On the interchange instability

Details On the interchange instability On the interchange instability

Aug 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986jgr....91.8837r&link_type=abstract

Journal of Geophysical Research (ISSN 0148-0227), vol. 91, Aug. 1, 1986, p. 8837-8845.

Physics

21

Earth Magnetosphere, Magnetic Flux, Magnetohydrodynamic Stability, Planetary Atmospheres, Planetary Magnetic Fields, Coriolis Effect, Cylindrical Plasmas, Magnetohydrodynamic Flow, Potential Energy

Scientific paper

The approximate low-beta interchange stability criterion is derived for a simple toroidal field and plasma geometry by determining the change in potential energy caused by the familiar interchange of two equal-flux tubes of force (Chandrasekhar, 1960), and results are compared to exact equations for arbitrary beta. The standard method is shown to be correct up to and including terms of order of the ratio of plasma to magnetic pressure (beta). It is shown that toroidal equilibria having beta of order unity or larger can be analyzed by: (1) interchanging tubes of unequal flux such that to first order in displacement, the surroundings are left unperturbed, changes in the magnetic energy being taken into account; and (2) considering the displacement of a single flux tube, taking into account resulting changes in the energy of the tube as well as the environment. In a rotating system, Coriolis effects can make a significant stabilizing contribution to the interchange energy, and it is shown that sufficient stability criteria can be obtained for general uniformly rotating equilibria by including centrifugal effects but not Coriolis effects.

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