A two-nonlinearity model of dissipative drift wave turbulence

Abstract

A simple, one-field, two-nonlinearity, drift wave model equation is derived to describe the dynamics of a nonuniform magnetized plasma by taking into account the effects of dissipative trapped electron response in the turbulence dynamics. Because of the nonadiabatic response of trapped electrons, mode couplings by both the E×B drift and the polarization drift nonlinearities are present. In this work, the statistical dynamics for this dissipative drift wave turbulence is investigated using the EDQNM (eddy-damped quasinormal Markovian) closure scheme. In particular, apart from the eddy viscosity, a large nonlinear frequency shift is shown to be induced by cross coupling of the two nonlinearities. Thus instability drive is modified by this turbulent back reaction. By taking into account this self-consistency effect, a wave kinetic equation is derived, and the density fluctuation spectrum is obtained in different parameter ranges. The results show that the dynamics of dissipative drift wave turbulence is fundamentally different from that of the familiar Hasegawa–Mima model, because E×B drift nonlinearity blocks the low-k condensation of fluctuation energy. It is shown that both the E×B drift nonlinearity and the nonlinear frequency shift effect transfer energy nonlocally from large to small scales and, in contrast to the predictions of dimensional analysis, their contribution to the nonlinear transfer processes are actually of the same order as that of the polarization drift nonlinearity, even within the Hasegawa–Mima regime. This results in a significant modification of the Hasegawa–Mima spectrum for the short-wavelength drift waves.