P.W. Terry and Derek Baver
Department of Physics, University of Wisconsin-Madison

Eduardo Fernandez
Center for Turbulence Research, Stanford University

A simple model for collisionless trapped electron mode turbulence (CTEM) shows that the electron nonlinearity leads to significant differences between the linear growth rate and the actual (nonlinear) growth rate.  These differences call into question 1) techniques for modeling transport that rely on linear growth rates to infer turbulence levels or turbulent diffusivities; 2) shear suppression thresholds that use a linear growth rate to compare with the ExB shearing rate; 3) bispectral deconvolution techniques that infer a linear growth rate from measured spectra; and 4) quasilinear approximations for transport fluxes.

The origin of nonlinear instability (and/or nonlinear dissipation) in CTEM turbulence is two-fold.  First, as with all fluctuations involving the nonadiabatic electron density, the dispersion (both linear and nonlinear) has at least two branches.  At infinitesimal amplitude, one yields the linear growth rate and the other is typically damped.  The electron nonlinearity, which dominates long wavelength dynamics in the collisionless regime, is quite efficient at exciting any branch that is damped.  Unless the damping rate greatly exceeds the nonlinear transfer rate the damped branch reaches finite amplitude and dissipates energy, changing energy balances and saturation.  Second, the electron nonlinearity directly affects the correlation of density and potential, the quantity that governs energy input (instability).  Analytic calculations suggest that the electron nonlinearity leads to nonlinear instability, and this is born out by measurement of the nonlinear energy input rate in numerical simulations.  These two mechanisms appear to work in different parts of the spectrum, with the anomalous damping operative at low k and the nonlinear instability at high k.  In contrast to the dissipative regime, they produce a noticeable modification of the density spectrum, so that it no longer follows the shape of the potential spectrum.

To assess the effect of these nonlinear processes on various analysis techniques we make comparisons between the linear growth rate and the nonlinear growth rate; the linear mixing length saturation estimate (given by the maximum value of the growth rate divided by the square of the wavenumber) and the measured turbulent diffusivity in saturation; and the quasilinear particle flux and the nonlinear flux.  The contribution of nonlinear excitation of the damped branch is quantified by incrementally suppressing it with successively larger damping.