Nernst advection and the field-generating thermal instability revisited

Abstract

It is widely held that the Nernst effect can drive instability in un-magnetised laser-plasmas by laterally compressing seed B-fields arising from the field-generating thermal instability [Tidman & Shanny, Phys. Fluids, 12:1207 (1974)]. Indeed, for wavelike perturbations, differential compression by the Nernst mechanism is thought to be most pronounced in the limit of low wave-number k → 0, and is considered particularly important given that it can ostensibly lead to instability when the more usual field-generating mechanism is stable. However, as part of a recent article [Bissell et al., New J. Phys., 15:025017 (2013)] we noted some irregularities to the Nernst mechanism which obscure its operation. For example, by taking characteristic density and temperature length-scales l_n and l_T respectively, we observed that consistent analytical treatment of the instability requires kl_n,T ≫ 1, preventing the peak-growth limit k → 0. Furthermore, the Nernst term—which compresses magnetic field perturbations—does not couple to a corresponding term acting on thermal perturbations, and as such does not describe an unstable feedback mechanism. In this article we probe the origin of such ambiguities more formally, and in so doing argue (contrary to reports existing elsewhere in the literature) that the Nernst effect does not drive instability in un-magnetised conditions, at least not in the fashion typically cited.