Whistler waves induced by relativistic electrons and limiting trapped electrons flux

Energetic electrons are injected in the magnetosphere during solar eruptions or by artificial means, increasing the electron fluxes in Van Allen belts. The presence of relativistic electrons in the magnetosphere induces whistler wave excitation due to various kinds of instabilities, such as temperature anisotropy, loss cone or beam type instability. Such studies on whistler wave excitation induced by energetic particles in the magnetospheric plasma are generally carried out for nonrelativistic electrons (CRRES, ARAKS, ECHO, SEPAC, Spacelab missions...). In this paper, first results that we have obtained concerning the whistler mode excitation for parallel and oblique propagation, and for relativistic electrons, are presented both for temperature anisotropy and beam type instabilities. The theoretical formalism that we have used to derive the wave dispersion equation is first described.