Coupling between upper-hybrid waves and electron holes in Earth’s magnetotail

Abstract

An analytic theory of the nonlinear interaction between electrostatic high-frequency upper-hybrid waves and the low-frequency electron holes in a magnetized plasma is presented. It provides an explanation for the simultaneous occurrence of upper-hybrid bursts and electron holes, observed recently by the WIND and CLUSTER spacecrafts in the vicinity of the X point during the collisionless reconnection in Earth’s deep magnetotail. Using a fluid description for the high-frequency mode and a drift-kinetic description for the low-frequency mode, a Zakharov-type system of equations is obtained that describes the interaction between the upper-hybrid and lower-hybrid waves in the presence of an oblique Buneman instability and resonant electrons. The saturation of the linear and explosive parametric instabilities is shown to result from the electron trapping in the combined low-frequency and ponderomotive potentials, yielding an oblique lower-hybrid hole. The presence of an electron hole produces the localization of the upper-hybrid waves, yielding either a bright nonlinear Schrödinger soliton trapped inside the hole or a dark soliton driven by the defocusing nonlinear Schrödinger nonlinearity, which is trapped outside of the hole.