Nonlinear elongation of two-dimensional structures in electron temperature gradient driven turbulence

The nonlinear evolution of the electron temperature gradient (ETG) driven mode can be described with a simple, two-dimensional reduced fluid model, similar to that used for the thermal Rossby wave system. Consistent with ballooning mode structure, primary instability drive with a strong anisotropy in wave number (i.e., k _y≫k _x) is considered for the inviscid limit of the ETG model. The amplitude equation, describing the initial envelope modulations of this system, is derived using reductive perturbation methods. The dynamics of the intensity field variance in radial and poloidal directions, i.e., the two diagonal elements of the covariance tensor), which follow from the amplitude equation, are investigated in an attempt to determine the basins of attraction for forming zonal flow and streamer secondary structures. It is found that the focusing (or diffracting) effect of Reynolds stress is essentially stronger in the radial direction than it is in the poloidal direction. Further analysis of the structure in the radially elongated limit of the amplitude equation yields interesting results, such as a poloidally localized sheared soliton solution. The approach used here is broadly applicable.