Lin Su

Peter F Caracappa

Tianyu Liu

Wei Ji

X George Xu

Xining Du

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ANS RPSD 2014 - 18th Topical Meeting of the Radiation Protection & Shielding Division of ANS 
Knoxville, TN, September 14 – 18, 2014, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2014) 
 
1 
 
Development of CSG-based radiation shielding module for ARCHER: 
preliminary results for photons 
 
Xining Du, Tianyu Liu, Lin Su, Wei Ji, Peter F. Caracappa, X. George Xu 
Nuclear Engineering Program, Rensselaer Polytechnic Institute, Troy, New York, USA; email: xug2@rpi.edu 
 
 
INTRODUCTION 
 
ARCHER [1] is a parallel Monte Carlo radiation 
transport code being developed for various hardware 
platforms including multi-core CPUs, the emerging 
Nvidia graphics processing units (GPUs) and Intel Xeon 
Phi coprocessors. Previous studies have demonstrated the 
accuracy and speed for CT imaging and radiotherapy 
dosimetry applications. Radiation shielding applications, 
however, require ARCHER to be more flexible in 
defining and handling geometries, in addition to the voxel 
phantom geometries that are commonly used in medical 
physics calculations.  
In this paper, we present the development of a 
general geometry module used for radiation protection 
and shielding problems in ARCHER. The methods of 
geometry design and particle transport for the GPUs are 
introduced.  Preliminary results comparing against the 
MCNP code for cases involving Cs-137 0.662MeV 
gammas are reported.  
 
DESCRIPTION OF ACTUAL WORK 
 
For handling common geometries encountered in 
radiation protection and shielding design, we adopted 
constructive solid geometry (CSG) definitions used by 
MCNP/MCNPX codes [2], In CSG, complex 3-
dimensional objects are modeled using Boolean 
operations to combine basic objects. A series of surface 
primitives are first defined in ARCHER. These include 
planes, spherical surfaces and cylindrical surfaces. Table 
1 lists the surfaces that are supported in the geometry 
module and the definition parameters. A cell is described 
as the intersection of a group of half-spaces, which are 
defined as the region with relative orientations (sense) to 
corresponding surfaces. Each cell is either filled with 
certain material, a universe, or a lattice structure. A 
universe is defined as a space that contains one or more 
cells. 
The new geometry module was integrated with the 
previously developed photon transport modules in 
ARCHER by replacing the geometry inquiry functions at 
every step of the transport process: instead of directly 
checking the position of each photon in different regions, 
e.g. a voxel human phantom or bowtie filters of the CT 
scanner model, the code now calls the geometry function 
and traverse all the cells to find the one within the particle 
is located. The ray-tracing algorithm was adopted for 
transporting photons in the CSG: At each step, the 
sampled photon collision distance, s, is compared with the 
distance to cell boundary surfaces, d. If s is larger than d, 
the photon will move to the nearest intersection point and 
repeat the sampling process. Otherwise the photon will be 
transported to the new position with step size s and the 
photon interaction outcome is sampled according to the 
corresponding cross sections. Figure 1 shows a simplified 
flow chart of photon transport involving the ray-tracing 
algorithm described above.  
 
Table 1. List of surfaces supported in the geometry 
module of ARCHER. 
 
 
Three interactions are considered for the MC 
transport of photons with energy in the range of 1 keV to 
1 MeV. These are Compton (incoherent) scattering, 
photoelectric effects and Rayleigh (coherent) scattering. 
Form factors are included for Compton and Rayleigh 
scattering to account for electrons' binding effect in the 
scattering interaction. 
With the radiation shielding module, ARCHER is 
capable of dealing with more complex user-defined 
geometries. In input files the users can define a series of 
surfaces and specify different cells by listing the 
associated half spaces (surface with sense).  The code 
then reads in all the geometry information, build a list of 
cells and store them in memory. 
Surface Equation Parameters 
Plane parallel to x-
axis 
00  xx  0x  
Plane parallel to y-
axis 
00  yy  0y  
Plane parallel to z-
axis 
00  zz  0z  
Sphere 
0)(
)()(
22
0
2
0
2
0


Rzz
yyxx
 
Rz
yx
,
,,
0
00
 
Cylinder parallel to 
x-axis 
0
)()(
2
2
0
2
0


R
zzyy
 
R
zy ,, 00
 
Cylinder parallel to 
y-axis 
0
)()(
2
2
0
2
0


R
zzxx
 
R
zx ,, 00
 
Cylinder parallel to 
z-axis 
0
)()(
2
2
0
2
0


R
yyxx
 
R
yx ,, 00
 
 
2 
 
We first developed the parallel CPU code and then 
ported it to the GPU platform using Nvidia's CUDA 
(Compute Unified Device Architecture) framework [3].  
 
