as well as the scales involved. We now go over some factors which influence the probability of LBL. As illustrated in Fig.8.1-2, and photons are emitted in a small cone around the z–direction, such that (assuming again a standard synchrotron spectrum) emission in the plane is entirely polarized in that plane. From the emission point, the photons travel (roughly) in the negative z-direction, with half-opening angle and momentum

Fig. 8.3-4 Despite the small half-opening-angle , the spread of the emitted radiation is still much larger than the beam waist of 10 the PW, due to the relatively large distance between emission and interaction points.

Fig.8.3-5 Photons are emitted in a small cone around the direction, from electrons moving in the plane. is the half-opening angle in the spectrum. is the azimuthal angle around the (primary) beam direction.

. (8.1.11)

We consider incoming photons with polarization in the plane, i.e. , and . We then calculate the probability for these photons to flip to the orthogonal state defined by the conditions and . This is then averaged over the azimuthal angle (as this angle does not appear in the synchrotron spectra). Hence we define, writing down only angular dependencies, the probability entering the outgoing spectral densitiesas

, (8.1.12)

where is the probability of polarisation flip for the stated angles and polarisation vectors. This is an approximation. However, subtleties in how to choose the polarization directions, the dependence on azimuthal , etc., are all rendered irrelevant by the smallness of the typical opening angle . (In fact we know that only photons emitted into a much smaller half-opening angle have a chance of flipping polarization state.) Practically, this means that all dependencies except for that on are negligible. The dependence on for example is extremely weak, and so instead of averaging as in Eq.(8.1.12) one can, numerically, simply set the average equal to the integrand at . Further, we can take and (which is natural for photons travelling directly down the z–axis) greatly simplifying the relevant formulae, without making any significant difference to the numerical results.

8.4 Timeline of implementation and milestones

The timelines in RA5-VBir is shown in Fig.8.4-1.

Fig.8.4-1 Timeline of RA5-VBir in Stage 4

8.5 Estimated Budget

Fig.8.5.1 Table of experimental items and the costs for the RA5-VBir proposal

9. Specific Needs and Utilities, Transversal Needs

9.1 Requirements regarding the laser beams

Possibility to compensate for a 8m difference in the optical path between the twin 100TW/1PW outputs, before entering experimental area E4;

Availability of 1PW laser beam at 1Hz repetition rate in the E7 experimental area, transported through any of the 10PW beamline pipes;

Variation of laser pulse energy, for all laser outputs (in E7 and E4);

Possibility to de-tune the 100TW and 1PW compressors in order to obtain longer pulses, up to a few hundreds fs;

Availability of a trigger signal with 10-100ms before the laser pulse, for all outputs/experimental areas;

Possibility to define pulse sequence for all outputs/experimental areas;

Adaptive optics elements for field correction and for variable focal number at 1PW and 100TW.

9.2 General requirements

According to the general lines followed in the ELI-NP buildings design, the maximum versatility of the electrical power, liquid nitrogen and compressed air supplies could only be achieved by letting the last (user-end) part of these networks to be built by each experimental area. That is, in the case of each utility type:

Electrical power: a connection point of a certain maximum power rating, three-phased, is defined at the exterior of each experimental room. At this point, a distribution panel must be fitted, constructed according to the requirements of the experiments TDRs. Then, according to the same, the distribution inside the experimental areas must be designed and built. For the E7 experimental area the maximum power rating is 50 KW.

Liquid nitrogen: a connection point will be available beneath each experimental hall, in the basement (under the stabilization concrete plate).

Compressed air: connection points will be defined in the basement of the building, being the experiments’ responsibility the distribution network for each experiment;

Cooling water: two heat exchangers for closed-circuit water cooling will be available in two locations, in the basement of the building, under the laser system and the electron accelerator areas. The connection to these and the following network to the, and inside, the experimental hall is in the responsibility of the TDR workgroups.

The characteristics of electrical power of high stability are still subject of discussions between the TDR workgroups and the ELI-NP engineering and building teams. There will be available in the ELI-NP experimental building two separate networks, one for heavy duty and the second devoted to sensitive detection systems and electronics. The two networks will have as an electrical ground a mesh of copper bars connected to the steel bars in the stabilized concrete plate (which are welded together), that is then linked to the earth connections foreseen around the building. This “mesh-type” approach will provide a solid base for the achievement of a reliable ground connection.

The infrastructure will feature an electrical generator that shall be started in case of blackout, while each experiment shall foresee adequate UPS capacity to hold until the operation in full of the generator and/or until safe shutdown of all equipment.

Floor space requirements and positioning

In order to perform combined experiments, with HPLS 10PW pulses and GBS gamma/electron bunches, the experiments will need a way of correlating the experimental data with the parameters of the beams themselves, which are measured by the large equipment or by additional setups. For this, an unique way of identifying the parameters of the pulses, or other parameters in the large machines that are important for the experiment is necessary.

10. Safety Requirements

Radioprotection and protection from Electromagnetic Pulse (EMP) are two very important areas for a high power laser infrastructure.

