Resonant three-wave interaction in the presence of suprathermal electron fluxes

C Krafft,A Volokitin

doi:10.5194/angeo-22-2171-2004

Abstract

Abstract. A theoretical and numerical model is presented which describes the nonlinear interaction of lower hybrid waves with a non-equilibrium electron distribution function in a magnetized plasma. The paper presents some relevant examples of numerical simulations which show the nonlinear evolution of a set of three waves interacting at various resonance velocities with a flux of electrons presenting some anisotropy in the parallel velocity distribution (suprathermal tail); in particular, the case when the interactions between the waves are neglected (for sufficiently small waves' amplitudes) is compared to the case when the three waves follow a resonant decay process. A competition between excitation (due to the fan instability with tail electrons or to the bump-in-tail instability at the Landau resonances) and damping processes (involving bulk electrons at the Landau resonances) takes place for each wave, depending on the strength of the wave-wave coupling, on the linear growth rates of the waves and on the modifications of the particles' distribution resulting from the linear and nonlinear wave-particle interactions. It is shown that the energy carried by the suprathermal electron tail is more effectively transfered to lower energy electrons in the presence of wave-wave interactions.

Highlights

Lower hybrid and whistler waves have been currently observed in space plasmas as the terrestrial magnetosphere or the solar wind
The study presented here, which models the interaction of a set of waves with a non-equilibrium electron velocity distribution in a magnetized plasma, contributes to clarify what mechanisms should to be taken into account or should be neglected for a correct description of physical situations as those cited above
In order to study the nonlinear interaction of such waves with electron beams and fluxes, two approaches have been mainly considered up to now in the literature (e.g. O’Neil et al, 1971; Shapiro and Shevchenko, 1968, 1971; Matsiborko et al, 1972, 1973; Kovalenko, 1983; Pivovarov et al, 1995; Volokitin and Krafft, 2000, 2001a, 2001b, 2004; Krafft et al, 2000; Krafft and Volokitin, 2002, 2003a): first, the study of the instability and the saturation processes of a single monochromatic wave, and second, the evolution of a wide spectrum of waves at the stage when the turbulence is well developed

Summary

Introduction

1998; Thejappa and MacDowall, 1998; Moullard et al, 1998, 2001) and in wave-particle processes occurring in the auroral ionosphere (Ergun et al, 1993; Muschietti et al, 1997) or in the terrestrial electron foreshock, for example (Hoppe et al, 1982; Zhang et al, 1999). This instability is worth being studied in the frame of our model, when one given wave is simultaneously involved in several resonant interaction processes; for example, a wave excited by the fan instability through its interaction with some tail electrons at the anomalous cyclotron resonance can be simultaneously damped at the Landau resonance (interaction with the thermal bulk electrons) and at the normal cyclotron resonance (interaction with a very small amount of electrons of negative parallel velocity) This competition between excitation and damping processes, which takes place for each wave, can lead in the nonlinear stage to new physical effects when considering a set of several waves: for example, if a wave is stable in the linear stage, it can become unstable during the nonlinear evolution as a result of the modification of the particles’ velocity distribution functions through the action of the other waves. This paper presents some relevant examples of numerical simulations showing the nonlinear evolution of a set of three waves interacting at various resonances (Landau, anomalous and normal cyclotron) with a flux of electrons which presents some anisotropy in the parallel velocity distribution; in particular, the case when the interactions between the waves are neglected (for sufficiently small waves’ amplitudes) is compared to the case when the three waves follow a resonant decay process

Nonlinear model for lower hybrid wave-particle interaction

Wave-wave interaction terms