 
Figure 1. Flow chart of photon transport using the ray 
tracing algorithm. 
 
In the CUDA framework, the CPU serves the role of the 
“host” as the main controller of the whole program. The 
GPU serves the role of an external “device” and performs 
the computationally intensive, parallelizable part of the 
work. Thousands of active threads can run concurrently 
on one GPU. In a typical CUDA program, the data is first 
transferred from host memory to GPU memory, then a 
kernel function is called by the CPU and executed on the 
GPU in parallel, finally the results are transferred back 
from GPU memory to host memory.  
 
RESULTS 
 
We tested the radiation shielding design module of 
ARCHER in a problem involving a 1-Ci Cs-137 point 
source located within a cylindrical lead shield 
(radius=0.1m, length=0.06m) in a 10m × 10m × 4m room 
of concrete walls. The geometry setup is depicted in Fig. 
2. MCNP and ARCHER were used to calculate the dose 
to cell 4 using the direct energy deposition tally. Several 
runs were performed with different thicknesses of the lead 
container represented by cell 2. In each run a total of 2.56 
× 107 photons with energy 0.662MeV are simulated.  
 
Figure 2. Setup of the radiation shielding design problem 
used for the test. 
 
We tested ARCHER and MCNP on a workstation 
equipped with a quad-core Intel Xeon E5507 2.26GHz 
CPU and an Nvidia Kepler K20 GPU card. For 2.56 × 107 
photons, MCNP running on the Intel E5507 with 4 
threads took about 118 seconds while ARCHERGPU 
running on the Kepler K20 took 13 seconds. Dose results 
from both codes are in reasonable agreement with each 
other.  We compared the performance of two methods for 
photon transport, namely the ray tracing algorithm and the 
Woodcock delta tracking algorithm [4], and found that the 
former is much more efficient than the latter for radiation 
shielding simulations. The reason is that in Woodcock 
delta tracking, the average step size is small due to the use 
of fictitious cross sections (the highest one among all 
materials). Thus significantly more steps are needed to 
transport the particles in the geometry with the penalty 
outperforming the time saved for the absence of boundary 
checking. On-going work is focused on applying variance 
reduction techniques, and integrating the electron 
transport model to ARCHER's radiation shielding 
module.   
CONCLUSION 
 
The radiation shielding design module of ARCHER 
has been developed, which supports general geometry 
setups in the CSG format. The code was implemented 
using CUDA on Nvidia GPUs, and the performance was 
benchmarked against the MCNP code for a simple 
radiation shielding problem. Results showed that 
ARCHER worked properly and achieved impressive 
speedup due to highly parallel computing nature of the 
Nvidia GPUs compared to the MCNP code running on 
multi-core CPUs. Further optimization of the geometry 
module will be carried out using advanced geometry 
structures and variance reduction techniques to improve 
the precision and performance of ARCHER. 
 
3 
 
 
ACKNOWLEDGEMENT 
 
This work was partially supported by the grant from 
NIBIB (R01EB015478).  
 
REFERENCES 
 
1. X.G. Xu, T. Liu, L. Su, X. Du, M.J. Riblett, W. Ji, 
“Update of ARCHER, a Monte Carlo Radiation 
Transport Software Testbed for Emerging Hardware 
Such as GPUs”. Transactions of the American 
Nuclear Society, Vol. 108, Atlanta, Georgia, June 
16–20, 2013. 
2. X-5 Monte Carlo Team, MCNP-a general Monte 
Carlo N-Particle Transport code, Version 5. Volume 
I: overview and theory, 2003. 
3. NVIDIA, CUDA C Programming Guide, 
http://docs.nvidia.com/cuda/cuda-c-programming-
guide/ 
4. E. Woodcock, T. Murphy, P. Hemmings, and T. 
Longworth, Techniques used in the GEM code for 
Monte Carlo neutronics calculations in reactors and 
other systems of complex geometry, 1965, Argonne 
National Laboratories Report ANL-7050. 


Development of CSG-based radiation shielding module for ARCHER: preliminary results for photons

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Development of CSG-based radiation shielding module for ARCHER: preliminary results for photons

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