s SRNA 3D Monte Carlo proton simulation Radovan D. Ilic Institute of Nuclear Sciences Vin~a

1. sSRNA3D Monte Carlo proton simulation Radovan D. Ilic Institute of Nuclear Sciences Vin~a Physics Laboratory. (010) Beograd, Yugoslavia Dubrovnik 2001

2. protontherapy The accelerator installation TESLA in Vin~a Nuclear Sciences Institute will produce protons of energies up to 30 MeV on the first, and up to 70 MeV on the second channel. On both channels, advanced experiments need numerical simulation of protons passage through different materials. The accelerator target geometry is usually complex, and protons arrive on targets with arbitrary spectrum. It is reasonable to accept that this geometry can be presented with planes and second order surfaces by RFG code. Inside this geometry, appear materials of different composes - compounds and mixture of elements. Therefore, numerical simulation of proton flow runs in 3D sources and 3D targets.

3. Protons energy on second channel, in the beginning of the program development, has determinate limit of protons energy in the range from 100 keV to 100 MeV. But accelerators elsewhere in the world produce protons up to 250 MeV for various investigation purposes and for tumor therapy. Because of need for wide international cooperation, it was necessary that upper limit of protons energy should be 250 MeV. • In proton experiments planing , it is understandable that proton beam is determinate by the shape of a channel, and that targets in beam are space adjustable according to experiment conditions. For numerical experiments, it is reasonable to accept fixed target, and that proton beam should be within space angle of 4p, according to symmetrical axis of a target. • Monte Carlo techniques make possible to record all protons stages, but usually only some of them are of interest. Space distribution of absorbed energy and absorbed energy per target zones are representative groups. That is why the greatest attention has been given to that kind of output data. In most experiments, beam has to be modified by the targets of complex form and contents. Adjustment of protons beam for experiment needs knowledge of space, energy and angular distribution - spectrum on the target. Therefore, it is necessary to record those distributions as well, and to present them graphically to the researcher

4. sSRNA physical model In this model is assumed that protons from the source do not mutually interact, and that they move to target without influence of outside forces. Proton is scattered with atom, and neighbor atoms do not take part in that. Also, it is supposed that material is homogeneous and that there are no changes of its density in process of energy absorption. During protons passage through materials, following processes happen: loss of energy in inelastic and elastic scattering with atoms, and loss of energy in nonelastic nuclear interactions. If protons trajectory is divided into huge number of steps, on each step, protons passage can be simulated according to the Condensed-Random-Walk model.

5. Step length is determinate by conditions of angular distribution and fluctuation of energy loss. Physical picture of these processes is described by ICRU49 functions of stopping power, Moliere's angular distribution, Vavilov's distribution with Sulek's correction per all electron orbits, and Young-Chadwick's cross sections for nonelastic nuclear interactions. ICRU49 tables include (dE/dx) for 74 elements and materials, and for other missing data, Ziegler's analytical methods from his TRIM program are used. Cross sections for nonelastic nuclear interactions were calculated by T2 group in Los Alamos National Laboratory by their GNASH-FKK - A Pree-Equilibrium, Statistical Nuclear-Model Code for Calculation of Cross Section and Emission Spectra. So far, the cross sections are available for O, C, N, Al, Si, Ca and Pb. Hence, simulation of nonelastic nuclear interactions is limited on these elements, for proton energies above 50 MeV. Bellow that energy, under certain conditions, nonelastic nuclear interactions can be disregarded.

6. Simulation model of protons passage is based on two groups of data. The first group contains data for average energy loss, cross sections for nonelastic nuclear interactions from LANL library, and atomic data for exitational potentials. The second group of data serves for inverse angular distribution calculation and for fluctuation distribution of energy loss and also for probabilities of nonelastic nuclear interactions on proton step calculations. Both groups of data are prepared by program SRNADAT, for each material in function of energy and angle. Model is as closer to physical picture of protons passage as data-base of prepared data is denser. Therefore, energy scale above 10 MeV is linear, and below that energy scale is logarithmic. Distributions are inverted with great number (100 - 1000) of values for preselected probabilities to avoid interpolation in simulation.

