The existence of stable BGK waves

TL;DR

This paper constructs the first examples of linearly stable BGK waves in the 1D Vlasov-Poisson system, addressing a long-standing open problem about their stability and potential role as attractors in plasma dynamics.

Contribution

It provides the first explicit construction of linearly stable BGK waves near homogeneous states in the Vlasov-Poisson system.

Findings

First stable BGK waves constructed near homogeneous states

Addresses the open problem of stability of BGK waves

Enhances understanding of plasma long-term behavior

Abstract

The 1D Vlasov-Poisson system is the simplest kinetic model for describing an electrostatic collisonless plasma, and the BGK waves are its famous exact steady solutions. They play an important role on the long time dynamics of a collisionless plasma as potential "final states" or "attractors", thanks to many numerical simulations and observations. Despite their importance, the existence of stable BGK waves has been an open problem since their discovery in 1958. In this paper, first linearly stable BGK waves are constructed near homogeneous states.