Nonlinear flux diffusion and ac susceptibility of superconductors: Exact numerical results

The ac response of a slab of material with electrodynamic characteristics E similar to j(kappa+1), kappa greater than or equal to 0, is studied numerically. From the solutions of the nonlinear diffusion equation, the fundamental and higher-order components of the harmonic susceptibility are obtained. A large portion of the data for every kappa can be scaled by a single parameter, xi=t(1/(kappa+2)). H-0(kappa/(kappa+2))/D, where t is the period of the ac field at the surface, H-0 is its amplitude, and D is the slab thickness. This is, however, only an approximate scaling property: The held penetration into a nonlinear medium is a more complex phenomenon than in the linear case. In particular, the susceptibility values are not uniquely defined by a set of only two parameters, such as kappa and xi, while one parameter, i.e., t(1/2)/D, is sufficient to describe the electrodynamic response of a Linear medium. (C) 1996 American Institute of Physics.