The continuous spectrum of an axisymmetric self-gravitating and static equilibrium with a mixed poloidal and toroidal magnetic field

Details The continuous spectrum of an axisymmetric self-gravitating and static equilibrium with a mixed poloidal and toroidal magnetic field The continuous spectrum of an axisymmetric self-gravitating and static equilibrium with a mixed poloidal and toroidal magnetic field

Oct 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985a%26a...151...16p&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 151, no. 1, Oct. 1985, p. 16-26.

Astronomy and Astrophysics

Astrophysics

27

Continuous Spectra, Magnetic Field Configurations, Magnetohydrodynamic Waves, Plasma Equilibrium, Stellar Magnetic Fields, Axisymmetric Bodies, Compressibility Effects, Eigenvalues, Magnetohydrodynamic Stability, Polarization Characteristics, Poloidal Flux, Stellar Gravitation, Toroids

Scientific paper

The continuous spectrum of the linearized equations of ideal MHD is investigated for an axisymmetric, self-gravitating equilibrium with a mixed poloidal and toroidal magnetic field. The continuous spectrum for a purely poloidal magnetic field is treated as a special case. The continuous spectrum of a purely poloidal magnetic field is given by an eigenvalue problem of two uncoupled ordinary second order differential equations along the magnetic field lines, so that there are two uncoupled continuous parts of the spectrum: an Alfvén continuum and a cusp continuum. Variational expressions for the continuum frequencies are derived for each of the two continua, and it is found that the Alfvén continuum is always on the stable side of the spectrum but the cusp continuum can be unstable. The continuous spectrum in the presence of a mixed poloidal and toroidal magnetic field is given by an eigenvalue problem of a fourth order system of coupled ordinary differential equations. A variational expression is derived for the continuum frequencies and it is found that the equilibrium gravitational field can lead to an unstable continuous spectrum.

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