Math. Meth. in the Appl. Sci. 15, 365 - 374 (1992)
Existence of stationary, collisionless plasmas
on bounded domains
G. Rein
We consider a collisionless plasma, which consists of electrons and positively
charged ions and is confined to a bounded domain in R³. The distribution
functions of the particles are assumed to satisfy
specular reflections on the boundary
of the domain and the boundary
is assumed to be perfectly conducting. We establish
the existence of stationary plasmas in the non-relativistic,
electrostatic case described
by the Vlasov-Poisson system as well as in the relativistic,
electrodynamic case
described by the relativistic Vlasov-Maxwell system.
Gerhard Rein (rein@rz.mathematik.uni-muenchen.de)