Global approach to the spectral problem of microinstabilities in tokamak plasmas using a gyrokinetic model

A solution to the full two-dimensional eigenvalue problem of electrostatic microinstabilities in a tokamak plasma is presented in the framework of gyrokinetic theory. The approach is the generalization of methods previously developed for a cylindrical system [S. Brunner and J. Vaclavik, Phys. Plasmas 5, 365 (1998)]. By solving the spectral problem in a special Fourier space adapted to the curved geometry, orbit width as well as Larmor radius can be kept to all orders. For a first numerical implementation, a large aspect ratio plasma with circular concentric magnetic surfaces is considered. A root finding algorithm for identifying the eigenfrequencies, based on a higher order Nyquist method, enables straightforward implementation on a parallel computer. Illustrative results for ion temperature gradient-related instabilities are presented. These include scaling studies of the radial width, and toroidicity and magnetic shear scans, as well as the effects of nonadiabatic trapped electron dynamics.