Generalize boozer transform to multiple surfaces

[f0uriest]

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[dpanici]

https://drive.google.com/file/d/1mA8tmktuMO-bUwUVtD3LoIH2meHPesCd/view?usp=sharing

Some initial notes I had on this, trying to follow the usual Boozer transform way but with Fourier-Zernike basis instead of DoubleFourierSeries. I was hoping to see if we could get a way to relate the coefficients of nu with the coefficients of a quantity like the poloidal magnetic field, but there are some extra coupling terms that made it not obvious how to relate the coefficients themselves. Maybe another approach would be better, this is just what I've tried

[rahulgaur104]

@dpanici I am interested in this one but your notes are not accessible (due to permissions)

[dpanici]

Try the link noww

[rahulgaur104]

Yes, I can access the file now. Thanks!

[dpanici]

Make sure the components of B we try to find coeffs for are analytic functions at the axis

[dpanici]

@dpanici check where I did fits of Boozer/DESC B in FourierZernike

[unalmis]

e_theta is analytic. It's always zero on axis. e_zeta is also analytic. It is well defined on axis and always points in direction of B. See https://github.com/PlasmaControl/DESC/blob/87db5bec666e26f4a87310170a1d1ff86301b9f3/tests/test_axis_limits.py#L320

The covariant basis vectors are just derivatives of some position vector along a coordinate curve, so they will have nice analysis properties. So B is analytic implies B_theta and B_zeta are too.