Mathematics – Metric Geometry
Scientific paper
May 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992jgr....97.6429w&link_type=abstract
Journal of Geophysical Research (ISSN 0148-0227), vol. 97, no. A5, May 1, 1992, p. 6429-6438. Research supported by SERC.
Mathematics
Metric Geometry
31
Cold Plasmas, Coupled Modes, Earth Magnetosphere, Geomagnetic Pulsations, Magnetohydrodynamic Waves, Mathematical Models, Fourier Analysis, Perturbation Theory, Wave Excitation, Wave Functions
Scientific paper
The resonant coupling of linear fast and Alfven modes is considered in a cold plasma permeated by a curl-free background magnetic field. The medium is assumed to possess an invariant coordinate (e.g., slab or axisymmetric geometry). The problem is presented in terms of a set of orthogonal wave functions which describe the wave fields. Perturbations are Fourier analyzed along the invariant direction with wave number k(beta), which is subsequently employed as a second expansion parameter with which to expand the governing equations. These equations are then solved using time-dependent perturbation theory, familiar in quantum mechanics. The calculations provide generalizations to the results of previous authors, such as the excitation of resonant Alfven waves and the damping of the fast mode. To test the novel formulation, the results are compared with numerical solutions of the 'box' magnetosphere. For small azimuthal wave numbers (less than 3-4) the lowest-order estimates of the cavity mode damping rates are in excellent agreement with previous calculations.
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