Acceleration of charged particles by stochastic electrostatic waves

The velocity change of charged particles in a one dimensional electrostatic stochastic wave is investigated analytically. The reaction of the particle back on the wave is not taken into account. One model adopted is a wave, the phase of which is completely randomized after time intervals of length tau . The other model considers particles moving in fields of slowly changing amplitude so that their adiabatic invariant is conserved. Only untrapped particles are considered. In the frame where the wave is at rest, all particles are decelerated.