# Varying cross section superconductor

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 ?