Numerical experiments of Joule heat damage in superconducting transport

We examine a complete framework of the time-dependent Ginzburg-Landau equation coupled with the Maxwell and heat-discusion equations. The heat-discusion equation can be derived from the free energy conservation law, and both superconducting and normal components are proven to contribute to the heat discusion. Based on the framework, we perform numerical simulations of a superconducting thin film and show that collisions between vortices and antivortices bring remarkable production of Joule heat.