U.P.B. Sci. Bull., Series , Vol. , Iss. , 201 ISSN 1223 -7027 [612587]

U.P.B. Sci. Bull., Series …, Vol. …, Iss. …, 201 ISSN 1223 -7027
SIMULATIONS ON REDUC ING THE INFLUENCE OF
BACKSCATTERED SLOW P OSITRONS ON LIFETIME
MEASUREMENTS
Doru DINESCU 1*, Nikolay DJOURELOV 2
In the e+ lifetime measurements with slow e+ the incident e+ hit the target and
a fraction of them is backscattered. If the backscattered e+ reach back the
accelerator they can be reflected by the electric field and implanted into the sample
with a delay causing spectrum distortions. The method of guiding the e+ through a
bent tube equipped with steering coils will be implemented at the ELI -NP e+ line. To
understand the origin of these distortion s and to further improve the performance of
the system, comprehensive Comsol Multiphysics and Geant4 simulations were
performed.
Keywords : slow positron, backscattering, positron lifetime, Comsol, Geant4
1. Introduction
For the development of new functional materials, the investigation of
lattice defects and various atomic imperfections in solids constitutes an important
step. Conventional positron annihilation methods use energetic e+ directly emitted
from radioisotopes such as 22Na and are suited to study bulk materials. For
analyzing subsurface layers and thin films, slow e+ beams are necessary [1]. At
the European Light Infrastructure – Nuclear Physics (ELI-NP), a brilliant γ-beam
will produce fast e+ by the pair production mechanism in a suitable converter
made of tungsten foils, which also act as the e+ moderator [2].
One of the positron annihilation techniques , which over the years has
become an increasingly valuable tool for study of the defect structure in materials
is the Positron Annihilation Lifetime Spectroscopy (PALS) [3]. PALS is based on
measuring the lifetime of a e+ within a solid. Conventional PALS, which most
often uses a 22Na source, is a precise timer which measures the time between the
1274 γ -quant um released at the beta plus decay and one of the two 511 γ -quanta
emitted through the annihilation of the positron with an electron from the studied

1 PhD student: [anonimizat], Faculty of Applied Science s, Splaiul
Independentei, nr. 313, 060042, Bucuresti, Romania , *corresponding author e-mail:
doru.dinescu@eli -np.ro
2 Senior Researcher II, Extreme Light Infrastructure – Nuclear Physics, Horia Hulubei National
Institute for Physics and Nuclear Engineering, 30 Reactorului Street, 077125 Magurele, Ilfov
county, Romania

Doru Dinescu, Nikolay Djourelov

material. In order to perform PALS with a slow e+ beam a start signal is needed.
Different me thods have been designed and successfully applied for the generation
of a start signal: detection of secondary e- produced by incident e+ [4], e+
accumulated in a Penning trap and release d by a trigger [5], and chopping and
bunching technique to form ultra-short e+ pulses [6].
For depth profiling purposes, the slow e+ are accelerated by a few graded
electrodes to a desirable energy up to typically 30 keV. When incident e+ hit the
target a fraction of them is backscattered. If the backscattered e+ reach back the
accelerator they can be re flected by the electric field and implanted into the
sample with a delay from the initial e+ bunch. This causes significant distortions
in the PALS spectrum as satellite peaks [7-9]. In order to suppress the satellite
structures several methods have been applied: passing the accelerated incident e+
through a E×B filter [10], the implementation of an accelerator -decelerator
structure [11], and guiding the e+ through a 45˚ bent tube equipped with steering
coils after they pass the accelerator [7]. The last method is foreseen in the
design ed pulsing system to be implemented for the ELI-NP positron beam .
The aim of the study conducted in the present paper is to determine the
optimum parameters of the designed system in order to obtain PALS spectra with
minimum distortions ca used b y the backscattered e+.
2. Setup , simulation and analysis
Comsol Multiphysics was used for simulating the magnetic field that will
guide the e+ beam fr om the accelerator to the center of the sample, and for the
generation of the elec tric field of the accel erator [12]. The magnetic field was
generated by a series of multi -turn Helmholtz coils . In Fig. 1 the surface plot of
the magnetic and the contour lines of the electric 3D maps are shown on a cross
section along the central axis. The magnetic field is close to uniformity (60 ± 2 G)
along the axis. The electric field used for the acceleration of the particles towards
the sample was obtained by applying a potential Uacc equally spread on the graded
electrodes (having holes with diameter D = 60 mm) of the accelerator. The
Faraday cage with internal diameter 116 mm and length of 720 mm was kept at
the potential Uacc to act as a e+ drift region.
The 3D maps of the Comsol simulations were ex ported into an ASCII
format in which the values of the magnetic and electric fields were taken point by
point in a grid pattern, and imported into the Geant4 software where the
simulations regarding e+ backscattering were performed. The Geant4 simulations
were performed using the low energy physics model G4EmLivermorePhysics
which include ionization, bremsstrahlung and multiple scattering. The geometry
built in Comsol was reproduced in Geant4, thus the magnetic and electric fields
that were imported, perfectly overlap over the beam transport lines which was

