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MHD: Alfven Spectra in Magnetohydrodynamics

from the NEP Collection

Source: A. Booten, M.N. Kooper, H.A. van der Vorst, S. Poedts and J.P. Goedbloed University of Utrecht, the Netherlands
Discipline: Plasma physics

Large nonsymmetric generalized matrix eigenvalue problems arise in the modal analysis of dissipative magnetohydrodynamics (MHD). The MHD system combines Maxwell's and fluid flow equations. The physical objective of these MHD systems is to derive nuclear energy from the fusion of light nuclei. The plasmas generated exhibit both the characteristics of an ordinary fluid and special features caused by the magnetic field. The study of linearized motion in MHD has contributed significantly to the understanding of resistive and nonadiabatic MHD plasma phenomena such as plasma stability, wave propagation and heating.

The MHD equations are solved by applying a Galerkin finite element method, which leads to the generalized eigenvalue problem. The spectrum ranges over several orders of magnitude (see figures below) corresponding to the time scales of different aspects of nuclear fusion reactions. Details are given in the literature.

Matrices in this set come in pairs, corresponding to the matrices in the generalized eigenproblem Ax = (lamba)Bx. The matrices are named MHDnnnnA and MHDnnnnB, respectively.

Kerner reports difficulties in numerically computing the eigenvalues of the Alfven wave operator. The spectrum of this operator consists of three branches. More precisely, it is reported that the eigenvalues at the intersection of the branches are problematic.

Figure 1 displays the spectrum of the 1280 × 1280 MHD matrix computed by the QR algorithm. Figure 2 focuses on the intersection of the three branches (Alfven spectra).

The test matrix data was made available to us by Dr. Albert Booten, less than a month before his unexpected death by heart failure during a sports event on November 12, 1995. Albert was an able young scientist and a very friendly person and we will miss him very much. - NEP authors

Matrices in this set:

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