7. sSRNA algorithm According to physical picture of protons passage and with probabilities of protons transition from previous to next stage, which is prepared by SRNADAT program, simulation of protons transport in SRNA program runs according to usual Monte Carlo scheme: (1) proton from the spectrum prepared for random choice of energy, position and space angle is emitted from the source; (2) proton looses average energy on the step; (3) on that step, proton suffers a huge number of collisions, and its direction changes are randomly chosen from angular distribution; (4) random fluctuation is added to average energy loss; (5) protons step is corrected with data about protons position before and after scattering; (6) there is final probability on step for nonelastic nuclear interaction to happen, and for proton to be absorbed.

8. According to the Chadwick's model, compound nucleus decays with emission of secondary particles: proton, neutron, deuteron, triton, alpha and photon. Energy and angle of particle emission, and factor of multiplication are obtained from appropriate cross sections. Secondary protons are included in simulation as protons from the source. Neutral particles leave the target without interactions. Heavy charged particles are absorbed at place of their creation. History of proton is terminated after leaving target or when proton energy drops to the cutoff energy. Starting number of protons from the source is divided on more then 20 batches for use of statistical central theorem for errors estimation.

9. sSRNA Numerical experiments The numerical experiments with protons from 100 keV to about 50 MeV in arbitrary 3D geometry can be performed by SRNA transport package. SRNA can also treat proton transport above this limit, but only for materials with constitutional elements O, C, N, Al, Si and Pb, or with elements which have nonelastic nuclear reactions threshold greater than 250 MeV (for example H). On this site we present some examples of numerical experiments for comparison with experimental results and simulation results obtained by other programs.

11. sSRNA code status The Monte Carlo SRNA code and the SRNADAT program for probabilities preparation are academically versions for getting experience and upgrading models of probabilities preparation and protons transport . On the base of this, for routine experiment SRNA-2KG, and for advanced protontherapy SRNA-VOX are developing. SRNA-2KG version: proton sources are pencil beams or circular cross-section beams or rectangular cross-section beams. Direction of each beam is within 4p. Geometry of the target is described by planes and surfaces of second order. Within a maximum of 128 geometrical zones it is possible to distribute up to 36 different materials. Time for transport simulation of 10000 protons with energy of 250 MeV in water phantom on the PC 500 MHz is about 0.8 minutes.

12. SRNA-VOX version:Unchanged physical model of proton transport from previous version is adopted for using representative CT data for model density variation in a voxelized geometry. Functional dependence between CT data and materials and their elementary contents gives possibility for transition probabilities preparation by SRNADAT code. One geometry voxel corresponding to all voxels in CT data is a moving voxel in a virtual rectangular net for proton transport. The routine for voxel data calculation in identical or with different density for proton transport is working very fast. Prepared data for protons (energy, x-,y-z- coordinates, cosine and sine of polar and azimuthal angles) on the patient surface in a file SURF.INP is used for simulation. Simulation in this version under the same condition as in the previous version lasts about 0.6 minutes.

13. . Proton beam Yellow 1-20 White 20-50 Red 50-100

14. sReferences [1] Radovan D. Ilic, SRNA - Monte-Karlo vycisleniya dozovyh polej protonov na uskoritele TESLA, The 7th Russian Scientific Conference on Radiation Shielding of Nuclear Facilities, Obninsk, Russia, 22-25 Sept. (1998). [2] Joakim Medin and Pedro Andreo; PETRA - A Monte Carlo Code for the Simulation of Proton and Electron Transport in Water, Karolinska Institutet, Stocholm Univ., Dep. Med. Rad. Physics, Internal Report MSF 1997-1 (1997). [3] Ferrero M.I et all, Monte Carlo Simulation of Protontherapy System for the Calculation of the Dose Distribution in a Patient, TERA 95/4 TRA 14, May (1995). [4] R. D. Ilic, The proton transport by Monte Carlo techniques, Proceeding of the XX Yugoslav radiation protection society (in Serbian), Tara '99, 3-5. November (1999). [5] S. J. Stankovic, R. D. Ilic, M. P. Pesic and P. M. Marinkovic, Neutron emission spectra calculated for proton beam from 10 MeV to 75 MeV at lead target, III Int. Conf. Yugoslav Nucl. Sci., YUNSC'2000, Beograd, 2-5 Oct. (2000) E-mail:rasacale@beotel.yu; http://www.vin.bg.ac.yu/~rasa/hopa.htm