OPTIMAL-CONTROL MODEL FOR THE CRITICAL-STATE IN SUPERCONDUCTORS

Grounded an a variational principle, we present a generalization of th e standard critical-state approach in type-II superconductors. The fre e energy is minimized with the constraint \J(r)\less than or equal to J(c) for the macroscopic current density, posing the problem in the fr amework of the optimal control theory. The application of this mathema tical tool allows us to determine the critical state in which the syst em organizes itself. This permits to confirm the critical-state hypoth esis for an idealized one-dimensional geometry and to deal with multic omponent field situations, for which additional constitutive laws are provided. A geometrical picture of the field penetration process has b een developed and we obtain both analytical and numerical solutions fo r two-dimensional problems under an applied parallel field and superim posed transport current. [S0163-1829(98)06038-X].