10.1 Protection from EMP

Special provisions were taken to limit and efficiently damp the propagation of EMP out of the interaction chambers and outside the experimental areas. A report regarding EMP protection was contracted by ELI-NP in the early stages of the project, leading to the implementation in the construction of several elements for this purpose (see for example Fig. 11.1-1 for the protection of the doors of the experimental areas and Fig. 11.1-2 for the protection of the beamline tubes).

Figure 10.1-1 EMP protection for the doors of the experimental areas

Figure 10.1-2 EMP protection for a 10PW beamline tube.

Further provisions regarding EMP mitigation will be taken during the design of the interaction chambers and then at the beginning of operation (local protection provisions). However, because all RA5 experiments (at E4 and E7) propose the use of gas target or no target at all, the EMP-related issues shall be less stringent than for solid-target experiments.

10.2 Radiation Safety

Several source terms for ionizing radiation are present in the experimental area E7:

Electrons from the linear accelerator of the ELI-NP GBS, with maximum energy of 720MeV and flux of 2×1010 s-1 (one macro-bunch, that is 32 microbunches of 2ps separated by 16ns, each second) (Figure 11.2-1);

Laser-accelerated electrons at low energies: 20-100MeV: 1Hz or 1/minute repetition rate for a total of 6×1010 electrons/s, 1% energy spread (Figure 11.2-2);

Laser-accelerated electrons at high energies: 2.5-5GeV: 108 electrons/s (Figure 11.2-3);

Gamma photons from GBS, energies up to 19.5MeV, 1013 photons/s.

In the E4 experimental area, there is a source term due to accelerated electrons, up to energies of a few hundred MeV, and in any case less then 500MeV (used as an upper limit in the calculations). In E4 there is already foreseen a massive, complex structure beam dump, designed also for heavy ions acceleration with the lasers. Apart from that one, a second beam dump will be necessary for the gamma-gamma collider experiments, for the accelerated electrons. The beamdump from E7 for the 720MeV electrons can be used for this purpose (moved to E4 at the appropriate time, which is feasible considering the phasing of the experiments).

For these, beamdumps were devised in order to obey the limitations imposed by design to ELI-NP regarding the remanent doses and the dose rates at the cold sides of the walls of experimental areas. Numerical simulations using the MCNP and FLUKA codes have been performed and dose rate maps were produced for all experimental areas.

Figure 10.2-1 Total dose rate contours (µSv/hr) from the 720MeV electron source in E7

Figure 10.2-2 Total dose rate contours from the 100MeV electron source in E7. Calculation performed with a simple iron beam dump of 90cm diameter and 75cm length.

Figure 10.2-3 Total dose rate contours (µSv/hr) from the 5GeV electron source in E7

Two beamdumps are envisaged for the use during the experiments to be performed at E7. Their characteristics, resulting from calculations and simulations, are the following:

Core of lead 40 cm diameter and 40 cm length surrounded by a layer of 20 cm concrete on all sides. A hole at the entrance of the beam dump has diameter 1 cm and length 15 cm. For the 720 MeV and 100MeV electrons (may also be used in the RA5-GG experiments in E4);

Concrete (L=50cm) and lead (50cm), 50cm diameter and entrance penetration of 30cm (see Figure 10.2-3) for the GeV electrons.

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12. Appendices

12.1 Appendix A: Evaluation of the signal yield

Given the formulae in Refs.[Fuj11, Hom12a, Hom12p] and the correction suggested by [Ber13], we re-evaluate the signal yield with a more direct formulation than that based on the concept of cross section. The cross section is naturally applied to a beam flux normal to a target or the extension to head-on particle colliders where all beams are on the same axis. In QPS, however, this view point is not necessarily convenient due to the wide distribution of tilted incident fluxes. In such a case, we can adopt the more convenient formulation [Bjo64], which is useful, for instance, to evaluate the number of interactions in plasma where the concept of a beam flux to a target is no longer clear. With the notations in Fig.2 and the Lorentz invariant phase space factor

, (App.A.1)

the signal yield can be formulated as [Bjo64]

(App.A.2)

where is the Lorentz invariant transition amplitude as a function of incident angle with the normalized statistical weight due to the uncertainty of the incident angle, is time-integrated density and is the interaction volume per unit time. We note the dimensions explicitly with time s and length in [ ] of Eq.(App.A.2). On the other hand, it may be possible to factorize the yield based on the concept of time-integrated luminosity cross section as follows

(App.A.3)

where corresponds to the relative velocity of incoming particle beams for a given based

on the Møller’s Lorentz invariant factor [Moe46]. The relative velocity is defined as [Fur03]

, (App.A.4)

with the notation in Fig.2.1-2. If is a mere number, which is the normal case for collisions with two independent beams with a fixed relative velocity, this factorization is robust. In the case of the photon QPS, however, the concept of relative velocity between a pair of incident photons could be ambiguous due to spreads of single photon wave functions near the waist, while the squared scattering amplitude itself has to be averaged over a possible range on due to that unavoidable uncertainty. In order to recourse to the concept of a cross section, however, we need to choose a proper relative velocity value to convert a squared scattering amplitude into a cross section. We then face difficulty in uniquely determining a K-factor with respect to the averaged squared scattering amplitude over a range of in QPS. The formulation in Eq.(App.A.2) without recourse to the concept of a cross section, on the other hand, ambiguity originating from choices of a proper K-factor is all avoidable. Therefore, we re-formulate the signal yield based on Eq.(App.A.2) as follows. We first express the squared scattering amplitude for the case when a low-mass field is exchanged in the s-channel via a resonance state with the symbol to describe polarization combinations of initial and final states .

