Cyclotron amplification of whistler waves

Abstract Cyclotron wave-particle interactions in the case of well-organized distributions of energetic electrons in an inhomogeneous magnetic field are studied. Step and δ function distributions of field-aligned velocity are considered. The one-hop amplification of whistler waves is calculated analytically and by numerical computation. In rigorous approach, taking into account the third-order term in the spatial dependence of the electron phase with respect to the wave, some new features of the one-hop amplification rate Γ as function of frequency and electron beam parameters are obtained. Γ exhibits a quasi-periodic structure as function of frequency or characteristic electron parallel velocity. For the step-like distribution it remains positive. For the δ-function it changes sign. The dependence of Γ on the total energy, characteristic parallel velocity, position of the injection point in relation to the equator, and dispersion in parallel velocity of energetic electrons such as is discussed.