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Abstract
An electromagnetic gyrokinetic particle-simulation model based upon the parallel-canonical-momentum $(p\sb\Vert)$ formulation of the gyrokinetic Vlasov-Maxwell equation set is investigated in one-dimensional (1D) and two-dimensional (2D) slab geometries. Various numerical techniques and computer-code optimizations used in particle simulations of plasmas are explained. Tests of the $p\sb\Vert$ system in a 1D geometry with a tilted magnetic field reproduce the expected kinetic shear-Alfven modes. Thermal fluctuation levels are in agreement with calculations from the fluctuation-dissipation theorem for both low-beta ($\beta\ll m\sb{e}/m\sb{i})$ and moderate-beta $(m\sb{e}/m\sb{i}\leq\beta\ll 1)$ regimes. Simulations of finite-$\beta$ electron drift waves and ion-temperature-gradient (ITG) modes show reductions of linear growth rate with increasing $\beta$, as predicted from dispersion-relation analysis. A mode-coupling calculation is successfully used to estimate saturation levels for finite-$\beta$ drift waves in 1D nonlinear simulations. Trends of finite-$\beta$ ITG-mode stabilization with various plasma parameters are explored, and the physical mechanism for stabilization is described. 2D nonlinear finite-$\beta$ ITG simulations indicate that while ion thermal transport is reduced from the electrostatic case, electron thermal transport may be enhanced by magnetic fluctuations. Nonlinear generation of modes with $k\sb\Vert = 0$ and the effects of such modes on ITG turbulence are also studied. Mode-coupling analysis shows that coupling of ion perpendicular pressure and electrostatic potential can create the $k\sb\Vert = 0$ modes, which can then couple back to the linearly unstable modes and cause saturation. 2D gyrokinetic simulations with a reduced set of Fourier modes demonstrate this process and show that fully drift-kinetic electron response and finite-$\beta$ effects have little impact on $k\sb\Vert = 0$ modes. Development of analogous purely radial modes and their associated E x B flows is then studied in 3D full-torus electrostatic gyrokinetic simulations. Effects of self-generated flows on steady-state transport are found to be relatively minor for some typical plasma scenarios. Evidence for a theoretical model of turbulence-generated flows is seen in the simulations. The $\nabla B$ and curvature drifts and a parallel acceleration term due to magnetic-field-line curvature are shown to be equally important in reducing purely radial modes.
