Varying cross section superconductor

[Relena]

Here's the question: How can we describe a sudden change in the cross sectional area of a super conductor carying a current i from bigger A1 to smaller A2, such that the current density J after change is higher than Jc ?
I have one scenario in my mind, the tempreture rises in the non-superconductive length ? let's say we have a full control of heat so it doesn't go beyond the critical temprature, What changes will happen to the generated magnetic field ?

 

[f95toli]

The answer will depend on a number of factors; most notably the size of the constriction compared to the coherence length of the superconductor.

Try googling "constriction junction" (also known as ScS Josephson junctions). You can also try looking at some papers on phase slip.