Approximate Expressions for the Magnetic Potential and Fields of 2-D, Asymmetrical Magnetic Recording Heads

A 2-D asymmetrical magnetic head is characterized by the parallel inclination of the semi-infinite, inner gap walls, and where the gap length and head-to-underlayer separation are small compared with the other dimensions in the head. With head corner inclination, these structures contribute to the reduction in the effective gap length of the head and, therefore, the increase in the field magnitude and narrowing of the field distributions near the acute gap corner. Asymmetrical heads were, therefore, proposed for increasing the writing and readout resolutions in gapped magnetic head structures. There are currently no explicit or approximate analytical solutions for the potential and fields from 2-D asymmetrical magnetic heads. This paper is concerned with the detailed theoretical derivation of relatively simple closed-form approximations for the scalar magnetic potential and fields from 2-D asymmetrical magnetic heads and their Fourier transforms, applicable to any arbitrary corner inclination angle. A general theory based on the translated sine Fourier series is developed to model and study the reaction of a soft magnetic underlayer on the surface potential of any magnetic head structure, and applied to the asymmetrical head. The approximate potential and field expressions derived in this paper demonstrated a very good agreement with the finite-element calculations of the 2-D asymmetrical heads.