, (App.A.5)

where with the resonance condition for a given mass and is expressed as

(App.A.6)

with the resonance decay rate of the low-mass field

. (App.A.7)

The resonance condition is satisfied when the center-of-mass system (CMS) energy between incident two photons coincides with the given mass m. At a focused geometry of an incident laser beam, however, ECMS cannot be uniquely specified due to the momentum uncertainty of incident waves. Although the incident laser energy has the intrinsic uncertainty, the momentum uncertainty or the angular uncertainty between a pair of incident photons dominates that of the incident energy. Therefore, we consider the case where only angles of incidence ϑ between randomly chosen pairs of photons are uncertain within for a given focusing parameter by fixing the incident energy. The treatment for the intrinsic energy uncertainty is explained in Appendix B later. We fix the laser energy ω at the optical wavelength

(App.A.8)

while the resonance condition depends on the incident angle uncertainty. This gives the expression for as a function of

, (App.A.9)

Where

(App.A.10)

We thus introduce the averaging process for the squared amplitude over the possible uncertainty on incident angles

(App.A.11)

Where specified with a set of physical parameters m and is expressed as a function of , and is the probability distribution function as a function of the uncertainty on within an incident pulse. We review the expression for the electric field of the Gaussian laser propagating along the z-direction in spatial coordinates [Yar97] as follows:

(App.A.12)

where electric field amplitude, , , is the minimum waist, which cannot be smaller than λ due to the diffraction limit, and other definitions are as follows:

, (App.A.13)

(App.A.14)

(App.A.15)

(App.A.16)

With being an incident angle of a single photon in the Gaussian beam, the angular distribution can be approximated as

(App.A.17)

where the incident angle uncertainty in the Gaussian beam is introduced within the physical range as

(App.A.18)

with the wavelength of the creation laser , the beam diameter , the focal length , and

the beam waist as illustrated in Fig.2.1-1. For a pair of photons 1, 2 each of which follows , the incident angle between them is defined as

(App.A.19)

With the variance , the pair angular distribution is then approximated as

(App.A.20)

where the coefficient 2 of the amplitude is caused by limiting to the range , and is taken into account because in Eq.(App.A.18) also corresponds to the upper limit by the focusing lens based on geometric optics. This distribution is consistent with the flat top distribution applied to Ref.[Hom12a, Hom12p] except the coefficient.

We now re-express the average of the squared scattering amplitude as a function of in units of the width of the Breit-Wigner (BW) distribution a by substituting Eq.(App.A.5) and (App.A.20) into Eq.(App.A.11) with Eq.(App.A.10)

, (App.A.21)

where we introduce the following constant

(App.A.22)

with

. (App.A.23)

In Eq.(App.A.22) the weight function is the positive and monotonic function within the integral range and the second term is the Breit-Wigner (BW) function with the width of unity. Note that is now explicitly proportional to a but not . This gives the enhancement factor compared to the case where no resonance state is contained in the integral range controlled by experimentally. The integrated value of the pure BW function from to gives , while that from to gives . The difference is only a factor of two. The weight function of the kernel is almost unity for small , that is, when a is small enough with a small mass and a weak coupling. For instance, in the coupling-mass range covered by Fig.11, and gives , while and gives . In such cases the integrated value of Eq.(App.A.22) is close to that of BW, because the weight function is close to unity and also the upper limit of the integral range in Eq.(43) is large for by the dependence. In the Ref.[Hom12p], we thus approximate as for the conservative estimate.

Let us remind of the partially integrated cross section over the solid angle of the signal photon which corresponds to Eq.(11) in Ref.[Hom12p]. The expression before taking the average over , hence as a function of , is as follows

(App.A.24)

We then convert the interaction cross section into the interaction volume per unit time by simply multiplying the relative velocity

(App.A.25)

where the creation laser wavelength , ith approximations and , and and are restored to confirm the dimension explicitly. The averaged value over is then expressed as

. (App.A.26)

where Eq.(App.A.21) and a in Eq.(App.A.6) are substituted in the second and third lines, respectively, and via Eq.(App.A.8) is identified for the last line.

We now consider the time-integrated density factor in Eq.(App.A.2) applicable to free propagation of the Gaussian laser beam for creation as illustrated in Fig.2.1-1. We first parameterize

the density profile of an incident Gaussian laser beam being the focal point at with the pulse duration time propagating over the focal length f along z-axis as [Rei84]

, (App.A.27)

where the central position of the creation pulse in z coordinate is traced by the relation as a function of time while the pulse duration along -direction is expressed with the local coordinate , hence, , and is the average number of creation photons per pulse. Using the squared expression

(App.A.28)

based on Eq.(App.A.2), is then expressed as

(App.A.29)

where the time integration is performed during the pulse propagation from to , because the photon-photon scattering never take place when two photons in a pair are apart

from each other at .

