Are contravariant b fields in GPEC or RMATCH (or both) correct?

[matt-pharr]

In gpeq.f/gpeq_sol(psi), the contravariant magnetic fields are calculated -- this is also found in rmatch/match.f/match_output_solution(). In gpeq.f, the grad-psi component of the contravariant b field is:

bwp_mn=(chi1*singfac*twopi*ifac*xsp_mn)

However, in rmatch, it also calculates the magnetic field,

outtotsol(:,ip)=chi1*ifac*singfac*outtotsol(:,ip)

In Jong-Kyu's thesis, the contravariant B fields are found in equation 2.58, where it states,

$$\displaystyle \delta B^\psi = \frac{\chi '}{\mathcal{J}}\left(\frac{\partial}{\partial \vartheta} + q \frac{\partial}{\partial \varphi}\right) \xi^\psi$$

This makes sense as in both codes, singfac=m-nq, chi1$=2\pi\psi_o$. outtotsol is the same thing that gets written in the rpec workflow to make u1 in gpec, so those should be the same. The only thing different between them is a factor of $2\pi$. I am working on getting the code able to compare these, but what do you all think @logan-nc @parkjk ?

[parkjk]

Yes so bwp_mn = $J \delta B^\psi$. Extra $2\pi$ is because DCON uses normalized angles. So each (m,n) mode $\propto \text{EXP} (i2\pi(m\theta-n\phi))$.

[logan-nc]

I trust the GPEC. I suspect Zhirui either made a mistake or was doing something to compare to another code that used angles in radians. You can clearly see he was of two minds, since he has the 2pi earlier in the same file:

https://github.com/PrincetonUniversity/GPEC/blame/599132511440693c2edeed308c842ac4d869b341/rmatch/match.f#L643-L652

It seems at first look like the line in question,

https://github.com/PrincetonUniversity/GPEC/blame/599132511440693c2edeed308c842ac4d869b341/rmatch/match.f#L1563-L1569

should be changed to include the 2pi.

However, it would be best if @matt-pharr could (1) trace all the places outtotsol is used after this to make sure we aren't messing something else up and (2) double check that a twopi isn't already thrown in later in the RPEC workflow to compensate for this.

[matt-pharr]

For the sake of documenting, RMATCH was in fact missing the factor of 2 pi. After adding it in, the eigenmodes match, here is the $B$ field on a resistivity scan. There are two of each resistivity because I am showing the RMATCH calculated B field and the GPEC calculated B field. They are identical, so we only see one line of each color.

[logan-nc]

Thanks for fixing and documenting this!