Unrestricted second-order tensor virial equations for linear oscillations of magnetic configurations

Details Unrestricted second-order tensor virial equations for linear oscillations of magnetic configurations Unrestricted second-order tensor virial equations for linear oscillations of magnetic configurations

Feb 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979ap%26ss..60..401g&link_type=abstract

Astrophysics and Space Science, vol. 60, no. 2, Feb. 1979, p. 401-421.

Astronomy and Astrophysics

Astrophysics

3

Linear Systems, Magnetic Field Configurations, Oscillations, Tensor Analysis, Virial Theorem, Adiabatic Conditions, Astronomical Models, Integral Equations, Variational Principles, Vibration Mode

Scientific paper

This paper deals with the second-order tensor virial equations for the linear oscillations of a gaseous mass in the presence of a magnetic field. It is shown that the commonly used linearized versions of the tensor virial equations are restricted integral equations that incorporate the linearized equation of motion but not the boundary condition. These restricted equations only allow trial functions that fulfill the boundary condition and are of limited practical value. The unrestricted variational principle for the linear oscillations of a magnetic configuration is used to derive a more general formulation of the second-order tensor virial equations, so that the linear trial function can be used to study the oscillations of a configuration with a magnetic field that extends in the exterior vacuum. The unrestricted virial equations have been applied to Ferraro's model, and approximate results for the eigenfrequencies and eigenfunctions have been obtained for nine oscillation modes.

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