We now evaluate the effect of the inducing laser beam. The inducing effect is expected only when as a result of scattering coincides with a photon momentum included in the coherent state of the inducing beam. In order to characterize from the interaction, we first summarize the kinematic relations specified in Fig.2.1-2. Although the CMS-energy varies depending on the incident angle , the interaction rate is dominated at the CMS-energy satisfying the resonance condition via the Breit-Wigner weighting. Therefore, is essentially expressed with the condition in Eq.(7). With , we obtain following relations

and (App.A.30)

These relations imply that the spontaneous interaction causes ring-like patterns of emitted photons with cone angles and commonly constrained by , because the way to take a reaction plane determined by is symmetric around the -axis.

We then evaluate how much fraction of photon momenta in the inducing beam overlaps with the , in other words, the acceptance factor applied to the ideal Gaussian laser beam, which was discussed within the plane wave approximation in [Hom12p]. In the beam waist at , the angular spectrum representation gives the following electric field distribution as a function of wave vector components and on the transverse plane based on Fourier transform of [Nov12]

(App.A.31)

where the transverse wave vector component is introduced. With the paraxial approximation , we can derive exactly the same expression for in Eq.(App.A.12) starting from this representation [Nov12]. We apply Eq.(App.A.31) to the inducing beam represented by the subscript 4 with using the first in Eq.(App.A.30) and . For a range from to by denoting the underline and overline as the lower and upper values on the corresponding variables, the acceptance factor is estimated as

(App.A.32)

where the approximation in the first line is based on , is substituted in the second line, and with due to the common focusing geometry d and f to those of the creation beam is substituted in the third line by defining . We note that Eq.(App.A.32) now has the quadratic dependence on while the corresponding acceptance factor in [Hom12p] was proportional to due to the plane wave approximation.

Because of the common optical element sharing the same optical axis, in advance, the spatial overlap between creation and inducing lasers is satisfied in QPS. In actual experiments, however, it is likely that the time durations between the two laser pulses are prepared as for inducing and creation beams, respectively, because shortness of is more important to enhances via the quadratic nature on the pulse energy. Therefore, we further introduce a factor representing the spacetime overlap by assuming the pulse peaks in spacetime coincide with each other. Hence, the entire inducing effect is expressed as

. (App.A.33)

Therefore, the overall density factor including the laser effect is expressed as

(App.A.34)

where corresponds to the combinatorial factor originating from the choice of a frequency among the frequency multimode states in creation and inducing lasers as discussed in Ref.[Hom12p].

Based on Eq.(App.A.2) with Eqs.(App.A.26) and (App.A.34), the re-evaluated signal yield is finally expressed as

(App.A.35)

where the parameters specified with [eV] apply natural units. We note that the re-evaluated signal yield depends on compared to the m2 dependence in Ref.[Hom12p]. The additional dependence is caused by multiplying -factor in Eq. (App.A.25) and the dependence is further added by Eq.(App.A.32) due to the ring-image acceptance for the inducing effect. The sensitivity to lower mass domains thus diminishes.

12.2 Appendix B: The effect of finite spectrum widths of creation and inducing laser beams

When creation and inducing lasers have finite spectrum widths, the effect has impacts on the interaction rate of four-wave mixing as well as the spectrum width of the signal via energy-momentum conservation within the unavoidable uncertainty of photon momenta and energies in QPS. We have considered the effect of the finite line width of the inducing laser field by assuming the line width of the creation laser is negligibly small [Hom12p]. In such a case, the energy uncertainties in the process of four-wave mixing with the convention used in Fig.2.1-2 are described as

, and , and (App.B.1)

for the creation laser, the inducing laser, and the signal, respectively, where denotes average of each spectrum, expresses the intrinsic line width caused by the energy uncertainty in the atomic process to produce the inducing laser beam, and arises due to the energy conservation [Hom12p].

In this case and in Eq.(App.A.35) via Eq.(3) solely originates from the intrinsic line width of the inducing laser field. However, this approximation is not valid for the case where the line width of the creation laser is equal to or wider than that of the inducing laser. We now provide the prescription for the following general case:

, and , and (App.B.2)

where the intrinsic line width of the creation laser is explicitly included. In this case, at a glance, Eq.(2) must be modified so that a finite net transverse momentum along the -axis in Fig.2.1-2 is introduced by the different incident photon energies and with corresponding incident angles and , respectively. These notations are for a nominal laboratory frame defined by a pair of asymmetric incident photons, referred to as -system. Here nominal implies that we cannot specify individual photon’s incident wavelength as well as incident angle physically, that is, what we know a priori is only the ranges of uncertainties on possible wavelengths and incident angles. Exactly speaking, all the calculations so far are based on the equal incident energy with the equal incident angle in the averaged laboratory frame, referred to as -system as illustrated in Fig.2.1-2, where the transverse momentum of the incident colliding system is zero on the average. We regard the effect of these nominally possible -systems as fluctuations around the averaged -system. We, therefore, attempt to transform -systems into a -system so that is effectively invisible as follows

, and , and , (App.B.3)

where in Eq.(App.B.2) is absorbed into the effective line widths of the final state photon energies in the -system resulting in denoting as the effective width in the -system and accordingly arises via energy-momentum conservation in that system.

