Magnetohydrodynamic spectroscopy: Large scale computation of the spectrum of waves in plasmas

Abstract

A systematic study of the spectrum of magnetohydrodynamic (MHD) waves in thermonuclear and astrophysical plasmas is presently undertaken at the FOM Institute for Plasma Physics. This study is based on the fact that the macroscopic waves and instabilities in both thermonuclear confinement machines and in astrophysical magnetic flux loops are described by the MHD equations. The linearised interaction between plasma and magnetic field leads to large-scale non-symmetric eigenvalue problems for free oscillations and to temporal evolution problems for forced (externally driven) oscillations. These problems have been cast in the form of a set of two modular computer programs, called CASTOR for tokamaks and POLLUX for coronal flux tubes, exploiting identical solvers for the resulting very large systems. CASTOR is extensively used at JET (the Joint European Torus experiment at Culham) for the interpretation of measured MHD spectra, whereas POLLUX is presently used for the study of Alfvén wave heating of the solar corona and will be used in the near future for the interpretation of observed x-ray emissions from the SOHO satellite which will be launched by ESA and NASA in 1995. For the interpretation of actual plasma dynamics in tokamaks and solar coronal loops it is crucial to understand the non-linear phase of the evolution of MHD phenomena as well. This adds two complications: non-linear mode coupling of hundreds of small-scale modes and enormous discrepancies between the different dynamical time scales. We have developed numerical codes that simulate the non-linear temporal evolution of plasma columns under external excitation. These codes have been modelled after the linear ones, with a finite difference discretisation in the radial direction and a spectral discretisation in the two other directions. A relatively simple and flexible semi-implicit predictor-corrector scheme has been used for the time stepping. This allows time steps up to a factor 1000 larger than the largest time steps allowed for explicit methods. Because of the many modes involved, memory requirements and CPU time requirements soon become prohibitive. Hence, the new physics in the non-linear plasma dynamics regime requires parallel computing.