Magnetorotational instabilities in a dusty plasma

Abstract

The charged dust effect on stability of a magnetized rotating plasma is analysed using approximation of immobile dust. In the presence of the dust, a term with the electric field appears in the one-fluid equation of plasma motion. This electric field affects the equilibrium plasma rotation and also gives rise to a family of instabilities of the rotating plasma called dust-induced rotational instabilities (DRIs). The DRIs are related to the charge imbalance between the plasma ions and electrons because of the charged dust. In contrast to the wellknown magnetorotational instability driven by the radially decreasing plasma rotation frequency, the DRI can appear for an arbitrary rotation frequency profile. A mathematical technique for the analysis of the magnetorotational phenomena is presented. It is based on the one-fluid magnetohydrodynamic approach developed for a pure plasma and generalized to include the immobile dust effects. The mode equation and local dispersion relation are derived in terms of the canonical parameters.

Magnetorotational instability in dissipative dusty plasmas

“…which is identical with the dispersion relation derived in Ref. 70. For ⍀ d = 0, the earlier result 4 is recovered.…”

“…As reported in Ref. 70, a new kind of axisymmetric instability, referred to as dustinduced rotational instabilities, which corresponds to low ␤, can be aroused in the absence of differential plasma rotation.…”

“…Recently, dust-induced effect on MRI has attracted attention. 19,70,71 For instance, Mikhailovskii et al 70 studied the MRI in dusty plasmas ͑as opposite to the pure plasmas͒ based on the one-fluid magnetohydrodynamic ͑MHD͒ approach generalized to include the immobile dust effects. The mode equation and local dispersion relation were derived.…”

Density gradient effects on the magnetorotational instability

“…Since that term is proportional to 1/(kL D ), it should be neglected according to the WKB approximation. Consequently, the growth rate expressed in equation (14) becomes zero. However, we are concerned about the density gradient effects on the MRI and hence, we cannot adopt the WKB approximation directly.…”

Magnetorotational instability in a collisionless plasma with heat flux vector and an isotropic plasma with self-gravitational effect

“…After the seminar monograph of Balbus and Hawley 3 in 1991, MRI has attracted more and more attention in terms of theoretical analysis, numerical examination, and experimental observation by taking into account many complex and realistic assumptions such as resistivity, 4 viscosity, 5 the Hall term, 6 dusty grains, 7 and neutrals 8 to investigate how the non-ideal mechanism affects the linear and non-linear properties of MRI. This is due to MRI's important applications on the astrophysical objects such as magnetized accretion disks, 9 protoplanetary disks, 10,11 protostellar and stellar radiative zones, 6,12 core-collapse supernovae, 13 protoneutron stars, 14 and so on (see reviews, for example, Refs.…”