Multi-fractal properties of the nonlinear electromagnetic response of irreversible type-II superconductors

Using the Grassberger-Procaccia method for calculating correlation dimensio n D-2, we show that the nonlinear response of a hard superconductor to an e xternal two-harmonic magnetic field possesses multi-fractal properties. The response is described in the frame of the Bean critical-state model. The n umber of attractors in the reconstructed phase-space of the response depend s on the ratio Omega of the harmonic frequencies. D-2 increases as Omega be comes irrational, indicating a transition of the superconductor to the chao tic regime. (C) 2000 Published by Elsevier Science B.V. All rights reserved .