As long as a resonance state with a finite mass is formed, a range in Fig.2.1-1 eventually contains the resonance angle which satisfies the condition that the center-of-mass system energy coincides with the mass m in the -system, and any nominal -systems which satisfy the resonance condition can be generally formed by a transverse Lorentz boost of the -system with the relative velocity with respect to the velocity of light . Assigning the positive direction of to the positive direction of -axis in Fig.2.1-2, the energy and the transverse momentum relations between a -system and the -system are connected via [Ber12k]

,

(App.B.4)

with , where the subscripts 1 and 2 correspond to the photon indices in Fig.2.1-2, respectively. Since the relations of the energy components in Eq.(App.B.4) indicate that experiences frequency-down shift, while does frequency-up shift, we introduce another definitions of energy components of and after the transverse boost by

(App.B.5)

where a relative line width with respect to the mean energy of the creation laser is implemented. We note the following physical and experimental conditions:

and (App.B.6)

respectively. For convenience, we tentatively distinguish for by the subscripts in the following discussion.

As for , from the first of Eq.(App.B.5) with , we obtain the following equation

(App.B.7)

With the solutions by assuming

, (App.B.8)

where

. (App.B.9)

Requiring gives a physical constraint

. (App.B.10)

If this is satisfied, with gives

(App.B.11)

The double-sign symbol in Eq. (App.B.8) gives following two solutions:

,

, (App.B.12)

where only is physically acceptable, while is not, because the limit of must correspond to in our discussion.

Let us move on to discuss . From the second of Eq. (App.B.5) with , we get

(App.B.13)

with the solutions by assuming

(App.B.14)

where

. (App.B.15)

The approximation with gives

. (App.B.16)

The double-sign symbol in Eq.(70) gives following two solutions:

,

, (App.B.17)

where only is physically acceptable, while is not due to the same reason as in addition to the positivity condition.

A common is eventually determined as

(App.B.18)

Based on Eqs.(App.B.12) and (App.B.17). By substituting in Eq.(App.B.18) into Eq.(App.B.10), the range of is expressed as

. (App.B.19)

Among within , is effectively enhanced based on the Breit-Wigner distribution in the averaging process of the square of the invariant scattering amplitude around [Hom12a]. Therefore, for a given mass with , the effective physical limit on is expressed as

. (App.B.20)

On the other hand, an instrumental full line width of a creation laser is given by the creation laser intrinsically. Therefore, the range of can be maximally covered by

(App.B.21)

based on the relation in Eq.(App.B.18). If is smaller than , however, the instrumental condition limits to before reaching the physical limit for a given mass parameter. Therefore, we are required to choose smaller , either or , depending on the relation between an experimentally given line width of the creation laser and a given mass parameter we search for.

Given a possible range of based on the relation between an intrinsic line width of the creation laser and a given mass m, we can construct a unique -system by inversely boosting individual -systems, where the intrinsic line width is effectively broaden. This is because a spectrum width is effectively embedded by the possible range of inverse boosts for a chosen among in individual -systems. Therefore, combining the inverse-boost-originating spectrum width with the intrinsic line width of the inducing laser provides the effective inclusive range of defined in Eq.(3) in the -system.

We first evaluate how much the common inverse boost originating from the line width of the creation laser solely changes the range of from to in the -system for a within the line width of the inducing laser field. By inversely applying the boost in Eq.(20) to in Fig.2.1-2, we can express the upper and lower edges of the broadened energy range of with the approximation , respectively,

(App.B.22)

where represents the process to choose a within the relative line width with being the average value , subscripts and in the right-hand side denote the cases where and are used, respectively, and requires to choose smaller one between and .

We then discuss the inclusive range of by combining the broadened in the -system with the intrinsic line width of the inducing laser. We introduce a notation reflecting the combining process in the -system

(App.B.23)

where with being the average value , is a coefficient describing the uncertainty by the inverse transverse boost discussed above. Since the intrinsic energy uncertainties of creation and inducing laser beams are independent, the quadratic error propagation gives the following inclusive uncertainty on in the -system

. (App.B.24)

Finally this gives the inclusive uncertainty on

, (App.B.25)

and the upper and lower limits on , which replace the limits in Eq.(10) with

and (App.B.26)

respectively, are obtained.

As a summary based on Eq.(App.B.22), the effect of the line width of the creation laser is less significant compared to that of the inducing laser for a smaller mass range, while it has some impact for a larger mass range, as long as the line width is comparable to or larger than that of the inducing laser.

