Two-dimensional models of the magnetic-field enhancement at pit and bump

TL;DR

This paper derives mathematical formulae for magnetic field enhancement at two-dimensional semi-elliptical bumps and pits with chamfered edges using conformal mapping, providing models for real-world imperfections.

Contribution

It introduces new conformal mapping-based formulae for magnetic field enhancement at specific geometric features, including chamfered edges, improving modeling accuracy.

Findings

Derived explicit formulae for semi-elliptical bumps.

Provided approximate models for pits with round edges.

Enhanced understanding of magnetic field behavior at surface irregularities.

Abstract

Formulae of magnetic field enhancement at a two-dimensional semi-elliptical bump and a two-dimensional pit with chamfered edges are derived by using the method of conformal mapping. The latter can be regarded as an approximated model of the two-dimensional pit with round edges.