Theory of a spherical probe in a collisionless magnetoplasma

Abstract

A theory is presented for a spherical electrostatic probe in a collisionless, Maxwellian plasma containing a uniform magnetic field. The theory yields two upper bounds and an adiabatic limit for collection of the attracted particle species (either electrons or ions). For the repelled species, it yields a lower and an upper bound. The theory is similar in concept to existing theories for cylindrical probes by Laframboise and Rubinstein. It is applicable when the ratio of probe radius to Debye length is small enough, and/or the probe potential is large enough, that no potential barriers exist near the probe. Otherwise, a theory of Sanmartin applies. The attracted-particle current in the adiabatic limit, i.e., when mean gyroradius≪Debye length, shows negative-resistance behavior. One of the upper bounds is based on the use of particle canonical angular momentum conservation to define allowed and forbidden regions for particle orbits, and generalizes an existing theory by Parker and Murphy to include particle thermal motion.