Streamer formation and collapse in electron temperature gradient driven turbulence

A simple model is useful to understand the formation and persistence of radially elongated structures (streamers) in electron temperature gradient (ETG) driven modes. The ETG model is very similar to the thermal Rossby wave model, a system of broad interest. The detailed correspondence of these two models is discussed. Streamer formation in this simple model is analyzed using the modulational stability method. In the inviscid limit of the model, an amplitude equation similar to the nonlinear Schroedinger equation (NLS) is derived. This equation has a second derivative cubic nonlinearity and is identified as a special case of a more general higher order NLS. Analytical solutions are found in the form of travelling waves and a localized thorn. Using the Lagrangian structure of the amplitude equation, it is shown that one-dimensional collapse in the poloidal direction is possible in this system for certain parameter values, and for sufficiently localized initial flow. This identifies a parameter regime basin in which there is an attractor with the structure of a thin extended streamer. In the viscous limit, another amplitude equation, which is a certain special case of the generalized complex Ginzburg-Landau equation, is obtained. Fixed points of the corresponding dynamical system are identified and their stability is investigated