Numerical Simulation of Driven Electron Acoustic Waves.

Eulerian and PIC code simulations of the electron acoustic wave (EAW) are presented. This novel, low amplitude, BGK wave has the approximate dispersion relation $\omega \simeq 1.3 \, \bar{v}_e k$, where $\bar{v}_e$ is the electron thermal velocity and the wave number $k$ is assumed to be small (i.e., $k \lambda_D \ll 1$).\footnote{J.P. Holloway and J.J. Dorning, Phys. Rev. A {\bf 44}, 3856 (1991).} Within linear theory, the wave is heavily Landau damped, but the damping does not occur for a BGK wave since the electron distribution is flat (i.e., $\partial f_e / \partial v = 0$) in the immediate vicinity of the phase velocity. Simulations of a collisionless plasma show that an EAW is excited by a low amplitude resonant driver if the driver is applied over a long enough time (several trapping periods). When collisions are included in the simulation, successful excitation requires a sufficiently large driver amplitude. The trapping period for the driver must be short compared to an effective collision time--the time for small-angle Coulomb scattering to produce velocity diffusion over the width of the trapped-particle plateau.