The spectrum of an ideal linear magnetohydrodynamic model with translational symmetry

Article type: Research Article

Authors: Raikov, G.D.

Affiliations: Laboratory of Differential Equations in Physics and Technology, Institute of Mathematics, Bulgarian Academy of Sciences, P.O. Box 373, 1090 Sofia, Bulgaria

Note: [] Partially supported by the Ministry of Culture, Science and Education under Contract No. 52.

Abstract: We consider an ideal linear magnetohydrodynamic model with translational symmetry and investigate the spectral properties of the force operator Ak with a fixed longitudinal wavenumber k. We establish that the essential spectrum of Ak consists of two bounded segments (slow magnetosonic and Alfvén continuum). Next, we show that the isolated eigenvalues of Ak do not accumulate to the tips of the Alfvén continuum. Further, we obtain detailed information about the asymptotics of the eigenvalues of Ak which lie to the right of the essential spectrum and tend to +∞. At last, in the case when the two segments of the essential spectrum of Ak are disjoint, we find that, generically, the isolated eigenvalues of Ak accumulate to the right tip of the slow magnetosonic continuum, and calculate the first asymptotic term of the corresponding infinite eigenvalue sequence.

DOI: 10.3233/ASY-1990-3101

Journal: Asymptotic Analysis, vol. 3, no. 1, pp. 1-35, 1990