Thermal Wave Propagation in a Superconducting System as an Autowave Process

Abstract

A superconducting system (SCS) may be treated as an object where the autowave processes can be realized, which essentially affect its operational characteristics and determine the uppermost achievable parameters and stability regions. There are several lines of argument for this. The thermal state of a SCS is described by a quasilinear parabolic equation (in the general case, by a system of equations). The heat released by the current in an overheated superconductor serves as a distributed energy source. Strong nonlinearities in the temperature dependences of heat release and of equation coefficients may generate various autowave regimes (such as development of local overheated regions or propagation of thermal waves, etc.), which are dangerous for stable SCS operation. When a local overheating region with the temperature above a critical value T_C (so-called normal zone) arises in a current-carrying superconductor, it can then propagate along with a constant velocity bringing the system into the emergency (normal) state. The dependence of propagation velocity on the current is one of the most important characteristics of SCS. Earlier the velocity was evaluated in the framework of the simplified model [l] with constant coefficients or by numerical simulation of a given system. Meanwhile, the autowave approach and analogy with combustion theory and other fields will enable one not only to elaborate a general view on the superconductor stability problems but also to obtain new concrete results.