Coherent structures in ion temperature gradient turbulence-zonal flow

Nonlinear stationary structure formation in the coupled ion temperature gradient (ITG)-zonal flow system is investigated. The ITG turbulence is described by a wave-kinetic equation for the action density of the ITG mode, and the longer scale zonal mode is described by a dynamic equation for the m = n = 0 component of the potential. Two populations of trapped and untrapped drift wave trajectories are shown to exist in a moving frame of reference. This novel effect leads to the formation of nonlinear stationary structures. It is shown that the ITG turbulence can self-consistently sustain coherent, radially propagating modulation envelope structures such as solitons, shocks, and nonlinear wave trains