Eur. Phys. J. D (2014) 68: 363
https://doi.org/10.1140/epjd/e2014-50170-y

Regular Article

Instability conditions for some periodic BGK waves in the Vlasov-Poisson system^*

¹ Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois St., Golden, 80401 CO, USA
² Space Science Center and Department of Physics, University of New Hampshire, 8 College Rd., Durham, 03824 NH, USA

^a e-mail: pankavic@mines.edu

Received: 2 March 2014
Received in final form: 15 September 2014
Published online: 2 December 2014

Abstract

A one-dimensional, collisionless plasma given by the Vlasov-Poisson system is considered and the stability properties of periodic steady state solutions known as Bernstein-Greene-Kruskal (BGK) waves are investigated. Sufficient conditions are determined under which BGK waves are linearly unstable under perturbations that share the same period as the equilibria. It is also shown that such solutions cannot support a monotonically decreasing particle distribution function.