Dommaschk Potential Issues

[dpanici]

It seems that for certain Dommaschk potentials, the results do not align with past publications.

Examples are in this paper, HELIOTRON-E apparently gives some surfaces but with helical excursion which is incorrect, and the other two give no flux surfaces at all.

Things to check

• Implement the HELIOTRON-E myself and check - seems to have a helical axis when it should be planar
• check AD B versus finite difference B for different step sizes (maybe I did not do the gradient right, though I doubt it)
• Implement optimization with the potentials to see if that helps uncover any issues (if this does not work at all maybe there are some issues numerically with implementation?)
• look at algorithm closer and compare to how Dommaschk originally implemented them, see if there are parts prone to numerical error (in orig. paper, he mentions that the factorial can cause very large denominators for some terms)
  • could try implementing with a higher precision library (mpmath or sympy maybe) to see if it is precision issues, I have them in Sympy somewhere already I think
  • implement recursive version of the potentials (currently have nonrecursive implemented)