Monte Carlo simulations of production of collimated panoramic X-rays using a

conical anode-type X-ray tube

Andrii Sofiienko, PhD, University of Bergen Chad Jarvis, PhD, CMR Computing, Bergen

Ådne Voll, Visuray AS, Stavanger

2014 1

Introduction

The general purpose of this research was to investigate, using Monte Carlo simulations, the X-ray generation process in an X-ray tube with a conical tungsten anode and cylindrical symmetry. We determined the following: the intensity of generated X-rays in the energy range of

250-500 keV; the optimal target shape; the angular distribution of the intensity of the generated X-

rays and collimated through a cylindrical hole from an external collimator;

the efficiency of X-ray generation.

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Monte Carlo simulations

The Monte Carlo simulations were generated with the program GamBet based on the package PENELOPE. The solution volume for the object mesh had different ranges for the apex angle (ɣ) of the tungsten conical anode and for the different radii of the electron beam (re). The electron energy was 250 keV, 300 keV and 500 keV. 3

Figure 1: A geometrical model of the conical

tungsten target and electron beam that were used

for the MC simulations.

Figure 2: A geometrical model of the collimating system

of X-ray tube with conical anode.

Modelling of the external collimator

To simplify the MC simulations, the simple numerical method was used to simulate an

external cylindrical collimator with any thickness ∆R and any radius Rc. First, it is

necessary to know the spatial distribution of the photons on the first surface of the collimator

(with inner radius Rc) and on the second surface of the collimator (with outer radius Rc + ∆R).

This spatial distribution can be calculated using two translations of the spatial positions of

the photons on the surface with radius Rc and then to the surface with new radius Rc + ∆R;

moreover, it is necessary to estimate the geometrical position of the collimator hole. 4

Figure 3: A schematic (side view) of the measurement of the number of photons (generated by MC) that can pass

through the collimator slit.

Linear coordinate transformation:

The direction vector (xdi, ydi, zdi) is formed by the

normalized components of the momentum vector.

2

2

2

i i di i

i i di i

i i di i

x x x t

y y y t

z z z t

2 2 2

2 2i i cx y R

2 2 2 2 2

22 21 1

di di i i ci ii

di di i i

di di

di di

x y x y Rx y yt

x y x y

x

yx

2

2

sin

c c cc i c

R R rZ Z Z

tg tg

Results

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Figure 4: The angular distributions of the intensity of collimated X-ray photons in cylindrical

geometry at different values of the apex angle of the anode when the electron energy is equal

to 250 keV and the electron beam radius is equal to 2.0 mm. The parameters of the collimator

are following: Rc = 10 mm, ∆R = 3.5 mm and rc = 0.45 mm.

Results

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Figure 5: The dependences of the inclination angle, associated with the maximum value of the

intensity of collimated X-rays (upper plot), and of the maximum value of the intensity of collimated

X-rays (lower plot) on the value of the apex angle of the conical anode at an electron energy equal

to 250 keV and electron beam radii equal to 0.5 mm (1), 2.0 mm (2) and 5.0 mm (3). The

parameters of the collimator are following: Rc = 10 mm, ∆R = 3.5 mm and rc = 0.45 mm.

Thank you for your attention!

Any questions?

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