Mechanism of Fermi acceleration in dispersing billiards with time-dependent boundaries

The paper is devoted to the problem of Fermi acceleration in Lorentz-type dispersing billiards whose boundaries depend on time in a certain way. Two cases of boundary oscillations are considered: the stochastic case, when a boundary changes following a random function, and a regular case with a boundary varied according to a harmonic law. Analytic calculations show that the Fermi acceleration takes place in such systems. The first and second moments of the velocity increment of a billiard particle, alongside the mean velocity in a particle ensemble as a function of time and number of collisions, have been investigated. Velocity distributions of particles have been obtained. Analytic and numerical calculations have been compared. Zh. éksp. Teor. Fiz. 116, 1781–1797 (November 1999)