Temperature factor for magnetic instability conditions of type – II superconductors

Abstract

The macroscopic development of interrelated electrodynamics and thermal states taking place both before and after instability onset in type-II superconductors are studied using the critical state and the flux creep concepts. The physical mechanisms of the non-isothermal formation of the critical state are discussed solving the set of unsteady thermo-electrodynamics equations taking into consideration the unknown moving penetration boundary of the magnetic flux. To make it, the numerical method, which allows to study diffusion phenomena with unknown moving phase-two boundary, is developed. The corresponding non-isothermal flux jump criteria are written. It is proved for the first time that, first, the diffusion phenomena in superconductors have the fission-chain-reaction nature, second, the stability conditions, losses in superconductor and its stable overheating before instability onset are mutually dependent. The results are compared with those following from the existing magnetic instability theory, which does not take into consideration the stable temperature increase of superconductor before the instability onset. It is shown that errors of isothermal approximation are significant for modes closed to adiabatic ones. Therefore, the well-known adiabatic flux jump criterion limits the range of possible stable superconducting states since a correct determination of their stability states must take into account the thermal prehistory of the stable magnetic flux penetration. As a result, the calculation errors in the isothermal approximation will rise when the sweep rate of an external magnetic field or the size of the superconductor’s cross-sectional area increase. The basic conclusions formulated in the framework of the critical state model are verified comparing the experimental results and the numerical analysis of the stability conditions and the temperature dynamics of the helicoid-type superconducting current-carrying element having real voltage–current characteristic.On the whole, the non-isothermal stability conditions expand the existence of allowable stable superconducting states. The non-isothermal approximation permits also to link the theories of the losses, the magnetic instability and the thermal stabilization of superconductors, which are independently developed.