Pergamon www.elsevier.nl/locate/asr zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Adv. Space Res. zyxwvutsrqponmlkjihgfedcbaZY Vol. 24, No. 1, pp. 95-98, 1999 Q 1999 COSPAR. Published by Elsevier Science Ltd. AI1 rights reserved Printed in Great Britain 0273-1177/99 $20.00 + 0.00 PII: SO273-1177(99)00432-9 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML CYCLOTRON AMPLIFICATION OF WHISTLER WAVES Y. Hobars’.‘. V. Y. Trakhtengcrts 2, A. G. Demekhov’, and M. Hayakawa’ ’ Department zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA of Electronic Engineering, The University of Electra-Communications. 1-5-l. Chofugaoka. Chofu. 182-8585 Tokyo, Japan 21nstitute of A pplied Physics, 46 Ulyanov Street, 603600 Nixhny Novgorod, Rus.yia ABSTRACT Cyclotron wave-particle interactions in the case of well-organized distributions of encrgct,ic electrons in an inhomogeneous magnetic field are studied. Step and 6 function distributions of field-aligned velocit,y 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 terrn in the spatial dependence of the electron phase with respect to the wave, some new features of the one-hop amplification rate r as function of frequency and electron beam parameters are obtained. I’ exhibits a quasi-periodic structure as fimction of frequency or characteristic electron parallel velocity. For the step-like dist,ribution it, remains positive. For the h-function it changes sign. The dependence of l-’ 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. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 01999 COSPAR. Published by Elsevier Science Ltd. INTRODUCTION The cyclotron interaction of whistler waves with beams of energetic electrons in an inhomogeneous mag- netic field attracts a lot of interest in connection with some important problems of magnetospheric physics. such as triggered ELF/VLF emissions, chorus generation. wave generation in the aurora1 ZOIIC. The beam is represented by parallel velocity distribution functions with as step-like, and 6 functions, rcspect,ivcly. Step-like distribution is formed by quasi-linear relax&ion of the beam-plasma and Cyclotron inst,abili- t,ies (Ivanov, 1977; Trakhtengerts et aZ. 1986). Dirac-type distribution funct,ion is produced in the process of cyclotron interaction of quasi-monochromatic whistler packet with radiation belt electrons (Karpman et al. 1974: Nunn, 1974). Both types of distribution functions arc suit,ablc for wave generation with fine structures. In this paper we analyze the cyclotron inst,ability in the presence of a beam with arbitrary in- jection point along can inhomogeneous magnetic field. A small dipersion spread of the field-aligned velocity component, which can exist in a beam source or appears urldcr the expansion of a beam in the inhomoge- neous geomagnetic field is taken into account. The problem is solved in the regime of stationary injection and stationary amplification, when the second-order cyclotron resonance effects are absent,. FORMULATION Cyclotron Amplification. We shall consider the case when the beam density is small and the change of phase between wave and