Nonlinear coupling of electromagnetic and electrostatic modes via density and pressure fluctuations: The case of Weibel instabilities

Abstract

Both the pressure anisotropy-driven Weibel instability and the momentum anisotropy-driven current filamentation instability make a quasi-static magnetic field linearly grow. In some conditions, this growth couples with electrostatic perturbations, and an electrostatic field component growing twice as fast as the magnetic field was noticed since the early numerical simulations of these phenomena. We herein provide an interpretation of this process in terms of the electron density concentration induced by the differential rotation of current filaments around the maxima of the magnetic field. We then discuss how this effect, which is both of second order with respect to the amplitude of the electromagnetic Weibel mode and an ingredient of the linear instability itself, anisotropically couples with fluctuations of the distribution functions associated with the pressure tensor components. The analytical estimates are consistent with nonlinear kinetic simulations performed with both the semi-Lagrangian Vlasov code VLEM and with a reduced multi-stream model for the Vlasov–Maxwell system.