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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.
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