Kinematics of electrostatic 3-wave decay of generalized Langmuir waves in magnetized plasmas

Abstract

The decay of generalised Langmuir waves L into backscattered (generalised) Langmuir waves L and ion acoustic waves S or ion cyclotron waves IC, represented by L→L′+S and L→L′+IC, is a fundamental nonlinear process relevant to beam-plasma instabilities in space and laboratory plasmas and to multiple solar system radio emissions. Both magnetization and arbitrary wavevector directions are included for the generalised Langmuir waves, thereby naturally encompassing both conventional Langmuir waves and upper hybrid waves. A recent 1D analysis for L waves with wavevectors closely parallel to the ambient magnetic field B0 in weakly magnetized plasma (angular electron cyclotron frequency Ωe much less than the angular electron plasma frequency ωp) showed that the electrostatic (ES) decay L→L′+S persists for kL<k0, reversing the old prediction based on the unmagnetized dispersion relation. Here, the kinematics for the processes L→L′+S and L→L′+IC are derived in 2 dimensions for approximately electrostatic waves in arbitrary magnetized plasmas and for all wavevector orientations relative to B0. ES decay processes are shown to exist in both weakly and strongly magnetized plasmas and, under most circumstances, for arbitrary L-wavevector directions, including close to perpendicular to B0, and wavenumbers. For L-wavenumbers kL≳2k0, the decay process is very similar to the standard unmagnetized decay for kL close to parallel with B0, proceeding primarily as a backscatter to kL′≈(kL−k0)kL/kL and a trivial forward-scatter solution with kL≈kL. (Here, k0=2ωpvS/3Ve2, VS is the ion acoustic speed, and Ve is the electron thermal speed.) In addition, the decay persists for kL<k0 to very small kL′≈k*=(ωp/c)(1+fp/fce)−1/2 for arbitrary magnetizations and orientations of kL relative to B0, at least for sufficiently large ion-to-electron temperature ratios Ti/Te. Thus, once magnetization effects are included, the decay is kinematically allowed for essentially all initial wavevectors and can proceed for the very fast beams (with kL<k0) for which modulational instability and not ES decay was previously expected to dominate the nonlinear evolution.