Accurate approximation of fields and spectral response functions for perpendicular recording heads

Solutions for the magnetic potential in rectangular regions with simple boundary conditions are used to approximate the two-dimensional potential in the head face plane of a recording head. This method of approximation can be applied to any recording head with rectangular corners, in the presence of an underlayer. The slot approximation is demonstrated for ring heads and shielded (magnetoresistive) pole heads. The quarter plane approximation is given for application to finite-length heads. Estimates of the field components and the spectral response function are derived from the approximate potential. The simple slot approximation is shown to be at least as accurate as other, often more complicated, methods of approximation. Most significantly, both the slot and the quarter-plane approximations are easy to apply and need no prior knowledge of the head field of the particular geometry under consideration. Index Terms - Approximations, digital recording, magnetic recording/reading heads, mathematics.