Transition from Langmuir-Jeans to Alfvén-Jeans Modes in Dusty Plasmas

Abstract

Dusty plasmas are a mixture of standard plasma components together with charged and heavy dust grains, for which self-gravitational effects might become important. For parallel electrostatic modes Langmuir oscillations combine with the Jeans instability, known from neutral self-gravitating systems, whereas at strictly perpendicular propagation the magnetosonic part of the extraordinary mode couples to the Jeans mode. Spurred by these limiting cases, we investigate oblique waves to show how self-gravitation goes over from parallel electrostatic to perpendicular magnetosonic modes, and give elements of the general dispersion law. The startling conclusion is that the critical Jeans lengths are exactly as derived from parallel electrostatic modes, except very close to perpendicular propagation, where an abrupt transition occurs to the critical lengths determined from the magnetosonic-Jeans modes. Furthermore, the inclusion of neutral dust or gas can drastically shorten the critical Jeans-like length scales.