Numerical analysis of drift resistive inertial ballooning modes

Three numerical techniques employing differentiation matrices are used to investigate the linear stability of drift-resistive-inertial ballooning mode for conditions that occur in tokamak edge plasmas. Hermite and Sinc spectral methods are applied to compute the ballooning mode eigenvalues and eigenvectors. In addition, a finite difference method is utilized to construct a differentiation matrix in order to verify results obtained using the spectral methods. It is shown that the spectral methods converge more rapidly than the finite difference method. Ballooning and strongly ballooning approximations are used to calculate the eigen-spectrum. The techniques that are utilized in this paper for calculating eigenvalues are quite general and are relevant to investigate other modes that use the ballooning mode formalism.