12.3 Appendix C: Thomson backscattering in the extended lambda cubed regime for extension of the available gamma energy above 100MeV range

Collaboration presenting the Letter of Intent

Authors: Daniel Ursescu (spokesperson), Laura Ionel, and the experimental team of the Solid State Lasers Laboratory at National Institute for Lasers Plasma and Radiation Physics, INFLPR, Romania

Madalina Boca, Viorica Florescu, University of Bucharest, Romania

Dino Jaroszynski and the team, University of Strathclyde, UK

Scientific case

Understanding the behavior of the matter in electric and magnetic fields remains a central point of interest in science. Extreme electric fields up to the 1016V /cm exist in the vicinity of multiple ionized heavy nuclei, but in tiny volumes, less than cubic Angstrom [1]. Complementary, strong fields at the micrometer scale can be produced using lasers. Since ’60es, the laser produced fields strength registered an exponential increase, based on three directions of development, namely, the reduction of the pulse duration, of the focal spot area and the increase of the pulse energy.

Combining the spatial and temporal approaches, the planned Extreme Light Infrastructure facility [3] will break into the ultra-relativistic regime and beyond, in generation of particles from the vacuum (polarization and boiling of the vacuum experiments). For such experiments, huge electric fields have to be created using tightly focused ultrashort laser pulses (TFP), i. e. in λ3 regime. The effects expected in such experiments depend on the spatial and temporal extension of the huge electric fields generated by TFPs.

Example of calculations for the EM field distribution for a laser with a 800 nm central wavelength using different f# optics are presented in the figure below, for pulse durations of 2.5, 11.8 and 59 periods. It is clear that both spatial and temporal extent of the pulses can play a major role in the way the scattered photons are generated.

Although there are now simple codes to predict the scattering field emitted in the Thomson scattering process, they are typically obtained using the monochromatic plane wave approximation (see Alexandru Popa, Phys. Rev. A 2011 and the code there attached [4]).

This is no longer the case for TFPs. To show this, we represent in the figure 2 the amplitude of the electron oscillation in an infinite plane wave aw, to be compared with the waist w0 of the beam obtained with TFP. At the crossing of the lines, the electron oscillation amplitude and the waist become equal and the approximation no longer holds.

Also, if the normalized vector potential a is of the order of 100, the radiation reaction effects (ignored in most of the existent theoretical predictions) start to play a significant role. As a consequence, tuning the normalized vector potential up to values of the order 100 and measuring e.g. angular distribution and emission spectrum from electrons in such fields will help to understand these radiation reaction effects.

Figure 1: The electromagnetic field distribution in the focal region for different pulse durations (expressed in periods of the field T) and for different f# focusing optics, specified on each frame

However, the theoretical modeling using infinite plane wave approximation predicts that the scattered signal contains also harmonics of the fundamental incoming field. As an example, we illustrate in figure 3, the computed harmonics intensities of the scattered field, for a normalized vector potential of a=65.9 . This implies the presence of gamma radiation with significantly higher energy than the backscattered fundamental radiation. For the 4g2 energy boost factor for the photon energy in the backscattering process, we obtain photons with energies of 4jg2hn , while we have to take into account also the order of the harmonics j (h is the Plank constant and n is the laser frequency in the lab frame). This corresponds to energies of 240MeV for j=20 at 800nm for a 10PW laser system interacting with 700MeV electrons. However, within this model, photon energies in excess of 1 GeV are predicted (e.g. at j=100, see fig. 3).

Figure 2: The dependence of the Gaussian beam waist (w0) and of the electron excursion amplitude (aω ) of the obtained peak intensity

Figure 3: The spectrum of the normalized total scattered radiation for a=65.9. (Ij is the intensity of the jth harmonic radiation).

This implies a significant possible extension of the gamma radiation spectrum production at ELI-NP, as requested in other experimental proposals at ELI-NP, related to light assisted electron-positron pair creation.

Methodology

Further theoretical computation and modeling of the process has to be performed, under coordination of the group at the University of Bucharest authoring the present proposal.

The experimental testing of the theory and its limitations can be performed at different levels, in different experimental areas at ELI-NP.

For the experiment to take place, one needs a beam of quasi-monoenergetic electrons, such as the ones from the gamma beam facility, or a bunch of laser accelerated electrons. Both approaches have advantages and disadvantages, so several experimental campaigns are proposed:

at E7 experimental areas, using the electron beam from the gamma beam and laser power up to 10 PW. The main problem here is the limited spot size of the beam and the expected low electron bunch density. The electron beam should be focused as tight as possible. For the laser beam low f# optics should be used.

At an experimental area where we can get two laser beams, one to generate a very dense bunch of laser-accelerated electrons and one to provide the counter-propagating EM field to be scattered. In this case the electron bunch is less monochromatic but it can be significantly more dense and energetic than the one provided by the gamma beam facility.

Electron bunch synchronization with the laser pulse should be realized with a resolution several times below the electron bunch duration.

Alignment procedure should allow the focus positioning for both laser focus and electron beam focus with micrometer accuracy.

