Theory of Magnetostatic Modes in Long, Axially Magnetized Cylinders

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Abstract
The characteristic equation determining the eigenfrequencies of the magnetostatic modes is derived from the equations of motion and the boundary conditions. The solutions may be classified as pertaining to surface and to volume modes. Surface-mode solutions exist only for sufficiently small wave numbers, and their eigenfrequencies are larger than those of volume modes. The eigenfrequencies generally decrease with increasing wave number. Approximate, analytic expressions for the dependence of the eigenfrequencies on wave number have been obtained for the regions in which the wavelength is either much smaller or much larger than the cylinder radius. The approximate expressions are compared with numerical results obtained by means of an electronic computer.