Abstract
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.