An Opticom Method for Computing Eigenpairs

Abstract

Solving the linearized and five-dimensional gyrokinetic equations can already be used to retrieve the microinstabilities driving the microturbulence of a hot magnetized plasma. The microinstabilities can be computed by calculating the eigenvalues of the linear gyrokinetic operator, which have a positive real part. The growth rate and frequency of the instability is given by the computed eigenvalue and its structure by the respective eigenvector. Due to the moderately high dimensionality, the sparse grid combination technique is used to tackle the curse of dimensionality for solving the gyrokinetic eigenvalue problem with the already highly optimized plasmaturbulence code GENE. Whereas the classical combination technique can retrieve approximation of the searched eigenvalues, the combination of the eigenvectors requires the application and reformulation of the optimized combination technique (OptiCom). The reformulation and an algorithm for solving the reformulated system to compute the eigenpairs is proposed in this paper. A first analytical test problem is solved and the applicability of the method is shown. Show more