Analytic solution of the critical-state model for an elliptical cylinder with field-dependent critical current density

We present an exact solution of the critical-state model for a cylinder of elliptic cross section, and derive the equations for the constant-B contours. A method of obtaining magnetization curves is presented for the case where the critical current density ${\mathit{J}}_{\mathit{c}}$ is a general function of the field. The explicit cases of ${\mathit{J}}_{\mathit{c}}$ decaying exponentially with the field, and also according to Kim’s model, are solved. Numerical results are presented for the exponentially decaying ${\mathit{J}}_{\mathit{c}}$. The relevance of this calculation to the problem of sandpiles is discussed.