ANALYTIC SOLUTION OF THE CRITICAL-STATE MODEL FOR AN ELLIPTIC 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 J(c) is a general function of the field. The explicit cases of J(c) decaying exponentially with the field, and also according to Kim's model, are solved. Numerical results are presented for the exponentially decaying J(c). The relevance of this calculation to the problem of sandpiles is discussed.