Nuclear Science and Technology - Volume 9, Number 2, June 2019

tem [7]. 
This paper presents results of applying 
Simion program to build some design models 
for the system based on design principles of 
some built systems in the world and propose a 
feasible conceptual design of the system that 
can be used to prepare for the stage of detailed 
engineering design and construction of the 
system in the future. 
II. CONTENTS 
A. Overview of Simion program 
Simion is a software package used 
primarily to model electrostatic and magnetic 
fields and calculate trajectories of charged 
particles in these fields when introducing the 
electrode configuration with voltage and initial 
conditions of the particles [8]. Simion is 
intended to provide direct and highly interactive 
methods for simulating a wide variety of general 
ion optics problems such as modeling ion source 
and detector optics, ion traps, quadrupoles, etc. 
Electrostatic and magnetic fields can be 
modeled as boundary value problem solutions 
of a partial differential equation called the 
Laplace equation (or the Poisson equation). The 
specific method used within Simion to solve this 
equation is an over-relaxation technique, which 
is a finite difference method to obtain a best 
estimate of potentials for each point within the 
fields. After the electrostatic and magnetic fields 
have been obtained, a standard fourth-order 
Runge-Kutta method is used for numerical 
integration of the charged particle trajectory in 
three dimensions based on the particle definition 
parameters provided by users. In particular, 
Simion provides functions of extensive support 
in the definition of geometry, data logging, and 
visualization. One of the most useful features of 
Simion is the capability of using user programs 
inside the program. This feature allows users to 
directly utilize a variety of programming 
languages including Lua, C++, C, PRG, etc. to 
flexibly and efficiently extend simulation 
capabilities of the program. 
B. Methods 
According to several reference system 
designs, we have successfully built some 
simulation models that can be possible designs 
for the system by using Simion. Due to 
application limitations of the program, the 
design models are only used to simulate the 
operating principle of slow positron beam 
systems rather than specify detailed 
engineering designs. Three main individual 
simulation models of the slow positron beam 
system have been built including: 
CAO THANH LONG et al. 
47 
- The straight-shaped model using the 
ExB filter (figure 1). 
- The 500 bent-shaped model based on the 
design of the SPONSOR system [9, 10] (figure 2). 
- The 900 bent-shaped model based on 
the design of a slow positron beam system 
from Martin Luther University Halle-
Wittenberg, Germany [11] (figure 3). 
Fig. 1. The straight-shaped model using ExB filter. 
Fig. 2. The 50
0
 bent-shaped model. 
Fig. 3. The 90
0 
bent-shaped model. 
Some positron trajectory calculation tests 
have been performed for each model in order to 
investigate the influence of design parameters of 
each model on the quality of positron beam 
obtained on targets, thereby determining which 
model was the most reasonable design. The 
selected model has been proposed as a feasible 
conceptual design for the future system. Tables 
of design parameters for the proposed conceptual 
design include geometry parameters, electric 
parameters and design parameters of coils 
creating magnetic fields. 
CONCEPTUAL DESIGNING OF A SLOW POSITRON BEAM SYSTEM USING  
48 
C. Results and Discussions 
Case 1: Simulation of the trajectory of a 
monoenergetic positron beam 
Simion has been used to calculate the 
trajectories for 1000 monoenergetic positrons 
in a beam emitted isotropically from a circular 
uniform distribution source with a radius of 2 
mm for each model. The initial kinetic energy 
of the beam was 3 eV. The voltages that were 
applied to the pre-accelerator and the 
accelerator of each model were 27 V and 30 
kV, respectively. The simulation results are 
shown below in table I, figure 4 and figure 5. 
