The Fourier method is used to provide new analytic solutions for idealized mathematical models of double-element shielded magnetoresistive (MR) recording heads. The general two-dimensional model allows analysis of various recording head configurations; a single pole head, a ring head, a dual stripe head and a differential head. The analysis accommodates both longitudinal recording (with no soft magnetic underlayer present) and perpendicular recording (in the presence of a soft underlayer). Typical field, spectral response function and output voltage pulse plots for double-element MR heads are given and compared to published, approximate solutions. The integrals arising in the determination of the Fourier series coefficients, magnetic potential and magnetic field components are expressed either as rapidly convergent infinite series or in terms of special functions to provide a more efficient means of evaluation than numerical integration. It is shown that, in many situations, it is only necessary to take the first Fourier coefficient in the calculation of output voltage pulse shapes in order to achieve sufficiently accurate results. Bi-variate regression techniques are used to provide a convenient method to approximate the first Fourier series coefficient for a broad range of typical head dimensions. The thesis goes on to examine high speed switching behaviour in two classes of recording media by considering two different particle orientation distributions; 2D random media - intended to simulate a modern thin film rigid disk, and 3D oriented media- simulating a single domain particulate tape media. The gyromagnetic switching constant of a medium is calculated directly from the Landau - Lifshitz - Gilbert (L-L-G) equation of motion, which is solved numerically. The switching constants produced are discussed and compared with published experimental values for different media.

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