1. CEA – Saclay, DRT/LNHB/LMD, 91191 Gif-sur-Yvette, France
COMPUTATION OF PHOTON IRRADIATION FACILITY PROBLEM USING THE PROGRAM PenEasy
J. GOURIOU
CEA – Saclay, DRT/LNHB/LMD, Gif-sur-Yvette, France
CONTEXT
Conrad problem P4 “Photon irradiation facility”, question 1 has been analyzed using the general-purpose main program PenEasy (v ) [1] compatible with version 2005 of the PENELOPE Monte Carlo code [2] and the Fortran compiler Pathscale 95 (with the compiler options -O3 - OPT: Ofast) under a Linux environment (Red Hat Enterprise Linux 4). The simulations have been made on a PC under a 64 bits architecture with one bi-processors AMD 2Ghz.
The main purpose of the problem is to study the uncertainty budget associated with the air kerma delivered by a simplified 137Cs calibration beam. Several parameters have been calculated considering different source and collimator geometries.
Another Monte Carlo code (MCNP4) has been also used to validate the calculated results.
TOOLS & METHODOLOGY
PenEasy
2 billion of primary particles, i.e. photons with an initial kinetic energy set equal to MeV, are simulated during each PenEasy process. Each point of disintegration is emitted with an isotropic direction from all the radioactive volume of the source. The detector is modelized by a sphere filled with air and located to 50 cm from the centre of the radioactive volume of the source. The maximum fluctuations for a given studied parameter remain in a reasonable domain of +/- 1 cm in dimension and +/- 1 g/cm3 for the density. The geometric model used by PenEasy to simulate the 137Cs irradiator is given in figure 1.
There is only one Monte Carlo simulation by specific geometry and density values. The simulation of the cylindrical geometry including the source and the detector is made into one step. There is no phase space file used or no splitting method employed. The simulations are made only under the photon mode (the energies cut-off Eabs for the electrons and the positrons are set equal to 1 MeV) in order to limit the execution time and to carry out the various geometries suggested by the question 1 of the problem P4. The other parameters are set as following: Eabs for the photons=1 keV, C1=C2=0.1, WCC=WCR=1 keV and DSMAX=1E30 cm (same parameter values as in the penmain.in file included into the PenEasy distribution).
Two types of tally have been used with PenEasy:
● The energy deposited, like the tally *F8 calculated by the MCNP Monte Carlo code [3]. These quantities scored into the detector volume are divided by the mass of the detector.
● The averaged photon fluence over the detector volume, like the tally F4 of MCNP. The detector fluence is estimated from the total photon track lengths calculated into the detector volume. With this approach, the fits of the conversion coefficients between the fluence (number of particles/cm2) and the air kerma (pGy) described in the table 2 of the problem P4 are used. The fits are determined with the software Origin (thanks to Guilhem Douysset for his help).
According to the type of tally used, some adaptations or variance reduction techniques were employed:
● Tally *F8
The interaction forcing into the detector volume is used after checking that there is no modification of the measured spectrum. This reduction method (IFORCE parameter set equal to 300) reduces significantly the uncertainty of the deposited energies.
● Tally F4
To calculate the fluence, the PenEasy program is used instead of the standard Penmain included into the PENELOPE Monte Carlo code distribution. Indeed, the Penmain program calculates only the surface fluence (i.e. the impact fluence between the particle and the surface detector). To the opposite, PenEasy calculates by default the fluence based on the track length determination. Moreover, the subprogram tallyFluenceTrackLength.f has been modified, in order to record a fluence according to a linear scale (5 keV for each bin).
Several preliminary tests have been made:
● A source which emitted particles preferentially in the direction of the detector (angle less than 130 degrees). As notable differences in the photon spectrum and the mean energy are observed, this method has not been used.
● A spherical detector with different radii, with a size smaller than the source radius, for checking if there is no modification of the measured spectrum (idem for the mean energy). To keep under this condition, the radius of the spherical detector is taken equal to 1.5 cm for all the PenEasy simulations.
MCNP4C
Several complementary simulations have been made with the MCNP Monte Carlo code version 4C [3]. The tallies F4 and F5 are recorded into a sphere detector of 2 mm radius. For each studied case, 250 million primary particles are simulated under the mode P E (the transport of electrons and photons are modelized). The cut-off energy for the photon is set equal to 1 keV into the entire simulated geometry. The cut-off energies for the electron are respectively equal to 50, 700 and 100 keV for the source, the walls of the irradiator and for the others areas. No specific variance reduction technique was used.
RESULTS
The data calculated by PenEasy, with the tallies F4 and *F8 methods, are summarized respectively into the following tables 1 and 2. Note the great increase in uncertainty associated with Monte Carlo calculations compared to the previous tally.
The data calculated by MCNP4C with the tallies F4 and F5 are presented into the following tables 3 and 4.
Table 4. Summary of the results calculated with MCNP4C (Tally F5). The air kerma are determinated as the product of the photon fluence by the conversion coefficients (see table 2 of the problem P4).
Table 3. Summary of the results calculated with MCNP4C (Tally F4). The air kerma are determinated as the product of the photon fluence by the conversion coefficients (see table 2 of the problem P4).
Table 2. Summary of the results calculated with the program PenEasy (PENELOPE 2005). The air kerma are determinated as the energy deposited into the spherical detector divided by the mass of the detector.
Table 1. Summary of the results calculated with the program PenEasy (PENELOPE 2005). The air kerma are determinated as the product of the photon fluence by the conversion coefficients (see table 2 of the problem P4).
Figure 1: Cut view of the geometric model used by PenEasy to simulate the 137Cs irradiator (with the software Gview3D).
DISCUSSION
Compared to Monte Carlo uncertainty, a relatively good agreement is observed between the data calculated by PenEasy tally F4 and MCNP tally F5 except for the radial shift of the source. These two sets have the lowest Monte Carlo uncertainty.
This variation is not seen for the value obtained by MCNP with the tally F4 (the data are compatible for all the studied cases), nor with PenEasy tally F4 with cylinders of radii ranging from 2, 4 to 8 mm remaining in the field of direct vision of the source (same order of magnitude but with a higher uncertainty than with the sphere detector case).
Who rightly?: the most precise approach or the method employed?. Lastly, the results obtained by PenEasy with the tally *F8 shows only one significant variation (the opening collimating diameter) with the data calculated by PenEasy Tally 4. The ΔK value is almost 5 times smaller.
The reader will pay attention to the index of uMC/ΔK which must be lower than 0.1 to be valid. As an indication, the ratio ΔKair/ΔK is indicated. It will be noticed that this criterion can give different information: for a poor Monte Carlo uncertainty, the ratio ΔKair/ΔK could be less or equal to 0.1 (same requirement as uMC/ΔK). Contrary, a good Monte Carlo uncertainty could be associated in some cases to a poor uncertainty on the ratio ΔKair/ΔK.
REFERENCES
[1]
[2] F. Salvat, J.M. Fernandez-Varea, J. Sempau, PENELOPE – A code system for Monte Carlo simulation of Electron and Photon transport, Workshop Proceedings Issy-les-Moulineaux, France, ISBN , (2003).
[3] J.F. Breismeister, MCNP, A General Monte Carlo N-particle Transport Code – Version 4C, Manual LA M, (2000).
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