A new method for superconductor magnetization curve computing

A mathematical method using geometrical transformations (reflections and translations) on an arbitrary chosen curve - called the profile function - which describes the magnetic field distribution inside the superconductor sample is presented. This profile function must be strict monotone increasing and positive. By this method we have calculated the expression of 'jump' portion that connects the ascending and descending field branches and non-primitive minor loops. Also we propose a new model (called critical field model) based on a bounded profile function at some value B-cr. explicit expressions for computing all the branches of the hysteresis loop are derived. The comparison between the values of critical current density computed from the vertical width of the hysteresis loops Delta M and that deduced from the chosen profile function shows a good agreement for B-a > B-p. Finally, we present an exact relation between Delta M and J(c) and its derivatives for an arbitrary positive J(c) function. (C) 1998 Elsevier Science Ltd. All rights reserved.