Ambipolar acceleration of ions in a magnetic nozzle

This paper describes a magnetic nozzle with a magnetic mirror configuration that transforms a collisionless subsonic plasma flow into a supersonic jet expanding into the vacuum. The nozzle converts electron thermal energy into the ion kinetic energy via an ambipolar electric field. The ambipolar potential in the expanding plume involves a time-dependent rarefaction wave. Travelling through the rarefaction wave, electrons lose some kinetic energy and can become trapped downstream from the mirror throat. This work presents a rigorous adiabatic description of the trapped electron population. It examines the impact of the adiabatic cooling of the trapped electrons on the ambipolar potential and the ensuing ion acceleration. The problem is formulated for an arbitrary incoming electron distribution and then a “water-bag” electron distribution is used to obtain a closed-form analytical solution.