Paper title
crosschecked by monitoring whether the primary e+
beam trajectories, simulated
using the Geant4 software, hit the target center.

Fig. 1. The cross section of the 3D maps along the central beam line axis represented by a surface
plot of the magnetic field and contour lines of the electric field in the case of a straight tube and
potential Uacc= -2 kV.
For each Geant4 simulation 1×106 e+ were shot towards the sample . The
e+ backscattering coefficient strongly dependent on the average atomic number Z.
The higher Z the more the backscattering [13]. Our choice of a sample with
relatively low Z, namely silicon with Z = 14, is to underline the significance of the
studied effect. Fig. 2 shows an example of e+ trajectories as obtained by Geant4
for low statistics. It is seen that accelerated e+ hit the sample, a fraction of them
are backscattered, reach the accelerator, where they are reflected, and then
reimplanted into the sample.

Fig. 2. The trajector ies of the primary 2 keV e+ beam and the event of e+ backscattering with 300
incident particles. Example of a straight tube obtained by Geant4 .

Doru Dinescu, Nikolay Djourelov

Fig. 3a shows the time of annihila tion within the target of e+ accelerated
to E+= 2 keV in a straight geometry as shown in Fig. 2. The very sharp peak
corresponds to e+ which are directly implanted into the target. The very broad
peak is due to e+ backscattered, reflected from the accelera tor electric field and
then imp lanted into the target. The delayed e+ can significantly distort the long –
lived components when measuring a PALS spectrum.

Fig. 3 Histogram of the time at which the e+ annihilate within the target for the geometry shown in .
Fig. 4 a) e+ accelerated to E+= 2 keV and b) e+ accelerated to E+= 10 keV.
Fig. 3b shows the time of annihilation for the same geometry but for e+
accelerated to E+= 10 keV. Due the higher energ y, the delay of the backscattered
positrons is smaller which may not only affect the longest -lived component but
also the shorter -lived ones in the PALS spectrum . In Fig. 3b an additional ,
intermediate peak is present right after the initial beam of particles is implanted
into the sample. It is due to the fact that for high energies the positrons which are
backscattered at a bigger angle from the sample will have larger Larmor radii and
may hit the wall of the Faraday cage close to the target position (see Fig. 5) and
part of them after backscattering from the wall can return to the targ et (due to the
low statistics in the visualization can't be followed in Fig. 5). The last effect has
been observed previously [14]. One solution is to use a sample chamber with a
large diameter , however, this would lead to reduced count rates in experiments
with detectors placed from the lateral sides . Another solution is to in crease the
strength of the guiding magnetic field to reduce the Larmor radii [15].
The stop signal in the PALS measurement comes from the detection of the
annihilation 511 -keV gamma rays. A gamma detector made of BaF 2 was
implemented in Geant4 placed right behind the silicon target (see Fig. 2). In order
to account only events which can produce signal like in a real experiment the
gamma quanta that deposited less than 300 keV in the B aF2 were rejected. Lead

Paper title
around the gamma detector was used to shield from the gamma rays not
originating from the silicon target .

