Stochastic acceleration of charged particles by an electrostatic wave in a magnetized plasma

Nonlinear motion of charged particles in the presence of a uniform magnetic field and of a monochromatic electrostatic wave propagating perpendicularly to the magnetic field is studied. Appearance of islands in phase space is discussed and by taking account of the overlapping of secondary islands, a wave amplitude necessary for the onset of stochasticity is estimated analytically. The results are compared to numerical results. It is shown that high-energy particles are produced most efficiently if the wave frequency is the multiple of the cyclotron frequency. As the wave amplitude increases, numerical calculations show that a steady velocity distribution is insensitive to the wave frequency