EFFECT OF A LARGE-AMPLITUDE WAVE ON THE ONE-DIMENSIONAL VELOCITY DISTRIBUTION OF PARTICLES IN A LINEARIZED FOKKER-PLANCK COLLISIONAL PLASMA

The evolution of a one-dimensional velocity distribution is studied in the presence of a monochromatic large-amplitude periodic force which is turned on adiabatically. The periodic Vlasov-Poisson equations are solved in the presence of a linearized Fokker-Planck collision term. F or a constant driving force, the system is found to approach, after tr ansient oscillations, a steady state which is maintained by one wave a t the driving frequency. This is in contrast to the result in the abse nce of collisions where the steady state tends to be supported by seve ral waves. An analytical solution for the steady-state distribution fu nction in the presence of a driven large-amplitude wave is obtained by a Hamiltonian approach. The distribution function is expanded in powe rs of a small parameter Gamma proportional to the collision strength. From the expansion, the zeroth order term is shown to give the space-a veraged distribution function correct to first order in Gamma. Compari son with the results of the simulations and of the harmonics expansion method shows that the solution estimates the distribution with good a ccuracy. The plateau in the wave trapping regime is analyzed, and the current driven by the large-amplitude traveling wave is determined.