Magnetic Readback Signal Model by Means of Inversion of the Schwarz-Christoffel Integral

An analytical model for the readback pulse from a shielded magnetoresistive head used in storage devices in studied in terms of conformal map of the domain associated with the geometry of this head. It leads to the famous problem on the Schwarz-Christoffel integral inversion. In the Part I of the paper we discuss different methods to invert the Schwarz-Christoffel integral and discuss the link of the problem with various aspects of complex analysis. To proceed we use different methods of the hyperelliptic abelian functions theory: the standard theta functional approach, Hyperelliptic Kleinian functions theory and the Weierstrass-Poincare reduction theory of Riemann theta functions and Abelian integrals to lower genera. The Part II is devoted to the application of the theory developed above to the problem of analytical description of the readback signal for the shielded magnetoresistive head and calculation of its sensitivity function.