Nonlinear susceptibility study in superconductors based on Bean and Kim - Anderson models

Many papers have been published about nonlinear susceptibility [1.7-1.22]. In most of these, this phenomenon was discussed quantitatively. The origin of the nonlinear susceptibility of type II superconductors is discussed in the present work. There are various critical state models that predict the response of these superconductors to the applied magnetic field. Different assumptions about the dependence of the critical current on the applied magnetic field produce different critical state models [1.2, 1.23, 1.24]. The Bean model and Kim - Anderson model are the two models considered in the present work. The Bean model states that there could be only three states for critical current: no current, and +/-Jc, where Jc is the critical current density [1.2]. In the Bean model the critical current profile is a discontinuous line. The Kim - Anderson model states that the critical current varies with the position within the sample and is inversely proportional to the field. In the Kim - Anderson model, the critical current profile is a continuous curve [1.7]. In the present work, an extensive numerical study was undertaken for both the slab and cylinder sample geometries. The magnetic field in each case was applied along the vertical axis. The nonlinear AC susceptibility was investigated quantitatively. Nonlinear susceptibility depends strongly on the geometry and symmetry of the system, the applied field, and the critical state model considered.