Unstable Disturbances in Flows of Dusty and Self-Gravitational Plasmas

Abstract

Stationary magnetic, electric or gravitation fields are nearly always present in space, affecting the motion of different kinds of particles in different ways. Quite often, the result may be a relative motion of particles. Consider, for example, the vicinity of a magnetized planet. For heavy particles near the planet, gravity prevails independently of their electric charge, and hence such particles move through the gravitation field of the central body in accordance with Kepler’s laws. Contrary to this, the motion of microparticles (i.e. electrons and ions) is governed by electromagnetic forces greatly exceeding the gravitation. In most cases, the microparticles are entrained by the planetary magnetic field and corotate with the planet. As for electrically charged dust grains, they “feel” both gravitation and electromagnetic forces. As a result, the macroscopic particles do not move around the planet at the Kepler velocity VK but rather at a somewhat different velocity V₀,_α. The difference δV _α = V₀,_α ‒ V _K is determined by the charge/mass ratio, hence it may vary for particles with different Q _α /m _α even at the same orbit. In particular, the linear velocity of a particle of species α moving along an equatorial-plane circular orbit of radius R is

$$ {V_{0,\alpha }} \simeq {V_k}\left[ {1 + \frac{{{\Omega _{B,\alpha }}}}{{2\Omega _k^2}}({\Omega _k} - {\Omega _p})} \right] $$

((1))

(cf. Equation (33) of Chapter 2).