Electron range evaluation and X-ray conversion optimization in tungsten transmission-type targets with the aid of wide electron beam Monte Carlo simulations

1. Electron range evaluation and X-ray conversion optimization in tungsten
transmission-type targets with the aid of wide electron beam
Monte Carlo simulations
Andrii Sofiienko1
, Chad Jarvis2
, Ådne Voll3
1
University of Bergen, Allegaten 55, PO Box 7803, 5020 Bergen, Norway. E-mail: asofienko@gmail.com
2
Christian Michelsen Research AS, Fantoftveien 38, PO Box 6031, NO-5892 Bergen, Norway. E-mail: chad.jarvis@cmr.no
3
Visuray AS, Strandbakken 10, 4070 Randaberg, Norway. E-mail: david.ponce@visuray.com
Introduction
X-ray tubes are one of the most common and safest sources of X-rays and are used in many medical
[1-3] and industrial applications [4-6]. Among the many types of X-ray tubes that are available, the
transmission type features the simplest target design [7, 8] and is widely used in X-ray inspection [9,
10]. Despite the widespread use of transmission-type X-ray tubes, there is no detailed study of the
characteristics of the X-ray generation process for wide electron beams (when the beam diameter is
not much smaller than the diameter of the flat target). Additionally, there is no detailed information
about the effect of the geometrical parameters of the electron beam on the angular distribution of the
generated X-rays at accelerating voltages within the range of 250-500 kV, which are interesting for
industrial applications. The general purpose of the presented work was to investigate, using Monte
Carlo simulations, the X-ray generation process in a transmission-type X-ray tube with a wide
electron beam. We determined the following parameters for use in practical applications: approximate
electron range in a tungsten target over an energy range of 250-500 keV, the optimal target thickness,
the angular distribution of generated X-rays and the efficiency coefficient for the transfer of energy
from an electron beam to generated X-rays.
Monte Carlo simulations
MC simulations were performed using the Xenos software suite by Field Precision [12]. The
particular program is called GamBet. GamBet combines Field Precision's technology for finite-
element codes with the package PENELOPE [13]. The solution volume for the mesh created in all
cases had the following range: X-axis [-1.0 mm, 1.0 mm], Y-axis [-1.0 mm, 1.0 mm], Z-axis [0.0
mm, 0.5 mm]. The tungsten target was centred at (0.0 mm, 0.0 mm, 0.4 mm). Outside of the
tungsten target, the voxel size was (25 μm, 25 μm, 10 μm); inside the tungsten target, the voxel size
was (2.0 μm, 2.0 μm, 0.1 μm). The electron source file contained 4.6∙105
electrons with momentum
along the positive Z-axis. MC simulations were generated for target thicknesses equal to 1.0, 2.5,
5.0, 10, 20, 30, 35, 60 and 70 μm and electron source energies equal to 250, 300 and 500 keV. The
electrons were Gaussian-distributed in a regular pattern with diameter De = 0.25 mm perpendicular
to the Z-axis:
The efficiency of X-ray generation for different target thickness
Conclusions
Using Monte Carlo simulations of the X-ray generation process in a transmission-type X-ray tube
with a wide (unfocused) electron beam, several important parameters were determined: the
approximate electron range in tungsten over the energy range of 250-500 keV, the optimal target
thickness for different electron energies, the angular distribution of the flux of generated X-rays and
the efficiency coefficient for the transfer of energy from an electron beam to a generated X-ray flux.
Simple analytical relations were obtained for the electron range in tungsten and for the optimal target
thickness. It was demonstrated that the angular distribution of a flux of generated X-rays in the
forward direction has the same maximum output angle for different acceleration potentials of an X-
ray tube and that the angular distribution is more isotropic at higher energies. The efficiency
coefficient for the transfer of electron energy to a flux of generated X-rays depends on the tungsten
target thickness and compares well with the commonly used empirical relation proposed in [11].
These results can be used in practical applications to design transmission-type X-ray tubes with wide
electron beams to calculate the flux (including the angular dependence) of the generated X-rays.
This work was partially funded by the Research Council of Norway under contract 200888.
References
[1] D. N. Zeiger, J. Sun, G. E. Schumacher, S. L. Gibson, ‘Evaluation of dental composite shrinkage and leakage in extracted teeth using X-ray
microcomputed tomography’, Dental Materials, 25, 1213-1220, 2009.
[2] L. Goldstein, S. O. Prasher, S. Ghoshal, ‘Three-dimensional visualization and quantification of non-aqueous phase liquid volumes in natural
porous media using a medical X-ray Computed Tomography scanner’, J. of Contaminant Hydrology, 93, 96-110, 2007.
[3] M. Lindner, L. Blanquart, P. Fischer, et.al., ‘Medical X-ray imaging with energy windowing’, NIM: Section A, 465, 229-234, 2001.
[4] K. Wells, D. A. Bradley, ‘A review of X-ray explosives detection techniques for checked baggage’, Applied Radiation and Isotopes, 70,
1729-1746, 2012.
[5] L. Auditore, R. C. Barna, U. Emanuele, D. Loria, A. Trifiro, M. Trimarchi, ‘X-ray tomography system for industrial applications’, NIM: Section
B, 266, 2138-2141, 2008.
[6] R. D. Luggar, E. J. Morton, P. M. Jenneson, M. J. Key, ‘X-ray tomographic imaging in industrial process control’, Rad. Phys. and Chem., 61,
785-787, 2001.
[7] H. H. Sung, I. Aamir, O. C. Sung, ‘Transmission-type microfocus x-ray tube using carbon nanotube field emitters’, Applied Physics Letters, 90,
183109, 2007.
[8] L. M. N. Tavora, E. J. Morton, W. B. Gilboy, ‘Design considerations for transmission X-ray tubes operated at diagnostic energies’, J. Phys. D:
Appl. Phys., 33, 2497, 2000.
[9] B. Achmad, E. M.A. Hussein, ‘An X-ray Compton scatter method for density measurement at a point within an object’, Appl. Radiation and
Isotopes, 60, 805-814, 2004.
[10] Y. Gil, Y. Oh, M. Cho, W. Namkung, ‘Radiography simulation on single-shot dual-spectrum X-ray for cargo inspection system’, Appl.
Radiation and Isotopes, 69, 389-393, 2011.
[11] S. A. Ivanov, G. A. Shchukin, ‘Rentgenovskie trubki tekhnicheskogo naznacheniya (X-ray Tubes for Technical Purposes), Leningrad:
Energoatomizdat, 1989 [in Russian].
[12] S. Humphries, ‘Computational Techniques in Xenos - Integrated 3D Software Suite for Electron and X-ray Physics’, IEEE 34th International
Conference ICOPS 2007.
[13] F. Salvat, J. M. Fernández-Varea, J. Sempau, ‘PENELOPE-2011: A code system for Monte Carlo simulation of electron and photon transport’,
OECD Nuclear Energy Agency, 2011.
 
