Numerical simulation of ion temperature gradient driven modes in the presence of ion-ion collisions

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 2/2 d linearized gyro-kinetic 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 LTi/R0, an upper bound on kχ, 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. 44 refs., 12 figs