Table I. The simulation results for trajectory of a monoenergetic positron beam 
Straight-shaped 
model 
50
0
 bent-shaped 
model 
90
0
 bent-shaped 
model 
Total number of positrons from 
source 
1000 1000 1000 
Total number of positrons 
coming to target 
789 807 795 
The ratio of positron number 
coming to target to total positron 
number 
78.9% 80.7% 79.5% 
Beam radius on target 2.75 mm 2.39 mm 2.79 mm 
Fig. 4. Spatial distribution of positron beam on the target of the straight-shaped model (left), the 50
0
 bent-
shaped model (middle) and the 90
0 
bent-shaped model (right) 
Fig. 5. Energy distribution of positron beam on the target of the straight-shaped model (left), the 50
0
 bent-
shaped model (middle) and the 90
0
 bent-shaped model (right) 
(FWHM = 5.50 eV) (FWHM = 1.34 eV) (FWHM = 5.71 eV) 
CAO THANH LONG et al. 
49 
From the simulation results, it has been 
found that the quality of positron beam 
obtained on the targets is influenced by the 
model designs. The models with the different 
designs do not have completely identical 
uniform magnetic fields along their axes, 
resulting in different qualities of obtained 
positron beam on the targets. 
The results of the beam radius of 
positron beam on the targets show that 
obtained positron beam in case of using the 50
0
bent-shaped model has better convergence 
compared to the others. Furthermore, full width 
at half maximum (FWHM) of the energy 
distribution of positron beam on the target for 
the 50
0
 bent-shaped model was smaller than 
those of the others. It has shown that the 
obtained positron beam of the 50
0
 bent-shaped 
model was more mono-energetic than those of 
the others. 
Case 2: Simulation of the trajectory of a 
monoenergetic positron beam in case that a 
solenoid deviated from its original position 
Another trajectory calculation test has 
been done for each model with the same 
monoenergetic positron beam in case that the 
solenoid surrounding the accelerator of each 
model deviated from its original position. 
Distributions of positron beam on the target of 
each model have been investigated for 
comparison. We have simulated two situations 
that the solenoid deviations were 1 cm and 2 
cm. The simulation results are shown below in 
figure 6, figure 7 and figure 8. 
Fig.6. Spatial distribution of positron beam on the target of the straight-shaped model in case of solenoid 
deviation of 0 cm (left), 1 cm (middle) and 2 cm (right). 
Fig.7. Spatial distribution of positron beam on the target of the 50
0 
bent-shaped model in case of solenoid 
deviation of 0 cm (left), 1 cm (middle) and 2 cm (right). 
CONCEPTUAL DESIGNING OF A SLOW POSITRON BEAM SYSTEM USING  
50 
Fig. 8. Spatial distribution of positron beam on the target of the 90
0
 bent-shaped model in case of solenoid 
deviation of 0 cm (left), 1 cm (middle) and 2 cm (right). 
The comparison results have shown that 
the solenoid deviation influenced the quality of 
the positron beam that comes to the targets. For 
the straight-shaped model, there were a few 
positrons obtained on the target in case of 
solenoid deviation of 1 cm. In the case of a 
solenoid deviation of 2 cm, we have even got 
no positrons coming to the target. For the 90
0
bent-shaped model, the obtained positron 
beam has deviated much more from the target 
center compared with that of the 50
0
 bent-
shaped model. The beam has even distorted its 
shape when increasing the solenoid deviation 
to 2 cm. Therefore, we have concluded that 
the 50
0
 bent-shaped model in this simulation 
case would be the optimal model compared 
with the others. 
III. CONCLUSIONS 
We have come up with the selection of 
the 50
0
 bent-shaped model as a conceptual 
design for our slow positron beam system 
based on simulation test results and 
consideration of the design feasibility of the 
simulation models. The proposed model can be 
a good basis for detailed engineering design 
and construction of the system in the future. 
The study results have also demonstrated that 
Simion program is a very suitable tool for 
modeling and simulation of the trajectory of 
positron beam flying through electrostatic 
fields and magnetic fields of a slow positron 
beam system. Research of searching for other 
simulation programs to combine with Simion 
should be done to further optimize the 
conceptual design. 
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CAO THANH LONG et al. 
51 
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