Linear Vlasov Theory in the Shearing Sheet Approximation with Application to the Magneto-Rotational Instability

Abstract

We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to differentially rotating plasmas and can be used for wide range of kinetic stability calculations. We apply these results to the linear theory of the magneto-rotational instability (MRI) in collisionless plasmas. We show analytically and numerically how the general kinetic theory results derived here reduce in appropriate limits to previous results in the literature, including the low frequency guiding center (or "kinetic MHD") approximation, Hall MHD, and the gyro-viscous approximation. We revisit the cold plasma model of the MRI and show that, contrary to previous results, an initially unmagnetized collisionless plasma is linearly stable to axisymmetric perturbations in the cold plasma approximation. In addition to their application to astrophysical plasmas, our results provide a useful framework for assessing the linear stability of differentially rotating plasmas in laboratory experiments.

arXiv commentThis new version includes the changes mentioned in the erratum to the published version. 27 pages, 5 figures. Published in ApJ. The source code needed for reproducing the entire paper including the numerical data is available at http://github.com/tobson/vlasov-sheet

References in corpus (10)

• Linear Analysis of the Hall Effect in Protostellar Disks
• The Balbus-Hawley instability in weakly ionised discs
• Plasma instabilities and magnetic-field growth in clusters of galaxies
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• The Magnetorotational Instability in a Collisionless Plasma
• Viscous Shear Instability in Weakly Magnetized, Dilute Plasmas
• A nonlinear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma
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Cited by in corpus (8)

• Magnetorotational Turbulence and Dynamo in a Collisionless Plasma
• Laboratory Space Physics: Investigating the Physics of Space Plasmas in the Laboratory
• Braginskii viscosity on an unstructured, moving mesh accelerated with super-time-stepping
• Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability
• Linear Vlasov theory of a magnetised, thermally stratified atmosphere
• Onset of magnetic reconnection in a collisionless, high-beta plasma
• Spectral Analysis of Non-Ideal MRI Modes: The effect of Hall diffusion
• Spontaneous magnetization of collisionless plasma through the action of a shear flow