Of great interest is to resolve the Final State Conjecture of charged particles in the kinetic theory of plasma physics (borrowing words from general relativity, though amusingly lesser mathematical progress is made for the case of plasmas!), asserting the scattering to neutrality in the far field plus a superposition of coherent states or trapped particles, and identifying relaxation mechanism plays a fundamental role in resolving the conjecture. Despite an extensive list of works in the mathematical literature towards the understanding of the large-time dynamics of non-relativistic plasmas (already encoding extremely rich underlying physics and challenging mathematics – see Survival Threshold), very little is known in the case of relativistic plasmas, including the basic question of whether stable equilibria exist, not to mention the apparent lack of study on relaxation mechanism. In this blog article, I shall highlight my recent joint work with D. Han-Kwan (CNRS, Nantes) and F. Rousset (Paris-Sud, Orsay) which resolved the linear stability theory of relativistic plasmas near radial spatially homogenous equilibria, the first such a result, paving the waves for many possible future advances on the subject.
Figure: Depicted is a description of phase mixing on torus (in the whole space, particles simply scatter away), one of the key relaxation mechanisms in plasma physics.
, which reads
, with the relativistic velocity 
.
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