Transient Spin-Wave Buildup in Ferrites

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Abstract
The equations of motion for spin waves in a ferrite, together with the equations for the uniform mode, have been numerically integrated for the case in which the ferrite is spherical in shape and subjected to an applied magnetic field which rises linearly in time. The equations for the uniform mode are completely general and allow for arbitrary amplitude of the mode, so that parametric couplings which lead to spin-wave instabilities of various orders are accounted for, including the ordinary first-order and second-order spin-wave instabilities. The spin-wave equations are solved to first order in the spin-wave amplitudes. The equations have been solved under the conditions of a linearly rising magnetic field having arbitrary rate of rise, together with a dc applied magnetic field of arbitrary magnitude, and for arbitrary angle between the orientations of the rising and dc fields. Assuming that spin waves are initially excited to thermal amplitudes, a numerical integration is performed over k space to find the aggregate spin-wave growth as a function of time, and the energy in the uniform mode as a function of time in the presence of the amplified spin waves. These results define the conditions under which useful transient devices can be operated for the generation of microwave energy in pulsed magnetic fields, to take advantage of the large rf magnetization available in ferrites when operated beyond the usual limiting values of the uniform mode which apply under steady-state operation.