Study of nonlinear landau damping and formation of Bernstein-Greene-Kruskal structures for Collisionless, 1D Plasmas

Abstract

In the past, long-time evolution of an initial perturbation in collisionless Maxwellian plasma (q = 1) has been simulated numerically. The controversy over the nonlinear fate of such electrostatic perturbations was resolved by Manfredi[G. Manfredi, Phys. Rev. Lett. 79, 2815-2818 (1997)] using long-time simulations up to t = 1600 . The oscillations were found to continue inde nitely leading to BGK-like phase-space vortices (from here on referred to as `BGK structures'). Using a newly developed, high resolution 1D Vlasov-Poisson solver based on Piecewise-Parabolic Method (PPM) advection scheme, we investigate the nonlinear Landau damping in 1D plasma described by toy q-distributions for long times, up to t = 3000 . We show that BGK structures are found only for a certain range of q-values around q = 1. Beyond this window, for the generic parameters, no BGK structures were observed. We observe, that for values of q < 1 where velocity distributions have long tails, strong Landau damping inhibits the formation of BGK structures. On the other hand, for q > 1 where distribution has a sharp fall in velocity, the formation of BGK structures is rendered diffcult due to high wave number damping imposed by the steep velocity pro le, which had not been previously reported. Wherever relevant, we compare our results with past work.