The Effect of Trapped Ions and Current Drive on Tokamak Microinstabilities: Theory and Simulations.

In this work, a range of low-frequency microinstabilities in tokamaks and the related anomalous cross field transports have been investigated analytically and numerically. A unified theory of temperature gradient driven trapped ion modes and ballooning instabilities is developed using kinetic theory in banana regimes. All known results, such as electrostatic and purely magnetic trapped particle modes and ideal MHD ballooning modes (or shear Alfven waves) are readily derived from our single general dispersion relation. Several new results from ion-ion collision and trapped particle modification of ballooning modes are derived and discussed and the interrelationship between those modes is established. Ion temperature gradient driven modes in the presence of ion-ion collisions in a toroidal geometry with trapped ions have been studied by using a 1{2over 2}d linearized gyrokinetic particle simulation code in the electrostatic limit. The purpose of the investigation is to try to understand the physics of flat density discharges, in order to test the marginal stability hypothesis. Results giving threshold conditions of L_{Ti }/R_0, an upper bound on k_ chi, and linear growth rates and mode frequencies over all wavelengths for the collisionless ion temperature gradient driven modes are obtained. The behavior of ion temperature gradient driven instabilities in the transition from slab to toroidal geometry, with trapped ions, is shown. A Monte-Carlo scheme for the inclusion of ion-ion collisions, in which ions can undergo Coulomb collisional dynamical friction, velocity space diffusion and random walk of guiding centers, has been constructed. The effects of ion-ion collisions on the long wave length limit of the ion modes is discussed. Finally, the effect of current drive on the tearing modes in the semicollisional regime is analyzed using the drift-kinetic equation. A collisional operator is developed to model the electron parallel conductivity. For the pure tearing modes the linear and quasilinear growth rates in the Rutherford regimes have been found to have roughly the same forms with a modified resistivity as without current drive. One interesting result is the prediction of a new instability. This instability, driven by the current gradient inside the tearing mode layer, is possibly related to MHD behavior observed in these experiments.