Nonlinear dynamics of the critical state in hard superconductors and composites based on them

The nonlinear dynamics of the magnetic flux within a superconducting plate in response to the continuous rise in temperature over the course of the entire process of applying the magnetic field is investigated within the critical-state model. The results of numerical simulations based on a method developed to solve the system of Fourier and Maxwell equations with an unknown internal magnetic flux penetration boundary are compared with the corresponding analytical expressions of the isothermal theory. It is shown that the difference between the isothermal and nonisothermal models increases as the heat transfer coefficient decreases and as the rate of increase in the magnetic field strength and the transverse dimensions of the superconductor increase. The errors appearing in the isothermal approximation are very significant in the case of a thermally insulated, massive conductor. Consequently, the calculated values of the thermal losses occurring during the time period preceding the flux jump in the isothermal approximation can be significantly lower than the corresponding nonisothermal values. Zh. Tekh. Fiz. 67, 29–33 (September 1997)