Plasma instability at the inner edge of the accretion disk—I

In this paper, the analytical and numerical results of the stability analysis of the accretion disk at the inner boundary is presented. Including the effect of finite conductivity in the disk dynamics, a simple calculation considering only the radial perturbation has been carried out. Within local approximation, it is concluded that the disk is stable to Kelvin-Helmholtz and resistive electromagnetic modes whereas the magnetosonic mode can destabilise the disk structure.     

Plasma instability at the inner edge of the accretion disk— II

A two-dimensional instability analysis for a magneto-keplerian disk flow around a compact object is presented here. Using the eigenvalue technique, linearly coupled perturbed equations have been numerically solved within the local approximation. It is concluded that Kelvin-Helmholtz, magnetosonic (fast and slow) and resistive electromagnetic modes exist. However, only the magnetosonic mode can destabilise the disk structure. Further, we discuss the properties of different modes as a function of disk parameters and plot the eigenmode structures for different physical quantities.     

Magnetic field structure in differentially rotating discs

Abstract

In order to gain a better understanding of the processes that may give rise to non-axisymmetric magnetic fields in galaxies, we have calculated field decay rates for models with a realistic galactic rotation curve and including the effects of a locally enhanced turbulent magnetic diffusivity within the disc. In all cases we have studied, the differential rotation increases the decay rate of non-axisymmetric modes, whereas axisymmetric ones are unaffected. A stronger magnetic diffusivity inside the disc does not lead to a significant preference for non-axisymmetric modes. Although Elsasser's antidynamo theorem has not yet been proved for the present case of a non-spherical distribution of the magnetic diffusivity, we do not find any evidence for the theorem not to be valid in general.     

Subharmonic oscillations of a forced hydromagnetic cavity

Abstract

We study the propagation of nonlinear MHD waves in a highly magnetized plasma cavity. The cavity's moving boundaries generate Alfvén waves, which in turn drive and interact with slow magnetosonic waves. The interacting wave system is analyzed by a Galerkin and multiple-scale analyses leading to simple dynamical equations. When the frequency of the forcing provided by the moving boundaries and that of the fundamental Alfvén eigenmode are close, the cavity behaves like a Duffing oscillator. Application of the Melnikov function theory shows that the Alfvén wave's amplitude undergoes both flip and saddle-node bifurcations as the amplitude and the phase of the boundary forcing vary. Direct numerical integration confirms these results and provides an estimate of the amount of energy dissipated in the bifurcations.