Thermo-statistical study of evaporation effects in a non neutral plasma under an imperfect magnetic confinement

Abstract

Experimental studies of non-neutral plasmas in magnetic traps undergo, in some degree of affectation, the incidence of evaporation. For example, the existence of a finite threshold energy for the escaping of plasma constituents can be favored by the external electrostatic forces near the grounded conducting walls of a cylindrical Penning trap. In contrast, the conventional statistical mechanics description of these situations is performed assuming the existence of a rigorous thermodynamic equilibrium (Dubin and O’Neil 1999 Rev. Mod. Phys. 71 87), dismissing thus the existence of evaporation effects. We propose in this work a two-dimensional toy model that describes the incidence of evaporation on thermo-statistics of a pure non-neutral plasma (a system composed of a single charge species like an infinitely long electron column). Considering the existing connections between the macroscopic descriptions of pure non-neutral plasmas and astrophysical systems, the treatment of evaporation along a quasi-stationary regime is developed here in analogy to some astrophysical models proposed in the literature. We start from a regularized microcanonical description that only considers those microscopic configurations where particles are trapped inside a confinement region of radius Rc, which is implemented introducing a truncation of their velocity spectrum. These arguments lead us to a statistical procedure to predict the quasi-stationary particles distribution similar to the maximum entropy approach. According to our analysis, the influence of evaporation for a non-zero temperature T crucially depends on the saturation parameter , whose admissible values are located in the interval , with rB being the radius of Billouin steady state that appears in the limit . The theoretical profiles predicted from this model are then compared to the metastable radial density distribution reported by Huang and Driscoll (1993 Phys. Rev. Lett. 72 2187). This analysis suggests the effects of evaporation in this particular experiment are significant, being these data compatible with the range of values –0.59. To reach a major understanding of this experiment, we analyze the relation between our development and the so-called minimum enstrophy approach, which was invoked by these authors to fit their experimental data. We show that a variant of differential equation for particle density compatible with this extremal principle appears as an asymptotic case of the present proposal.