| Analytical studies of structure formation in electron temperature gradient driven (ETG) turbulence are presented, with a particular emphasis on Hamiltonian formulation, modulational interaction; secondary instability and selection of and competition between radially and poloidally elongated nonlinear structures. Along with the description of the ETG system as a Hamiltonian system, a previously unknown conservation law is presented.; Amplitude equations describing various limits of the ETG modulational evolution are given, and the implications of these nonlinear Shrodinger type equations are extensively studied.; 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 these amplitude equations, 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 then it is in the poloidal direction, when the primary source of instability has a large poloidal wave number (i.e. ky ≫ kx). This leads to a reduction over the streamer driven transport and renders the ETG mode irrelevant for electron thermal transport problem.; The numerical method and the results of a simple numerical study of the full equations, are also presented. The results show a qualitative agreement with the analytical results on anisotropic singularity formation. However due to the non-adaptive nature of the spectral methods that were used, the numerical study is not claimed to be conclusive on the issue of finite time singularity. |
