Abstract
A kinetic theory for the parametric instabilities of ion-cyclotron, drift-cyclotron, and drift-cyclotron-loss-cone modes of finite wavenumber in an inhomogeneous plasma is developed. The Vlasov equation is solved in guiding center coordinates for two types of equilibria, viz., Maxwellian and loss-cone velocity distributions. For flute modes (k∥=0) or modes with long parallel wavelengths (k∥vi∥<ω) the coupling coefficients are greatly simplified. Ion-cyclotron waves are seen to decay efficiently into low-frequency drift waves in tokamaks. In a mirror machine a high-amplitude drift-cyclotron-loss-cone mode of negative energy decays into low-frequency positive-energy modes, giving rise to explosive instability.
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