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Implement a regularized Dommaschk Potential least squares minimization #1499

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dpanici opened this issue Dec 28, 2024 · 0 comments
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dpanici commented Dec 28, 2024

Because the magnetic field from the Dommaschk potentials are linear in their coefficients, we can do a REGCOIL-like optimization with them. With no regularization, if we fix the B0 term, we can then solve for the combination of the rest of the coefficients which minimizes Bn on a given surface.

With regularization (on what exactly I am unsure) we can then vary between Bn and some complexity measure of the field.

Regularization Ideas

  • Just the coefficient magnitudes - issue with this is that each potential is of a vastly differing intrinsic magnitude, so I think it would have to be paired with some sort of normalization to make this more meaningful

  • some sort of measure relating to the corresponding coil complexity: this could be related to the poloidal or toroidal harmonic, penalizing higher order harmonics?

  • change Dommaschk least squares fitting to have an option to minimize just Bn on the given surface, fixing B0 or some linear combination of coefficients in order to respect Ampere's law for a given eq

  • implement regularization

@dpanici dpanici added the P2 Medium Priority, not urgent but should be on the near-term agend label Dec 28, 2024
@dpanici dpanici self-assigned this Dec 28, 2024
@dpanici dpanici added P1 Lowest Priority, will get to eventually P3 Highest Priority, someone is/should be actively working on this and removed P2 Medium Priority, not urgent but should be on the near-term agend P3 Highest Priority, someone is/should be actively working on this labels Jan 6, 2025
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