s SRNA 3D

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s SRNA 3D Monte Carlo proton
simulation Radovan D. Ilic Institute of Nuclear
Sciences Vina Physics Laboratory. (010) Beograd,
Yugoslavia
Dubrovnik 2001
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protontherapy

• The accelerator installation TESLA in Vina
  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.

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• 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

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s SRNA 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.

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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.
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• 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.

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s SRNA 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.

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• 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.

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s SRNA 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.

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s SRNA 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.

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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.
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• .

Proton beam
Yellow 1-20 White 20-50 Red 50-100
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s References

• 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_at_beotel.yu
• http//www.vin.bg.ac.yu/rasa/hopa.htm