The Hall instability of thin weakly-ionized stratified Keplerian disks

Abstract

The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio. The leading order of the asymptotic expansions in the aspect ratio is applied to both equilibrium as well as the perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial, and unstable to vertical short-wave perturbations. The marginal stability surface is found in the space of the local Hall and inverse plasma beta parameters, as well as the free parameter of the model which is related to the total current through the disk. To estimate the minimal values of the equilibrium magnetic field that leads to instability, the latter is constructed as a sum of a current free magnetic field and the simplest approximation for magnetic field created by a distributed electric current.

13 pages, 7 figures

References in corpus (9)

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• Linear Analysis of the Hall Effect in Protostellar Disks
• The Balbus-Hawley instability in weakly ionised discs
• The ionization fraction in alpha-models of protoplanetary disks
• Numerical simulations of mass outflows driven from accretion disks by radiation and magnetic forces
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Cited by in corpus (6)

• Hall equilibrium of thin Keplerian disks embedded in mixed poloidal and toroidal magnetic fields
• Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs
• Resonant instability of the nonlinearly-saturated magnetorotational mode in thin Keplerian discs
• The Magneto-Rotational Decay Instability in Keplerian Disks
• Current-driven instabilities in weakly ionized disks
• Explosive magnetorotational instability in Keplerian disks