Model for a flux pinning magnet

[sach1tb]

model for a flux pinning

What is the best model we can make for a flux pinned magnet? From readings on superconductor levitation research (https://www.amazon.com/gp/product/0471559253/?tag=pfamazon01-20), I found that the magnet feels a spring-like force and that the spring constant (K) depends, among other things, on the type of SC, the magnet and it's proximity. But that is only in the direction normal to the surface of the superconductor (axis y in the attached diagram). What about the other five DOF? Also, from experiments I can see that the magnet spins easily, or does not feel any torsion, along the magnetic pole axis (shown in the diagram, and this is perhaps because the positions of lines of force remain the same). But what is a good way to model the rest of the system? Mass-spring-damper in other directions?

This brings me to the second part. We are working on a project/research that requires building a non-contacting mechanical interface. We haven't been able to find any equation/formula through which we can get the forces (during flux pinning or otherwise) by simply plugging in values. Our next approach is to go backwards from experiments, and possibly, take readings for different combinations of superconductor and magnets. However, it would require an ambitious set up to measure forces/torque in all directions, when a flux pinned magnet is displaced or rotated.

In the attached diagram, it is seen that the magnet can be flux pinned in any of the different orientations between the two shown. Is it a good assumption to say that when the magnetic pole axis is normal to the surface of HTSC, as maximum flux will be pinned, we get the most stiff system?
A good model – or experiments – will help us in finding the best orientation and parameter values for a stiff arrangement.

Thanks a bunch for all your help !

-S

 

[pallidin]

This is interesting. Perhaps some experts or others can jump in.

 

[Gokul43201]

Small rotations about 2 of the 3 axes can be modeled in terms of (treat the rotated magnet as made of several tiny pieces displaced a little from its equilibrium height) the existing model for the force along the direction normal to these two axes. Unfortunately, in the limit of purely harmonic behaviour in the normal direction (F_up/down = -kx_up/down), you will get the result that these small rotations require no torque (or rotational stiffness = 0). Unless you include anharmonic terms, you will not get any rotational stiffness about these two axes.