Low frequency electrostatic mode generated by electromagnetic waves in the Earth’s inner magnetosphere with two distinct electrons

Abstract

The generation of low frequency electrostatic mode by parametric decay of electromagnetic waves (EMWs) in the Earth’s inner magnetosphere with exponentially truncated kappa distributed hot electrons and cold electrons is studied. Nonlinear dispersion equation for the parametric process is derived from kinetic theory. The parametric instability of EMWs decay into low frequency electrostatic normal mode (ion acoustic like wave modes and electron acoustic wave modes) and electrostatic quasi–mode in the Earth’s inner magnetosphere are numerically analyzed. It is shown that parametric instability occurs only when the EMW is sufficiently strong if the collisions between ions and electrons are taken into account. The growth rate and the threshold conditions of the decay instability depend on the concentration and distribution of hot electrons. Because they change the dispersion and the damping rate of normal mode, the collisional damping of sideband EMW. In addition, the excitation of electrostatic normal mode by parametric decay of EMWs is more difficult than the excitation of electrostatic quasi–mode. The growth rate of EMWs decaying into electrostatic quasi–mode is much larger than the ones of decaying into electrostatic normal mode. But the frequency of electrostatic quasi–mode corresponding to the maximum growth rate can be as low as a few tens Hz. The mechanism may excite the electrostatic mode with frequency comparable to those of the ultra–low frequency electric fields observed in the Earth’s inner magnetosphere.