Ac susceptibility components of a current-carrying thin type-II superconducting annulus

By assuming a spatial dependence on the sheet-current density, we have investigated the real ( chi ') and imaginary parts ( chi super( double prime ) chi double prime ) of the susceptibility of a thin type-II superconducting annulus (with the inner and outer radii a and b , respectively) in the absence and also in the presence of a radial transport current, using the Bean critical state model in which the critical current density is assumed to be independent of the local magnetic field. The results of our calculations on the components of the magnetic susceptibilities in two cases and for the different aspect ratios are compared with each other. The comparison shows that by applying a radial current to the sample, the imaginary part of the susceptibility is increased. We have studied the variations of the chi super( double prime ) chi double prime with respect to chi ' for a several aspect ratios. We also found that when a transport radial current is passed through the washer, by increasing the aspect ratio a /b in the parametric plot of chi super( double prime ) chi double prime vs. chi ', the imaginary part decreases and the peak of chi super( double prime ) chi double prime decreases in magnitude but shifted towards chi super( double prime ) chi double prime = 0.