The experiments have to be produced in vacuum, at least 10-5 mbar residual pressure.

The detection should be adequate for a broad range of gamma radiation detection, up to the 1 GeV range. Further detection of accelerated electrons up to the 2GeV range would also improve the quality of the results.

Laser produced electron bunches have to be investigated separately, previously and they have their own specific alignment and diagnosis requests.

Bibliography:

[1] D. F. A. Winters, T. Stoehlker, Atomic physics atstorage rings: Recent results from the esr and future perspectives at fair, International Journal of Modern Physics E 18 (2009) 359.

[2] G. R. Hays, E. W. Gaul, M. D. Martinez, T. Ditmire, Broad-spectrum neodymium-doped laser glasses for high-energy chirped-pulse amplification, Applied Optics 46 (2007) 4813–4819.

[3] ELI scientific case: Extreme light infrastructure, http://www.extreme-light-infrastructure.eu/ELI-scientific-case 2 4.php,

[4] A. Popa, Periodicity property of relativistic Thomson scattering with application to exact calculations of angular and spectral distributions of the scattered field, Phys. Rev. A 84, 023824 (2011)

12.4 Appendix D: Compton backscattering using x-ray lasers for the extension of the available monochromatic gamma energy in the 400MeV range

Collaboration presenting the LoI

Authors: Daniel Ursescu (spokesperson), Romeo Banici, Razvan Ungureanu, Gabriel Cojocaru, and the experimental team of the Solid State Lasers Laboratory at National Institute for Lasers Plasma and Radiation Physics, INFLPR, Romania

Scientific case

The planned Extreme Light Infrastructure facility will break into the ultra-relativistic regime and beyond, in generation of particles from the vacuum (polarization and boiling of the vacuum experiments). Such experiments request, as the ELI-NP White Book shows, photons in the energy range of few hundreds of MeV. Compton backscattering (CBS) with laser pulses in the visible range would request energies for the electrons at significantly higher energies than the value of 700MeV planned for ELI-NP. Alternative path for getting gamma rays in the few hundreds of MeV is to get shorter wavelength pulses. Such coherent, short wavelength, and brilliant sources exist in several versions, the most brilliant one being the plasma x-ray laser (XRL). Such lasers deliver energies up to mJ range in the quasi-steady state operation mode and up to 0.01 mJ in the transient collisional excitation (TCE) scheme. A CBS experiment with the electron bunches provided at ELI-NP needs pulses that have durations similar to the electron bunch duration, namely in the few ps regime. This selects TCE XRL as the source of choice for the CBS experiments at ELI-NP.

CBS XRL source scales the gamma energy inversely proportional with the wavelength of the driver XRL laser. As a consequence, with wavelength in the range of 20nm for the XRL, gamma energies 400MeV are in reach. One major advantage of this approach in gamma generation is the fact that the relative bandwidth of the gamma beam can stay very narrow, below 10-2 as the XRL have a very narrow emission line of the order of 10-4.

An alternative approach for production of gamma rays in the hundreds of megaelectronvolt range using the multi-PW laser system and a laser accelerated electron bunch is described in a parallel proposal. One major difference, beside the one related to the mono-chromaticity of the resulting gamma photons, is that here we are placed in a region where the electron rest mass is comparable with the energy of the incoming photon in the reference frame of the electron, due to the Doppler shift. Hence, we reach beyond the Thomson backscattering approximation, in the Compton regime.

The plasma X-Ray Laser to be used as the incoming photons source had an outstanding development during the last 30 years. The active medium of XRL is a plasma where population inversion occurs between specific ionic levels, such as 4d-4p transition in Ni-like ions or 3d-3p transition in Ne-like ions. Laser pulses are used to prepare the plasma. The pumping energy in the first experiments was in the order of 10kJ. Subsequently, with the introduction of the transient pumping scheme and grazing incidence pumping scheme, the energy needs decreased in the 1 J range and below. Recently, the group in INFLPR demonstrated that 200mJ are enough to produce a high gain Ag XRL (55/cm) emitting photons at about 89eV. In order to produce polarized and high quality emission, seeding technique was used. In this case, the XRL is used as a plasma amplifier, while the seed is produced in such a way that secures the request for the beam quality such as polarization and spatial profile. The seeded scheme was reported in several articles such as [1-6] and is a very active domain of research.

An alternative approach that can be followed is to use a Zn XRL pumped with relatively long pulses, in the 100ps range. It was already reported in [7] that the output energy of such an XRL system can reach the multi-mJ level. In this approach, the XRL pulse duration is significantly longer, in the range of 100ps while in the previous case the XRL pulse duration can vary from few hundreds of fs for harmonics seeding to few ps.

The backscattered gamma photon energy scales with the square of the Lorentz factor, implying a significant extension of the gamma radiation spectrum production at ELI-NP to the 400MeV range and even to the GeV range, as requested in other experimental proposals at ELI-NP, related e.g. to light-assisted electron-positron pair creation or to further nuclear physics experiments.

