Nonlinear evolution of drift cyclotron modes

The space-time evolution of the drift-cyclotron instability as influenced by the nonlinear shift in the ion-cyclotron frequency is studied analytically, numerically, and by computer simulation. The analysis is specialized to the case of a single coherent wave with frequency near both a cyclotron harmonic and the ion diamagnetic frequency. Such an analysis is motivated by observations of large-amplitude ion-cyclotron waves in the 2XIIB mirror experiment, which were highly monochromatic and often exhibited these frequency characteristics. A nonlinear dispersion relation describing saturation of the instability is derived by means of a self-consistent analytical solution of the Vlasov--Poisson equations to third order in the wave amplitude. Solitary wave and self-similar solutions are obtained that describe nonlinear wave propagation. Numerical solution of a nonlinear evolution equation and particle simulation confirm the analysis