Nonlocal theory and turbulence of the sheath-driven electron temperature gradient instability

A nonlocal linear theory of the sheath-driven delT(e) mode for a uniformly increasing temperature profile that properly includes effects of a varying Larmor radius has been developed. This theory was used to verify nonlinear fluid simulations of this mode in a two-dimensional slab. The nonlinear evolution of the mode was found to depend not only upon the growth rate, but also upon the variation of the ExB drift over the extent of the radial eigenmode. When the difference in the ExB drift frequency exceeded the growth rate, the linear mode structure was distorted at early times leading to a mixing of the vortices, which allowed a rapid nonlinear growth of the longer wavelengths. When the mode grew faster than any tilting of the vortices, the fluctuations remained coherent and localized for many growth times. Not until the fluctuations grew to very large amplitude (similar to 50%) did the longer wavelength modes grow and contribute to the turbulence. By comparing the analytical growth rate and the variation of the equilibrium drift frequency, a condition that predicts which state the mode will evolve to was derived in terms of physical parameters of the system. (C) 2001 American Institute of Physics.