New numerical tools to study waves and instabilities of flowing plasmas

Studying plasma waves and instabilities is an indispensable part of present thermonuclear fusion and astrophysical magnetohydrodynamics (MHD). Up till recently, spectral analysis was mostly restricted to static plasmas. However, the assumption of a static plasma is unrealistic not only for astrophysical but also for modern fusion research. Plasmas with flow have been shown to have spectra essentially different from those of static plasmas [Phys. Rev. Lett. 84 (2000) 2865]. We present two new numerical tools for spectral studies of plasmas with flow. The first one, a program called FINESSE (Finite Element Solver for Stationary Equilibria), computes equilibria of non-static plasmas for a variety of fusion and astrophysical configurations (tokamaks, solar loops, solar winds, etc.). Ideal and resistive spectra of the computed equilibria are studied with another tool, a program called PHOENIX. In PHOENIX, the large-scale generalized eigenproblems are solved with the recently proposed iterative Jacobi–Davidson method [SIAM J. Matrix Anal. Appl. 17 (1996) 401]. Our numerical examples show how FINESSE and PHOENIX can be used to study the effect of the poloidal flows on Toroidal Alfvén Eigenmodes.