Magnetic response of superconductors in various geometries

The complex ac susceptibility chi = chi' - (i)chi" of superconductors of various shapes in parallel or perpendicular magnetic field can be calculated from an integral equation for the current density J(tau, t) inside the superconductor. The superconductor is characterized by a general current-voltage law E(J), e.g. E(J) = E-c[J/J(c)(B)](n(B)) where E is the electric field, B = mu(o)H the magnetic induction, E-c a prefactor, J(c) the critical current density and n greater than or equal to 1 the creep exponent. For n > 1, the nonlinear ac susceptibility is calculated from the hysteresis loops of the magnetic moment. For n >> 1 the Bean critical state model results. For n = 1, and for any linear complex resistivity rho(ac)(omega) = E/J caused by thermally activated vortex motion, the linear ac susceptibility chi (omega) may be calculated from an eigenvalue problem. At high frequencies, the chi(omega) of thick discs in axial field omega crosses over from perpendicular to parallel behaviour since the skin effect forces the magnetic field lines to flow around the disc.