Effect of trapped ions on shielding of a charged spherical object in a plasma

Summary form only given, as follows. The problem of electrostatic shielding around a small spherical collector immersed in plasma, and the related problem of electron and ion flow to the collector, date to the origins of plasma physics. The earliest work by Langmuir was motivated by probe theory, but more recently there has been considerable interest in connection with the physics of "dust grains" in plasma. Theoretical analyses of these problems have generally been based on the assumption that collisions can be neglected, since the mean free path is typically long compared to shielding length scales, i.e. the Debye length lambda-D. However, investigators beginning with Bernstein and Rabinowitz (1959) have speculated that negative-energy trapped ions, created by occasional collisions, might be important. We have performed an analytic calculation of the density of both trapped and untrapped ions, self-consistent with a calculation of the potential. We show that under typical conditions for dust grains immersed in a discharge plasma, trapped ions dominate the shielding cloud in steady state, even in the limit of very long mean free path. In fact, the density of trapped ions in steady state is independent of the mean free path, as pointed out by Goree (1992). The problem depends mainly on two dimensionless parameters, Tn/Te and a/lambda-D, where Tn is the neutral molecule temperature, Te is the electron temperature, and a is the grain radius. The trapped ion density near the grain can be many times larger than the untrapped density in the regime a/sup /spl and//2/lambda-D/sup /spl and//2<\n\n\t\t