CYCLOTRON AMPLIFICATION OF WHISTLER WAVES BY ELECTRON-BEAMS IN AN INHOMOGENEOUS MAGNETIC-FIELD

Cyclotron wave-particle interactions in the case of well-organized dis tributions of energetic electrons under an inhomogeneous magnetic fiel d are studied. Step-like and delta function distributions over the fie ld-aligned velocity are considered. The one-hop amplification of whist ler waves is calculated by simple analytical solution and numerical co mputation based on strict approach. The strict consideration, taking i nto account third-order expansion of the spatial dependence of the ele ctron phase with respect to the wave, reveals some new important featu res of the one-hop amplification Gamma as a function of frequency and electron beam parameters. The main result is that Gamma exhibits a qua si-periodic structure as a function of wave frequency or characteristi c electron parallel velocity, remaining always positive in the case of the step-like distribution but being sign alternative for delta-funct ion. Dependence of Gamma on the parameters of energetic electrons such as their total energy: characteristic parallel velocity, position of the injection point in relation to the equator, and dispersion in para llel velocity is discussed.