Nonlinear saturation of the drift cyclotron loss‐cone instability

The nonlinear behavior of the drift cyclotron loss‐cone instability close to a stability boundary is considered. The time‐asymptotic small‐amplitude saturation of a single mode is determined by a variation of the Bogoliubov method. A collisionless plasma model is used with no mirror losses or particle sources. Flute‐like local perturbations are considered. The stability boundary in density, density‐gradient space is determined for several different ion loss‐cone distributions. The modified equilibrium ion distribution function, the electric field, and the amplitude of the fluctuating electrostatic potential are then obtained as a function of the fractional increase in density gradient above the critical value. The nonlinear frequency shift remains indeterminate. In all cases, stable saturation occurs and is due to a slight filling‐in of the loss cone. Comparison with numerical simulation results show good agreement when the high thermal level of neighboring modes is artificially suppressed.