The continuous spectrum of an axisymmetric, self-gravitating equilibrium in the presence of a poloidal magnetic field

Details The continuous spectrum of an axisymmetric, self-gravitating equilibrium in the presence of a poloidal magnetic field The continuous spectrum of an axisymmetric, self-gravitating equilibrium in the presence of a poloidal magnetic field

Nov 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984esasp.207..297h&link_type=abstract

In ESA Plasma Astrophys. p 297-300 (SEE N85-22270 12-90)

Astronomy and Astrophysics

Astrophysics

3

Continuous Spectra, Magnetic Field Configurations, Plasma Equilibrium, Poloidal Flux, Eigenvalues, Magnetohydrodynamics, Plasma Pinch, Variational Principles

Scientific paper

The continuous spectrum of oscillation frequencies is examined for an axisymmetric, self-gravitating equilibrium in the presence of a purely poloidal magnetic field. It is shown that the continuous spectrum is given by an eigenvalue problem of two uncoupled ordinary second orders differential equations along the magnetic field lines. The two decoupled continuous spectra have modes that are polarized either perpendicular or parallel to the magnetic field lines and may be called Alfven continuum and cusp continuum in analogy to the linear diffuse pinch. Curvature and toroidicity influence the two continua, but only the cusp continuum is affected by gravity and compressibility. Variational expressions for the continuum frequencies are derived and it is found that only the cusp continuum can attain negative values. The stability depends on the distribution of density, pressure, gravity, and magnetic field along the magnetic field lines.

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