Stochastic theory of planar channeling

Starting from the first principles the analysis of stochastic properties of random forces acting on the charged particle channeled in planar channels due to thermal vibrations of crystal atoms and electron scattering has been done. The Fokker-Planck equation for the distribution function describing the state of channeled particles is built basing on the correlation functions of those forces and using usual methods of the stochastic processes theory. The dechanneling problem is solved as a particular case of the more general problem of the mean life-time determination for an arbitrary dynamic system under random forces influences. The simple analytical formulae are obtained for the particles distribution functions upon the transverse coordinate and energy as well as for the dechanneling length and dechanneling function (the normalized yield). The validity of the theory is verified by comparison of appropriate calculations for 0.5 / 12 MeV protons channeling in the { 110 } planar channels of tungsten crystal with the experimental data by Davies et al