Electric Field Parallel to the Magnetic Field in a Low-Density Plasma

Stationary states of a collisionless plasma in a one-dimensional magnetic mirror field are considered. Reflection and loss of particles in the presence of a parallel electric field are studied. In many cases the density can be expressed by Abelian integral transforms of monoenergetic distributions. The problem of determining the parallel electric field, necessary to maintain quasi-neutrality, is solved for a class of such distributions, and a couple of illustrating examples are presented. A few existence and uniqueness theorems for distributions and fields are proved.