Fig. 5 The trajector ies of the primary E+= 10 keV e+ beam and the event of e+ backscattering with
300 incident particles. Example of a straight tube obtained by Geant4 . The zoom shows e+ that are
backscattered at a big angle from the sample and hit the walls of the tube close to the target.
The histogram of the time of the gamma ra ys interaction with the BaF 2
detector obtained by Geant4 in the case of a straight tube and E+= 2 keV is
presented in Fig. 6. The physics models in Geant4 do not account for the e+
lifetime in a material and, that is why, the time histogram actually does not
represent a PALS spectrum but only the resolution function , R(t). If positrons
annihilate from a discrete number of states, the PALS spectrum can be described
as a convolution of the resolution function and the probabilities to decay from
those states
) ) () ( ()( )(
1B t exp I N tRtyi iin
it  
 
,
where τi is the lifetime of the i-th state(component), Ii is the intensity of the i-th
component, Nt is the total counts and B is the background.

Fig. 6 Histogram of the time of the gamma rays interaction with the BaF 2 detector obtained by
Geant4. Example of a straight tube (see Fig. 2) and E+= 2 keV .

Doru Dinescu, Nikolay Djourelov

In order to study the effect of backscattered e+, we simulated PALS spectra
convoluting the resolution function R(t) (see Fig. 6) with four components with
lifetimes [τ1, τ2, τ3, τ4] 0.1, 0.5, 3 , 20] ns with corresponding intensities [I1, I2,
I3, I4] 10, 60, 10 , 20]%. The obtained spectrum was also convoluted by a
Gaussian with FWHM = 0.15 ns to take into account the typical resolution of a
fast gamma detector (BaF 2 coupled with a photomultiplier tube) and Poison noise
was added.
Example of a simulated spectrum is shown in Fig. 7a. In Fig. 7b a simulated
spectrum with suppressed backscattering is shown for a compa rison. The
distortion in the PALS spectrum introduced by the backscattered e+ is clearly seen
in the example shown in Fig. 7a. In order to quantif y the distortion from the
model spectrum , the spectra are analyzed by LT9 software [16] to find the best fit
parameters and the deviations ( ) ⁄ (P = τ or I, and i = 1 to
4) are calculated .

Fig. 7 a) Simulated PALS spectra for a beam of E+= 2 keV in a straight tube geometry . b)
Simulated PALS spectra for a beam of E+= 2 keV in a straight tube geometry with suppressed e+
backscattering.
3. Results and discussion
The idea to reduce the effect of the backscattered e+ on the PALS spectra
by using an velocity filter between the accelerator and the sample originates from
the fact that e+ are backscattered with longitudinal energy smaller than that one of
the incident e+. Fig. 8 shows the longitudinal energy distribution of e+, accelerated
by Uacc= 2 kV , incident on the sample and of the e+ backscattered from sample.

Paper title

Fig. 8 Longitudinal energy of the incident e+ (accelerated by Uacc= 2 kV) on the sample and of the
backscattered e+ from the sample.

Fig. 9. The trajector ies of a 2 keV e+ beam and the event of e+ backscattering with 1000 incident
particles. Example of a 30˚ bend with an aperture of D = 15 mm obtained by Geant4 .
For minimizing the effect of e+ backscattering, two possible solutions
were simulated. The first solution is to add an aperture at the accelerator exit with
a diameter, D, comparable with the beam spot size. By applying this measure the
primary e+ beam will pass through the smaller opening towards the sample, but a
fraction of the backscattered e+ will not be able to enter the acc elerator through
the small aperture and instead they will annihilate on its walls . The second
solution is to pass the accelerated e+ beam through a bent tube equipped with
steering coils to act as a velocity filter as shown in Fig. 9. The Faraday cage is
composed of two part the bent tube with a fixed length of 450 mm followed by a
straight part of 270 mm in length. The magnetic field axis generated by t he
properly placed Helmholtz coils follows the bend and the magnetic field

Doru Dinescu, Nikolay Djourelov

generated by the steering coils is tuned in such a way that the primary e+ travel to
the target follow ing the central axis of the system . The backscattered e+ deviate
from the axis due to their lower longitudinal energy and will annihilate on the
Faraday cage walls far away from the gamma detector.

