Parametric instabilities of Langmuir waves in weak/moderate magnetic fields

Abstract

A general dispersion equation, which describes the parametric instabilities of some electrostatic waves in a weak/moderate magnetic field, is derived. The dispersion equation is solved numerically to study the effects of a moderately intense magnetic field on the parametric instabilities of relatively large amplitude Langmuir waves. A Langmuir pump wave can couple with various low-frequency branches such as lower-hybrid, electron-acoustic, ion-cyclotron, and ion-acoustic branches. The transverse modulational instability is most sensitive to a magnetic field. Even for a Langmuir wave with W̄∼0.1, where W̄ is the ratio of the time-averaged wave energy to the electron thermal energy, some portions of the transverse modulational instability in the direction exactly perpendicular to the external magnetic field are quite easily suppressed. However, some oblique instabilities may be enhanced by a magnetic field. In general, a moderate magnetic field suppresses most of the oblique instabilities, and the parametric instabilities become essentially one dimensional.