Dynamical and Secular Instability of a SelfGravitating Rotating Cylinder in a Toroidal Magnetic Field
Abstract
The oscillations and stability of a homogeneous selfgravitating rotating cylinder in a toroidal magnetic field are investigated. It is assumed that the field is proportional to the distance to the axis of the cylinder. We show the existence of four infinite discreta spectra of magnetic (or rotational) modes. Rotation stabilizes the magneticm=1 instability. The magnetic field decreases the growth rate of rotational instability and reduces the interval of unstable wavenumbers. Ifm=1, instability always occurs with the exception of the equipartition state. Ifm>1, the instability can be suppressed by a sufficiently large magnetic field. Resistivity decreases the growth rate of magnetic instability, but increases the growth rate of rotational instability. For zero wavenumber perturbations secular instability occurs due to the action of resistivity before a neutral point is attained where a second secular instabiliity initiates due to the action of resistivity.
 Publication:

Astrophysics and Space Science
 Pub Date:
 February 1988
 DOI:
 10.1007/BF00641913
 Bibcode:
 1988Ap&SS.141...27L
 Keywords:

 Dynamic Stability;
 Magnetic Effects;
 Magnetic Field Configurations;
 Secular Variations;
 Toroidal Plasmas;
 Cylindrical Plasmas;
 Stellar Evolution;
 Stellar Magnetic Fields;
 Astrophysics