Fig. 10 Fit parameter d eviation s from the model PALS spectr a for a 2 keV е+ beam without an
aperture ( a) and with an aperture of D = 15 mm (b) as a function of the bend angle . The trend lines
are added (except for τ1 and I1) just to guide the eye.
The study was performed for the acceleration potentials Uacc = 2, 5, 10 and
20 kV with angles of the bend between 0 and 40 ˚ following the procedure
described in the previous section in order to determine the deviations in each
case. In Fig. 10 are presented the f it parameter deviations from the model PALS
spectra for a 2 keV е+ beam without an aperture ( Fig. 10 a) and with an aperture of
D = 15 mm ( Fig. 10 b) as a function of the bend angle. The trend lines are added
just to guide the eye. There are no trend lines added for τ1 and I1, as they represent
the lifetime and intensity of the shortest lived component, wh ich is affected not by
the reaccelerated backscattered e+ but by the e+ backscattered at big angles
annihilating at short distance from the target on the walls of the Faraday cage (see
the discussion about Fig. 3b). Therefore, their deviations are expected to be
independent of the bend angle which is better seen in Fig. 11. Also, it was
impossible to do a reasonable fit of the simulated spectra with a four component
model in the case without aperture as shown by the shadowed area in Fig. 10 a. As
the angle of th e bend increases, the deviations of the fitted parameters decrease
from up to 60% for a 20˚ bend to deviations of less than 10% for a 4 0˚ bend of the
tube ( Fig. 10 a). If the size of the aperture is reduced to D = 15 mm, comparable to
the e+ beam diameter, the results show that the deviations from the model
parameters decrease to below 10% in the case of a straight tube geometry, and, as
the angle of the bend is increased, these deviations start to get closer to the PALS
spectrum model parameters ( < 5%), as it can be seen from Fig. 10 b.

Paper title
The study was performed for different incident e+ energies due to the fact
that the е+ backscattering coefficient depends on E+ [13]. The deviations from the
model parameters are decreasing with the increasing of the bend angle for E+ in
the interval 2 – 20 keV, showing the same trend lines in all the cases that were
studied ( Fig. 11). It can be seen that there is a saturation of th e deviations at
angles  30˚, meaning that any angle above this value constitutes a viable solution
for minimizing the effect of backscattered e+ by the studied energy filter.
As the energy of the incident e+ beam increases, the delay of the
backscattered e+ is smaller which means that they will start affectin g the shorter
lived components as well, as it was discussed in the previous section , and shown
in Fig. 3b.

Fig. 11 Fit parameter d eviation s from the model PALS spectra for a e+ beam of different energies:
a) Е+= 5 keV, b) Е+= 10 keV and c) Е+= 20 keV as a function of the bend angle . The trend lines
are added (except for τ1 and I1) just to guide the eye.
4. Conclusions
The performed Geant4 simulations have helped in identifying the origin of
the distortions in the PALS spectra caused by the e+ backscatter ing. The
simulations have shown that adding an aperture at the accelerator exit in
combination with bending a part of the Faraday cage , which acts as a velocity
filter , is a satisfactory solution to reduce the distortions. The aperture plays an
important role and it should be slightly bigger than the maximum d iameter of the
e+ beam cross section . The obtained results show tha t for bend angles  30⁰ the
deviation from the model parameters induced by the e+ backscattering starts to
saturate reaching < 5% for E+ in the interval 2 – 20 keV . The 30⁰ bend can be

Doru Dinescu, Nikolay Djourelov

considered as an optimum solution which should suffice for minimizing the effect
of the backscattered e+.
Acknowledgments
The work was support ed by the ELI -NP Phase II, a project co -financed by the
Romanian Government and the European Union through the European Regional
Development Fund – the Competitiveness Operational Program (1/07.07.2016,
COP, ID 1334).
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