A new method of determining the critical state in superconductors

A new numerical method for solving the critical state, based on the force–displacement curve of the flux lines, is described. The equation can be expressed in terms of the vector potential and can be solved by commercial finite element programs. It gives the critical state directly as a first approximation but a flux flow resistivity can easily be added. It avoids some of the numerical problems that occur if an E–J curve of the form is used with large values of n. It is particularly advantageous for problems involving trapped flux where a power law leads to decay at a rate dependent on the power assumed and the very low electric fields mean that the E–J curve is probably exponential. The flux flow resistivity can be included and since the relevant power law is 1/n rather than n the solutions are more stable. Multiphysics packages, such as FlexPDE, which allow simultaneous equations to be solved, can find the temperature distribution by adding the heat flow equation.