2 2
2 2
1
, , exp
2 2
4 4
e e
e e
x y
f x y D
D D

 
 
   
         
    
Figure 1: A schematic of the MC simulation of the transmission type target (on the left) and the angular distribution of the flux of
generated X-rays for the accelerating potentials of 250 kV and 500 kV (on the right)
The energy distributions of transmitted electrons with energies of 250, 300 and 500 keV were generated
by a MC method for different thicknesses of a tungsten target ranging from 1.0 μm to 70 μm. These
distributions were calculated to investigate the effect of the tungsten target thickness on the energy of
transmission electrons and their intensity behind the target. Integrating the energy distribution of the
transmitted electrons gives the relationship between the number of transmitted electrons and the target
thickness. A simple analytical expression for the estimated electron range in the tungsten target was
derived for the energy range of 250-500 keV: Re(E) = A·EB
, where A = (11 ± 1)∙10-3
(μm/keV) and B =
1.38 ± 0.07. An analysis of the dependence of the flux of generated X-rays on the tungsten target
thickness and electron energies produced a function that appoximates the optimal tungsten thickness as
a function of the electron energy as follows: dOptimal(E) = C· EP
, where C = (4.8 ± 0.3)∙10-3
(μm/keV)
and P = 1.48 ± 0.06. An analysis of the angular distribution of generated X-rays shows that the angles
with the maximum flux of generated X-rays fall within the same range (400
-600
in this case) for
different electron energies. This result may be caused by the beam size and by the electron density
distribution in the beam. However, the probability of X-ray generation in the forward direction varies
with initial electron energy. The obtained efficiency coefficients for the transfer of energy from an
electron beam to a flux of generated X-rays depends on the thickness of tungsten target and compares
well with following commonly used empirical relation: ηX = (8 ± 2)·10-10
·Z·eE, where Z is the atomic
number of the target media and eE is the enrgy of the incident electrons.
0 10 20 30 40 50 60 70
0,0
2,5x10
15
5,0x10
15
7,5x10
15
1,0x10
16
1,3x10
16
1,5x10
16
X-rayflux,s
-1
cm
-2
dW
, m
1
2
3
21 m
17 m
47 m
Figure 2: The flux of generated X-rays behind a tungsten target versus the thickness of the
target for different electron energies: 250 keV (1), 300 keV (2) and 500 keV (3)
10 100
0
1x10
14
2x10
14
3x10
14
7x10
14
8x10
14
9x10
14
1x10
15
E, keV
X
/E,keV
-1
s
-1
cm
-2
1
2
200 500
Figure 3: The energy distribution of the flux of generated X-rays (from MC simulations,
Figure 1) for a transmission-type X-ray tube at different acceleration potentials and target
thicknesses: 250 kV and 20 μm (1) and 500 kV and 60 μm (2)
0 10 20 30 40 50 60 70
0,000
0,005
0,010
0,015
0,020
0,025
0,030
0,035
Ee
= 250 keV
Ee
= 300 keV
Ee
= 500 keV
~ d
1.2
W
X
,arb.un.
dW
, m
~ dW
1
2
3
Figure 4: The efficiency coefficients for the transfer of energy from an electron beam to a flux of
generated X-rays versus tungsten target thicknesses for different electron energies: 250 keV (1), 300
keV (2) and 500 keV (3)