Cyclotron Wave Instabilities in a Plasma

Transverse electromagnetic waves that propagate along a uniform magnetic field in an unbounded, thermally anisotropic plasma are investigated. The linearized Vlasov equation is solved to obtain the dispersion relation for the electron- and ion-cyclotron waves. This dispersion relation is used to determine the critical frequencies and wavenumbers below which the wave is unstable. The electron-cylotron wave is unstable for T⊥e > Tze. Numerical solutions for the growth and damping rates of the waves obtained from the dispersion relation show that the maximum growth rate occurs at a frequency slightly below the marginally stable frequency. For the ion-cyclotron wave, both ion and electron thermal anisotropy are included, and cold electrons are shown to have a stabilizing influence on an unstable ion-cyclotron wave; however, when the electrons are thermally anisotropic, they have a destabilizing effect for T⊥e > Tze.