Quasilinear 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 non-linear 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_{max }/B_{min}) of the device. Direct experimental measurements are made of the wave properties including growth time, saturation amplitude, real frequency, and wavenumber. Simultaneous measurements determine the ion energy distribution as a function of time. The experimentally measured saturated state is compared to the predictions of a quasilinear diffusion theory. The quasilinear 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. Flexibility in the experimental rearrangement allows this process to be studied over a wide range of dependent parameters. Specifically, the mirror ratio, plasma ambipolar potential, and background neutral gas pressure are varied continuously to affect the saturation amplitude of DCLC. Quantitative comparisons between the measured and calculated saturated state agree very well over the full range of parametric variation, providing direct support of the quasilinear theory.