Abstract
A method for obtaining the critical state in three dimensions is described. This uses an extensionof a previous 1D model based on flux line motion in which the equations are not based on anE–J curve, which leads to time dependence. In order to make clear the connection betweenthe scalar potential, the particular vector potential derived and the electrostaticsurface charges, it has proved necessary to start from eddy currents in a normalconductor. The eddy current solutions for a normal conductor are the same asthose for a London superconductor in a DC field, except that although ascalar potential is needed there are no electrostatic charges. The problem of asuperconducting puck in a field parallel to the faces is solved. It is assumed that theelectric field is parallel to the current density which is quite probable for highTc superconductors, but other criteria could be used. Like other 3D solutions the computationtakes a long time; even this relatively simple case takes 7 h with a 1.3 GHz PC. However thiswas using a standard PC with default parameters in the finite element packageso there is room for optimization. All the results were obtained with FlexPDE.
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