Hydromagnetic Eigenmodes in Multipole Fields

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Abstract
A formalism is developed providing an exact analytical procedure for determining linearized hydromagnetic wave phenomena in a perfectly conducting plasma permeated by a static magnetic multipole field. All perturbations are harmonically represented by scalar and vector spherical harmonics. The vector wave equation for the perturbed electric field is then reduced to a set of coupled equations in the radial variable alone. Different harmonic modes are coupled because the vector wave equation is not simply separable in spherical coordinates (or any other known system of coordinates). The physical significance of operative couplings derives from parity and angular momentum conservation requirements. It is shown that the radial equations are generally soluble in principle.

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