Some nonlinear properties of drift-cyclotron modes

The nonlinear evolution of the drift-cyclotron instability has been investigated by means of analytical perturbation theory and computer simulations with a particle-fluid hybrid code. The nonlinear modification of the electrostatic ion response in the presence of a single drift-cyclotron mode is calculated. It is determined that a nonlinear shift in the effective ion cyclotron frequency can stabilize long-wavelength modes (kai∼N/κai, ω≊ω*≊Nωci, N = ±1, ±2, ...) at fairly small amplitudes of the electrostatic potential ‖eφ/Ti‖∼(me/mi+ω2ci/ ω2pi)1/2κai, where ω* is the ion diamagnetic drift frequency, ai is the ion gyroradius, Ti is the ion temperature, and κ−1 is the density-gradient scale length. These saturated states exhibit nonlinear oscillations, and analysis indicates that these states are stable to perturbations arising from other long-wavelength drift-cyclotron modes. A shift of the ion cyclotron frequency is not the dominant nonlinear feature in the case of more unstable short-wavelength modes [kai∼(me/mi+ω2ci /ω2pi)−1/2, ω≊Nωci∼ω*/2], and the nonlinear ion response is much more difficult to calculate. Simulations indicate that the short-wavelength modes eventually trap ions, as has been seen in previous simulations of ion cyclotron instabilities and the closely related lower-hybrid drift instability.