Theory of multiple-helicity interactions in dissipative trapped-electron drift wave turbulence

The two-nonlinearity model of dissipative trapped-electron drift wave turbulence [Y.-M. Liang et al., Phys. Fluids B 5, 1128 (1993)] is generalized to include the effects of a sheared magnetic field. Because of the coupling of drift waves with the damped ion-acoustic modes, the eigenmode k has a radial structure centered on its rational surface characterized by a mode width Δk. In this work, both the linear properties of the model, and the multiple-helicity nonlinear dynamics, including the interactions of the two nonlinearities, i.e., the E×B drift and the polarization drift nonlinearities, are analyzed in detail. In particular, a one-point renormalization is performed to investigate the nonlinear eigenmode properties and the saturation of the system in the multiple-helicity limit. It is shown that, for the ultrastrong magnetic shear limit where Δk≤2ρs, the polarization drift nonlinearity is the dominant nonlinear transfer mechanism. However, for the moderate-to-weak magnetic shear limit where Δk≫2ρs, both nonlinearities and cross-coupling effects will affect the nonlinear transfer processes. An analytic explanation of previous computational observation of the suppression of magnetic shear damping by turbulence [D. Biskamp and M. Walter, Phys. Lett. A 109, 34 (1985)] is also given.