Nernst advection and the field-generating thermal instability revisited

Abstract

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. It is widely held that the Nernst effect can drive instability in un-magnetised laserplasmas by laterally compressing seed B-fields arising from the field-generating thermal instability [Tidman & Shanny, Phys. Fluids, 12:1207]. 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.PACS codes: Authors should not enter PACS codes directly on the manuscript, as these must be chosen during the online submission process and will then be added during the typesetting process (see http://www.aip.org/pacs/ for the full list of PACS codes)

Suppression of the Biermann Battery and Stabilization of the Thermomagnetic Instability in Laser Fusion Conditions

“…For example, onset of the thermomagnetic instability has been proposed as one of the main causes of filamentary structures in coronal plasmas, and as an explanation behind the need for thermal flux inhibition when interpreting laser-plasma experiments [8][9][10][11]. Despite these important applications, however, studies of the instability have been limited to classical linear models, unsupported by numerical simulation, meaning that the relevance of the thermomagnetic mechanism to non-local, laser-fusion conditions has remained largely untested [6,7,[14][15][16][17]. It has long been known, for example, that classical transport models of laser-plasma coronas are invalid (because the plasma is typically so hot and rarefied that the electron mean-free-path λ ei is large compared to system scale-lengths), and under these conditions kinetic simulations become essential [12,25].…”

“…Growth-rates γ can be derived from a linear perturbation analysis of the classical transport equations [1] assuming δT, δB z ∝ exp(γt + iky), with wavenumber k [14][15][16]. In this way one obtains the dispersion relation…”

“…where log Λ ei is the Coulomb logarithm, v T = λ ei /τ ei = (2T e /m e ) 1/2 the thermal velocity, ǫ 0 the permittivity of free space, Z the atomic number, and n i ≈ n e /Z the ion number density [14]. The transport coefficients-the resistive diffusivity α ⊥ , the thermal diffusivity κ ⊥ , the Righi-Leduc coefficient κ ∧ , and the Nernst coefficient β ∧ -are dimensionless functions of Z, and the Hall parameter χ ≡ ω L τ B , with ω L = e|B|/m e ; these coefficients are expected to be strongly affected by non-local conditions [12,15,25].…”

“…Crucially for our study, the analysis used to derive equation ( 1) makes assumptions which will not hold rigorously in practical contexts [14]. For example, the Biermann term scales as…”

Thermomagnetic instability of plasma composition gradients

“…The spatial variation of the instability growth rate will naturally lead to x dependence of B 1 , invalidating this assumption. For a proper treatment of the Nernst advection, it is therefore necessary to retain the x dependence of the perturbed quantities, requiring a global two-dimensional x-y analysis 33 . This does not lead to a simple closed form linearized growth rate.…”