What is a plasma? A plasma is an ionized gas that consists of charged particles: positive ions and negative electrons. To describe the dynamics of a plasma, let be the (nonnegative) density distribution of ions and electrons, respectively, at time , position , and particle velocity (or momentum) . The dynamics of a plasma is commonly modeled by the Vlasov equations

## Archive for the ‘Plasma Physics’ Category

## Stability of a collisionless plasma

Posted in Kinetic theory, Plasma Physics, tagged Stability theory, Vlasov-Maxwell on September 10, 2015| Leave a Comment »

## Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits

Posted in Instabilities, New papers, Plasma Physics on July 1, 2015| Leave a Comment »

(this post was also posted here on my new blog address:http://blog.toannguyen.org/ )

Daniel Han-Kwan and I have just submitted a paper entitled: “Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits”, which is also available on arxiv: arXiv:1506.08537. In this paper, we study the instability of solutions to the relativistic Vlasov-Maxwell systems in two limiting regimes: the classical limit when the speed of light tends to infinity and the quasineutral limit when the Debye length tends to zero. First, in the classical limit , with being the inverse of the speed of light, we construct a family of solutions that converge initially polynomially fast to a homogeneous solution of Vlasov-Poisson in arbitrarily high Sobolev norms, but become of order one away from in arbitrary negative Sobolev norms within time of order . Second, we deduce the invalidity of the quasineutral limit in in arbitrarily short time.