Geodesic
Stochastic model of ultrarelativistic electrons passage through a~thick monocrystals
Matematičeskoe modelirovanie, Tome 12 (2000) no. 9, pp. 25-44.

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The model of electron dynamics is suggested for the high-energy beam passing through crystal, taking into account axial channeling, multiple scattering and radiation. The model represents homogenous Markov process with diffusion and jump components, described by a stochastic differential equation. Here diffusion corresponds to dissipation and jumps correspond to radiation of $\gamma$-quanta. This description is convenient for numerical calculations not only for passage but for other physical characteristics that are functional of Markov process paths, in particular for characteristics of radiation. 
@article{MM_2000_12_9_a2,
     author = {A. V. Lukshin and A. K. Maslov and I. V. Polimatidi and S. N. Smirnov},
     title = {Stochastic model of ultrarelativistic electrons passage through a~thick monocrystals},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {25--44},
     publisher = {mathdoc},
     volume = {12},
     number = {9},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2000_12_9_a2/}
}
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A. V. Lukshin; A. K. Maslov; I. V. Polimatidi; S. N. Smirnov. Stochastic model of ultrarelativistic electrons passage through a~thick monocrystals. Matematičeskoe modelirovanie, Tome 12 (2000) no. 9, pp. 25-44. http://geodesic.mathdoc.fr/item/MM_2000_12_9_a2/