Theoretical methods for the calculation of Bragg curves and 3D distributions of proton beams

Details Theoretical methods for the calculation of Bragg curves and 3D distributions of proton beams Theoretical methods for the calculation of Bragg curves and 3D distributions of proton beams

2010-08-21

arxiv.org/abs/1008.3645v1

Eur.Phys.J.ST 190:1-81,2010

Physics

Medical Physics

97 pages review paper

Scientific paper

10.1140/epjst/e2010-01335-7

The well-known Bragg-Kleeman rule RCSDA = A dot E0p has become a pioneer work in radiation physics of charged particles and is still a useful tool to estimate the range RCSDA of approximately monoenergetic protons with initial energy E0 in a homogeneous medium. The rule is based on the continuous-slowing-down-approximation (CSDA). It results from a generalized (nonrelativistic) Langevin equation and a modification of the phenomenological friction term. The complete integration of this equation provides information about the residual energy E(z) and dE(z)/dz at each position z (0 <= z <= RCSDA). A relativistic extension of the generalized Langevin equation yields the formula RCSDA = A dot (E0 +E02/2M dot c2)p. The initial energy of therapeutic protons satisfies E0 << 2M dot c2 (M dot c2 = 938.276 MeV), which enables us to consider the relativistic contributions as correction terms. Besides this phenomenological starting-point, a complete integration of the Bethe-Bloch equation (BBE) is developed, which also provides the determination of RCSDA, E(z) and dE(z)/dz and uses only those parameters given by the BBE itself (i.e., without further empirical parameters like modification of friction). The results obtained in the context of the aforementioned methods are compared with Monte-Carlo calculations (GEANT4); this Monte-Carlo code is also used with regard to further topics such as lateral scatter, nuclear interactions, and buildup effects. In the framework of the CSDA, the energy transfer from protons to environmental atomic electrons does not account for local fluctuations.

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