The current penetration in an infinite superconducting tape with elliptical cross-section in the critical state as a response to a perpendicular applied field is described by two models. One is a numerical model based on energy minimization after each field change. The second model is a simple analytic approximation for the flux fronts obtained by the numerical model. The magnetization, the ac susceptibility and the associated ac losses can be calculated. We provide an empirical expression for the position of maxima in the imaginary part of ac susceptibility. Then, the value of the critical-current density in a superconducting tape with elliptical shape of any dimensions can be extracted from ac susceptibility data.
