Quasi-linear saturation of the drift-cyclotron loss-cone mode

The drift-cyclotron loss-cone instability (DCLC) is observed to grow to large amplitudes and subsequently saturate through nonlinear processes in MIX-1, a small magnetic mirror machine. The amplitude at which the mode saturates is a sensitive function of the ion energy distribution function, and of the mirror ratio (B/sub max/B/sub min/) of the device. Direct experimental measurements are made of the wave properties including growth time, saturation amplitude, real frequency, and wave number. Simultaneous measurements determine the ion energy distribution as a function of time. The experimentally measured saturated state is compared to the predictions of a quasi-linear diffusion theory. The quasi-linear calculation predicts that the unstable wave will grow to a sufficient level so as to turbulently scatter trapped ions into the loss-cone region, thereby forcing the mode to marginal stability. This source of loss-cone ions balances the concomitant loss rate of unconfined ions, determining the self-consistent saturation amplitude