440 ISSN 1063-780X, Plasma Physics Reports, 2016, Vol. 42, No. 5, pp. 440–449. © Pleiades Publishing, Ltd., 2016. Analytical and Numerical Treatment of Resistive Drift Instability in a Plasma Slab 1 V. V. Mirnov, J. P. Sauppe, C. C. Hegna, and C. R. Sovinec University of Wisconsin-Madison and the Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas, Madison, WI, USA e-mail: vvmirnov@wisc.edu Received October 22, 2015 Abstract—An analytic approach combining the effect of equilibrium diamagnetic flows and the finite ion- sound gyroradius associated with electron−ion decoupling and kinetic Alfvén wave dispersion is derived to study resistive drift instabilities in a plasma slab. Linear numerical computations using the NIMROD code are performed with cold ions and hot electrons in a plasma slab with a doubly periodic box bounded by two perfectly conducting walls. A linearly unstable resistive drift mode is observed in computations with a growth rate that is consistent with the analytic dispersion relation. The resistive drift mode is expected to be sup- pressed by magnetic shear in unbounded domains, but the mode is observed in numerical computations with and without magnetic shear. In the slab model, the finite slab thickness and the perfectly conducting bound- ary conditions are likely to account for the lack of suppression. DOI: 10.1134/S1063780X16050123 1. INTRODUCTION Numerical modeling of two-fluid current-driven tearing modes in the presence of a pressure gradient [1] have revealed a fluctuation that is destabilized by diamagnetic effects even in the absence of magnetic shear. Linear computations using the NIMROD code are performed for plasma slab with cold ions and hot electrons in a doubly periodic box bounded by two perfectly conducting walls. Within this computational model, configurations with magnetic shear were shown to be unstable to current-driven drift-tearing instability. Our work was originally motivated by a desire to understand the behavior of the drift-tearing mode as it transitions from the collisional to semi-col- lisional regimes. Previous authors [2, 3] studied this in a periodic domain, and we sought to understand the transition in a bounded domain with perfectly con- ducting walls, while also including the effects of finite electron thermal conduction. In addition to the drift- tearing mode, when performing these simulations we observe another linearly unstable mode driven by the pressure gradient, which we identify as a resistive drift mode. The resistive drift instability, also known as the dis- sipative drift instability, was originally described in the potential approximation by S.S. Moiseev and R.Z. Sagdeev in [4]. A comprehensive electromag- netic theory of this instability was presented by A.B. Mikhailovskii in his fundamental work [5]. In that paper, he performed a self-consistent analysis of the electron temperature perturbations and derived an elegant condition for validity of the electrostatic approximation. The electromagnetic fluid model was later extended by Mikhailovskii to kinetic calculations with the use of the model collisional operator [6]. This allowed the author to investigate the transition from rare to frequent collisions and obtain a unified picture of the drift-Alfvén instability at arbitrary collisionality. Following Mikhailovskii’s works [5, 6], we present in this paper the analytical and computational results related to the electromagnetic resistive drift-Alfvén instability. Inclusion of finite resistivity is a key element in numerical modeling of both drift-tearing and dissipa- tive drift instabilities. In the drift wave case considered in the present paper, if the electrons are free to move along the magnetic field to cancel the charge separa- tion, the Boltzmann distribution (adiabatic response) is provided and the drift wave is stable. When the elec- tron motion is delayed by electron−ion collisions, a phase shift appears that results in instability. The resis- tive drift instability occurs on temporal and spatial scales that differ from those inherent to the drift-tear- ing modes. This motivated our interest in the develop- ment of a model where both instabilities can be con- sidered within the scope of one equilibrium configura- tion and dynamical framework. An additional motivating factor emerges from the series of preceding papers [2, 3, 7]. In spite of the sim- ilarity of our equilibrium configurations, observations 1 The article is published in the original. WAVES AND INSTABILITIES IN PLASMA