Computation of Growth Rates and Threshold of the Electromagnetic Electron Temperature Gradient Modes in Tokamaks

In this manuscript, eigenvalues of the Electron Temperature Gradient (ETG) modes and Ion Temperature Gradient (ITG) modes are determined numerically using Hermite and Sinc differentiation matrices based methods. It is shown that these methods are very useful for the computation of growth rates and threshold of the ETG and ITG modes. The total number of accurately computed eigenvalues for the modes have also been computed. The ideas developed here are also of relevance to other modes that use Ballooning formalism.