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. For a constant driving force, the system is found to approach, after transient oscillations, a steady state which is maintained by one wave at the driving frequency. This is in contrast to the result in the absence of collisions where the steady state tends to be supported by several waves. An analytical solution for the steady-state distribution function in the presence of a driven large-amplitude wave is obtained by a Hamiltonian approach. The distribution function is expanded in powers of a small parameter Γ proportional to the collision strength. From the expansion, the zeroth order term is shown to give the space-averaged distribution function correct to first order in Γ. Comparison with the results of the simulations and of the harmonics expansion method shows that the solution estimates the distribution with good accuracy. The plateau in the wave trapping regime is analyzed, and the current driven by the large-amplitude traveling wave is determined