Nonlinear stability and instability in collisionless trapped electron mode turbulence

A two-field model for collisionless trapped electron mode turbulence has both finite amplitude-induced stability and instability, depending on wave number. Effects usually identified with nonlinear plasma instability (self-trapping, kinetics, 3D mode structure, magnetic shear) are absent. Nonlinear stability and instability reside in ExB advection of density. It drives modes of a purely damped branch of the dispersion relation to finite amplitude and changes the rate at which free energy is released into the turbulence by shifting the density-potential cross phase. Analysis shows that modes of the purely damped branch cannot be ignored in saturation, and that the linear growth rate is a poor indicator of driving at finite amplitude, invalidating mixing length and quasilinear approximations. Using statistical closure theory, the nonlinear eigenmode and growth rate are determined from the saturation level of modes on all branches, stable and unstable, and the nonlinear cross phase that governs finite-amplitude instability.