Solution of hot particle ballooning mode integral equation in tokamaks

The solution for the stability of ballooning mode equations in tokamaks with hot particles is presented. The system of equations requires solving a combined set of differential and integral equations accounting for the detailed hot particle orbits. Special techniques are developed to describe the equilibrium, the linear set of matrix equations and the boundary conditions. A modified WKB technique is developed to treat the boundary conditions. A detailed discussion is given of how boundary conditions are determined. We rigorously show why, in some cases, the eigenfunction may be exponentially growing with an outgoing group velocity. Sample results are presented