Methodology

Seeded X-ray laser development can be performed in small scale laboratories and then further tested at the ELI-Beamlines facility, where harmonics seeding of XRL to reach 1mJ level is planned. As our goal is related to a very monochromatic gamma beam, the ELI-NP system should be different in terms of the seed, using a plasma XRL oscillator, most likely as proposed in [2], with some additional modification in XUV optics to get polarization control of the XRL. So, a modified optimized local test set-up at the ELI-NP facility has to be implemented, as shown in the figure below.

Multiple pulses with delays in the range from 100fs to few hundreds of ps, needed to pump the XRL are needed. A simple method to implement it in CPA laser systems such as ELI-NP multi-PW laser system was demonstrated in [8] and was later used for successful Ag XRL developments [9].

For the experiment to take place, one needs a beam of quasi-monoenergetic electrons, such as the ones from the gamma beam facility, or a bunch of laser accelerated electrons. Both approaches have advantages and disadvantages, so several experimental campaigns are proposed:

at E7 experimental area, using the electron beam from the gamma beam and laser energy up to few hundreds of Joule to pump the seeded XRL.

At an experimental area where we can get two laser beams, one to generate a very dense bunch of laser-accelerated electrons and one to pump the seeded XRL that provides the photons to be scattered. In this case, the electron bunch is less monochromatic but it can be significantly more dense and energetic than the one provided by the gamma beam facility. The XRL can also be focused in spots at the micrometer level. As a consequence, one can produce broadband gamma rays but with higher flux.

at E7 experimental area, using the electron beam from the gamma beam and the driver laser for the gamma beam that is planned to deliver above 150mJ energy at high repetition rate (120Hz), synchronous with the electron bunches from the gamma beam. In this case, an XRL with wavelength in the range of 18.9 nm can be produced with a relatively high flux of photons per second. In this case, the repetition rate of the XRL can compensate for the relatively low number of photons delivered by the XRL in one pulse.

Electron bunch synchronization with the laser pulse should be realized with a resolution several times below the electron bunch duration.

Alignment procedure should allow the focus positioning for both laser focus and electron beam focus with micrometer accuracy.

The experiments have to be produced in vacuum, at least 10-5 mbar residual pressure.

The detection should be adequate for a broad range of gamma radiation detection, up to the 1 GeV range.

Laser produced electron bunches have to be investigated separately, previously and they have their own specific alignment and diagnosis requests.

Bibliography:

[1] T. Ditmire, M. H. R. Hutchinson, M. H. Key, C. L. S. Lewis, A. MacPhee, I. Mercer, D. Neely, M. D. Perry, R. A. Smith, J. S. Wark and M. Zepf “Amplification of xuv harmonic radiation in a gallium amplifier”, Phys. Rev. A 51, R4337–R4340 (1995)

[2] J. Dunn, A. L. Osterheld, A. Ya. Faenov, T. A. Pikuz, and V. N. Shlyaptsev “Injector‐amplifier design for tabletop Ne‐like x‐ray lasers” AIP Conf. Proc. 641, pp. 9-14; (2002) X-RAY LASERS 2002: 8th International Conference on X-Ray Lasers.

[3] Momoko Tanaka, Masaharu Nishikino, Tetsuya Kawachi, Noboru Hasegawa, Masataka Kado, Maki Kishimoto, Keisuke Nagashima, and Yoshiaki Kato; “X-ray laser beam with diffraction-limited divergence generated with two gain media” Optics Letters, Vol. 28, Issue 18, pp. 1680-1682 (2003)

[4] Ph. Zeitoun, G. Faivre, S. Sebban, T. Mocek, A. Hallou, M. Fajardo, D. Aubert, Ph. Balcou, F. Burgy, D. Douillet, S. Kazamias, G. de Lachèze-Murel, T. Lefrou, S. le Pape, P. Mercère, H. Merdji, A. S. Morlens, J. P. Rousseau & C. Valentin; “A high-intensity highly coherent soft X-ray femtosecond laser seeded by a high harmonic beam” Nature 431, 426-429 (2004)

[5] Y. Wang, E. Granados, F. Pedaci, D. Alessi, B. Luther, M. Berrill & J. J. Rocca; “Phase-coherent, injection-seeded, table-top soft-X-ray lasers at 18.9 nm and 13.9 nm”, Nature Photonics 2, 94 – 98 (2008)

[6] E. Oliva, M. Fajardo, L. Li, M. Pittman, T. T. T. Le, J. Gautier, G. Lambert, P. Velarde, D. Ros, S. Sebban and Ph. Zeitoun, “Multi-tens GW, fully coherent femtosecond soft X-ray laser.”, Nature Photonics, accepted (2012)

[7] B. Rus, T. Mocek, A. R. Präg, M. Kozlová, G. Jamelot, A. Carillon, D. Ros, D. Joyeux, and D. Phalippou; “Multimillijoule, highly coherent x-ray laser at 21 nm operating in deep saturation through double-pass amplification” Phys. Rev. A 66, 063806 (2002)

[8] R. Banici, D. Ursescu; “Spectral combination of ultrashort laser pulses” EPL 94 44002 (2011)