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.

 

[Entropia]

A sudden change in the cross-sectional area of a superconductor carrying a current can result in a higher current density if the total current remains constant while the area decreases. This can be achieved by either increasing the applied voltage or decreasing the resistance of the superconductor. In the case of increasing the applied voltage, the current density will increase due to Ohm's law (J = V/R) where the resistance decreases as the area decreases. Alternatively, if the resistance remains constant, the current density will increase as the area decreases.

In terms of the generated magnetic field, a sudden change in cross-sectional area can also result in a change in the magnetic field strength. This is because the magnetic field strength is directly proportional to the current density, according to the Biot-Savart law. Therefore, as the current density increases, the magnetic field strength will also increase.

If the temperature of the non-superconducting length increases, it is likely that the superconductor will transition to a normal state due to the critical temperature being exceeded. This will result in a sudden increase in resistance and a decrease in current density. The generated magnetic field will also decrease as the current density decreases. However, if the temperature is carefully controlled and kept below the critical temperature, the sudden change in cross-sectional area can still result in a higher current density and therefore a stronger magnetic field. This is because the resistance of the superconductor will remain low and the current density will increase as the area decreases.

In conclusion, a sudden change in the cross-sectional area of a superconductor carrying a current can result in a higher current density and a change in the generated magnetic field. This can be achieved by either increasing the applied voltage or carefully controlling the temperature to prevent the superconductor from transitioning to a normal state. Further research and experimentation may be needed to fully understand and optimize the effects of varying cross-sectional areas on superconductors.