Local Stochastic Channeling Theory: Kinetic Functions in the Case of Interaction Between Fast Particles and Lattice Atoms

We investigate the motion of high-energy particles in a crystal with regard to their interaction with the thermal vibrations of the lattice atoms using analytic methods in the theory of Markov processes including the local Fokker–Planck equation. We construct a local matrix of random actions, which is used to introduce the main kinetic functions in the traverse-energy space, namely, the function $a(\varepsilon_{\perp})$ of energy losses due to the dynamic friction and the diffusion function $b(\varepsilon_{\perp})$. We show that the singularities of the functions $a(\varepsilon_{\perp})$ and $b(\varepsilon_{\perp})$ are related to the distinction between the contributions to the kinetics from particles moving in three different regimes, namely, in the channeling, quasichanneling, and chaotic motion modes.