Representing superconductors in ANSYS Maxwell and calculating mutual inductance.

  • Last Post 13 March 2019
ejp4568 posted this 07 March 2019

I would like to calculate the mutual inductance between a control line and a flux loop in a quantum chip design, which requires the use of superconducting materials.


In the past I have been using other materials to calculate values of the mutual inductance because I did not believe this would make a significant difference in the values achieved, but I know think otherwise. I have tried to remedy this by creating a material with near 0 (10^(-10)) value for the relative permeability, since a true superconductor would have a value of 0 here,  but Maxwell doesn't seem to be able to simulate something with a relative permeability of 0, and a large value for the conductivity (it starts throwing errors around 10^12). A relative permeability of 0 would give a magnetic susceptibility value of -1, but I have not been able to find a location that I can specific the chi value. The built in material 'perfect conductor' does not have the parameters that a true superconductor has, and also Maxwell does not allow conduction paths to be made out of this material. I'm mostly curious about a way that I can confidently represent the true mutual inductance of my chip and get around the restrictions maxwell has put on the material settings.


I also have the issue of the problem region I am solving over. Since I have a current entering and exiting the chip, I am only able to make the problem region flush with two of the sides, and then extend some distance on the others. I'm not sure what effect the problem region has with the values, but they seem to fluctuate significantly as I adjust the size of the region that I am solving over. But this still restricts me to have a gap of 0 on two of the sides, which seems like it is causing issues. What is the proper way to create a problem region to give me accurate results.


Summary: How do I accurately represent a superconductor in Maxwell for mutual inductance calculations and what is the proper way to create the problem region to solve over?



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kkeikhos posted this 13 March 2019


I know that Maxwell doesn't like super conductors in Magnetostatic solver. However you should be able to use relatively high conductance value to represent them as you mentioned. 

Eddy current is a good start if you are interested to study the inductance in different frequencies.


Regarding the region and excitation if I understood the question correctly, you can make a short conduction loop in your design and make an intersection and apply the current that way. that way you are not adding extra length to your design and region. Did I understand it correctly?



ejp4568 posted this 13 March 2019

Can you explain the short loop a bit further? does this mean having a line of conductor, but having a small loop at some point within the line and then applying it in that circle? would this require creating a insulating boundary condition on the line, and would that also represent the current flowing through the wire in the correct way? 


My main question with the region is that I am unsure of how large I should make it. Before i was partially limited due to the current excitations, but on the sides that were not if I increased the region size, it would increase the value calculated for the mutual inductance up to some point where it peaked. So I'm unsure how large to make the region to get an accurate number for how large the actual mutual inductance is. Should it be as large as possible for it to converge, as small as can fit around the model, or somewhere in between?