JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. A7, PAGES 11,689-11,700, JULY 1, 1993 Ion CyclotronHarmonicWave Generation by Ring Protons in SpacePlasmas K. G. MCCLEMENTS AND R. O. DENDY AEA Technology,Culham Laboratory, Abingdon, Oxfordshire, England Spacecraft such as the Active Magnetospheric Particle Tracer Explorers, Giotto and the Com- bined Release and Radiation Effects Spacecraft have shown that suprathermal protons with ring- like or shell-like distributions in velocity spaceexist in many spaceplasmas. Examples include the radiation belts, the auroral zones, the bow shock, and the solar wind. Ring proton distributions may excite obliquely propagating fast Alfv4n waves at harmonicsof the ion cyclotron frequency. In this paper we carry out an analytical study of this instability, restricting our attention to strictly perpendicularpropagation. In the caseof a monoenergetic proton ring in a cold plasma, we show that cyclotron harmonics can have a higher growth rate than parallel-propagating ion cyclotron waves, dependingon the ratio of the proton ring speedto the Alfv•n speed. Analytical stability boundaries in parameter space are determined, indicating that the threshold for the growth of cyclotron harmonics depends critically on the ion plasma beta, •3i. If •3i • 1, for example in the radiation belts or the auroral zones, the concentration of ring protons required for instability is very low. If, on the other hand, •3i ~ 1, for example in the bow shock or the solar wind, instability will only occur if the ring protons constitute a large fraction of the total ion density. In the bow shock case, the required concentrations may indeed occur. Growth rates are also calculated for the case of a ring proton distribution with a Gaussian spread of velocities, and it is shown that the instability persists even if the velocity dispersionis comparable to the ring speed itself. Our analysis is consistent with the observed excitation of perpendicular-propagating ion cyclotron harmonics in the vicinity of the Earth's plasmapause. 1. INTRODUCTION Dilute, highly anisotropic distributionsof suprathermal ions are known to exist in natural plasmasthroughout the solarsystem. The observed anisotropy is generally such that there is a deficiencyof particles with velocity vectorslying along the magnetic field. In the earth's magnetosphere, such ion distributions have been detected in the radiation belts [Lui et al., 1990], the plasma sheet [Chen et al., 1990], the auroralzones [Gorney et al., 19Sl], and downstream of the bow shock [Sckopke et al., 1990].In the case of the radiation belts, renewed interest in anisotropic ions has been stimu- lated recently by observations made by the Combined Re- lease and Radiation Effects Spacecraft (CRRES). The most extreme caseis that of an azimuthally symmetric distribu- tion of ions with a uniqueenergyand pitch angle,i.e., a ring (or ring-beam) distribution. Such distributions arebelieved to exist in the solar wind, the ions originating either from cometary nuclei[Johnstone, 1990]or from the interstellar medium [ Wu and Davidson, 1972]. Many authors have studied waveexcitation by anisotropic ions, and applied their results to space plasmas. To a large extent this work has beenconcerned with wavepropa- gation along the magnetic field: it is commonlyassumed that parallel-propagating waves have the highest growth rates. Kennel and Petschek [1966]pointedout that pro- tons trapped in the magnetosphere could excite left circu- larly polarized electromagnetic waveswith frequencies be- low the ion cyclotron frequency. Cornwall and Schulz [1971] Published in 1993 by the American Geophysical Union. Paper number 93JA00158. and Cuperman et al. [1975] studied this instabilityfor the case of a bi-Maxwellian ion distribution interacting with a cold background plasma. Wu and Davidson [1972]consid- ered the case of a cold ion ring drifting with respectto the background ions. Freundand Wu [198S] investigated the stability of shell-like ion distributions, finding that parallel- propagating ion cyclotronwaves could be excitedby an in- complete shell:it wasfoundthat complete (i.e., spherically symmetric) shellsdid not excite such waves. This study was motivated by observations of cometary ions picked up by the solar wind, indicating the presence of spherical shell distributions [Balsiger et al., 1986]. In this paper we carry out an analytical study of ion cy- clotron harmonicwavegeneration in space plasmas. Belikov and Kolesnichenko [1976] predicted that the perpendicular- propagating fast Alfv•n wave could be excited in a ther- monuclearplasma at cyclotronharmonics of the fusionions. They coined the term "magnetoacoustic cyclotroninstabil- ity" to describethis phenomenon and evaluated analytically the growth rate for the frequency regime w 2 >>Ft•, where Fti is the cyclotron frequencyof the background ions. It was shown that the instability has a banded structure: re- gionsof stability in wave vector space alternate with regions of instability. This is true whether the energeticions have a ringlike distribution or a shell-like distribution, although the maximum growth rate is slightly greater in the former case. The instability studied by Belikov and Kolesnichenko [1976] hasalso been investigated by •ul'elmi et al. [1975], Curtis and Wu [1979] and Pertaut et al. [1982], in re- lation to cyclotron harmonic wave generation by ions in the Earth's plasmasphere. Papadopoulos [1981],Smith and Gary [1987] and Wong et al. [1991]have studiedrelated 11,689