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Abstract
In this thesis, a detailed study of the nonlinear dynamics of gyrokinetic particle simulations of electrostatic collisionless and weakly collisional drift waves in a shear-free slab is given. The concentration is mainly on $2{1\over2}$-dimensional simulations in which there is an ignorable spatial coordinate. These gyrokinetic particle simulations were the first simulations of gradient-driven microinstabilities able to treat all of the nonlinear processes in a fully self-consistent manner. Previous studies$\sp1$ have found that the evolution in these simulations has a linear stage, a saturated stage, and a (fluctuating) steady-state stage, and that the wavenumber spectrum of the electrostatic potential is strongly dominated by the lowest available modes. Furthermore, the saturation levels and especially the particle fluxes have an unexpected dependence on collisionality. In this thesis, the explanations for these collisionality dependences are found to be as follows. The saturation level is determined by a balance between the non-self-consistent electron and ion fluxes. The non-self-consistent ion flux is due to either nonresonant diffusion or to advection of well-trapped regions of enhanced ion density and increases sharply once the potential becomes large enough to allow these enhanced density regions to form. The electron flux is caused mostly by E $\times$ B diffusion of near-resonant electrons. In the $2{1\over2}$-dimensional shear-free geometry, there is a rigorous constraint between the parallel acceleration and the E $\times$ B drift. Thus, in the collisionless motion, as the electrons diffuse, they are simultaneously accelerated away from the resonance, resulting in an inhibition of their diffusion. The collisionality dependence arises because the collisions provide the only mechanism that can repopulate the resonance. These results have important implications for the understanding of three-dimensional geometries as well. Partially linearized gyrokinetic particle simulation algorithms are developed. Some standing issues concerning the behavior of mode-truncated versions of the gyrokinetic system are also addressed. ftn$\sp1$Federici et al., Physics of Fluids 30, 425 (1986) (and references therein).
