UC Irvine

The convective cells are observed in the auroral ionosphere and they could play an important role in the nonlinear interaction of Alfv {e}n waves and disrupt the kinetic Alfv {e}n wave (KAW) turbulence. Zonal fields, which are analogous to convective cells, are generated by microturbulence and regulate microturbulence inside toroidally confined plasmas. It is important to understand the role of convective cells in the nonlinear interaction of KAW leading to perpendicular cascade of spectral energy. A nonlinear gyrokinetic particle simulation has been developed to study the perpendicular spectral cascade of kinetic Alfv {e}n wave. However, convective cells were excluded in the study. In this thesis project, we have modified the formulation to implement the convective cells to study their role in the nonlinear interactions of KAW. This thesis contains detail description of the code formulation and convergence tests performed, and the simulation results on the role of convective cells in the nonlinear interactions of KAW. In the single KAW pump wave simulations, we observed the pump wave energy cascades to waves with shorter wavelengths, with three of them as dominant daughter waves. Convective cells are among those dominant daughter waves and they enhance the rate of energy transfer from pump to daughter waves. When zonal fields are present, the growth rates of the dominant daughter waves are doubled. The convective cell (zonal flow) of the zonal fields is shown to play a major role in the nonlinear wave interaction, while the linear zonal vector potential has little effects. The growth rates of the daughter waves linearly depends on the pump wave amplitude and the square of perpendicular wavenumber. On the other hand, the growth rates do not depend on the parallel wavenumber in the limit where the parallel wavenumber is much smaller than the perpendicular wavenumber. The nonlinear wave interactions with various perpendicular wavenumbers are also studied in this work. When convective cells are excluded, the nonlinear wave interactions show exponential growth on the daughter waves, but at a rate about half of that of the wave interactions with convective cells. In the two pump wave simulations, six daughter waves dominate in the energy cascade process, and three of them are convective cells. The growth rates of the daughter waves are doubled compared with the growth rates of the daughter waves generated in single KAW pump wave simulation. The relationship between the growth rates of the daughter waves and pump wave parameters are studied. The growth rates of the daughter waves have a linear relationship with both pump wave amplitudes and the square of perpendicular wavenumber of the pump waves. On the other hand, the growth rates do not depend on the parallel wavenumber of the pump waves in the limit where the parallel wavenumber is much smaller than the perpendicular wavenumber. The growth rate dependence on one of the two pump waves shows that the time variation on the pump wave amplitudes must be considered.