Finite-Amplitude Collisional Drift Waves

Abstract

A calculation of mode-mode coupling for collisional drift waves demonstrates several inherently nonlinear phenomena, namely, amplitude saturation, harmonic generation, frequency shift, wave-associated transport across the magnetic field, and parametric excitation of subharmonics. There is qualitative agreement with published experiments; the introduction of some additional damping mechanism into the theory could narrow the broad quantitative discrepancy between theory and experiment. The analysis uses the nonlinear ion and electron fluid equations in which ion inertia, finite ion gyroradius, perpendicular ion viscosity, and resistivity terms have retained. No cross-B transport is produced by the large-amplitude steady-state oscillations in the absence of ion viscosity; non-ambipolar transport in the pump-out direction appears when ion-ion collisions are introduced. A byproduct of the calculations is a single nonlinear scalar wave equation for the collisional drift wave. Solutions to this equation show limit-cycle behavior, i.e., periodic but nonsinusoidal finite-amplitude oscillations which are stable (or unstable) against changes of oscillation amplitude. These nonlinear solutions are described by dispersion relations containing the oscillation amplitude as one of the parameters.