Stochastic motion of the untrapped particle in electrostatic mode

The stochastic energy diffusion of the untrapped particle in the electrostatic mode is investigated analytically. We find that the equilibrium electrostatic field of periodical structure plays the same role as the usual focusing magnetic field to lead the test particle to stochastic motion. The resonance overlapping criterion for the random state is given, and also the Fokker-Planck-Kolmogorov approach to diffusion is considered for our system. (author)