Long-Time Behavior of Nonlinear Landau Damping

The evolution of an initial perturbation in a collisionless, Maxwellian plasma is studied numerically. Accurate long-time simulations (up to 1600 inverse electron plasma frequencies) show that the electric field does not decay to zero, in disagreement with recent analytical results [M. B. Isichenko, Phys. Rev. Lett. 78, 2369 (1997)]. Instead, after some initial damping, the field amplitude starts to oscillate around an approximately constant value, and the phase-space distribution develops a vortex structure which survives throughout the simulation.