Validate geometry loading for spherical tokamaks

[theo-brown]

I think there's at least one assumption (maybe more) in the EQDSK loader (and maybe elsewhere) that breaks down for STs.

Examples:

$\frac{\partial V}{\partial \rho} = \frac{4\pi\Phi_b \hat{\rho}}{F \langle1/R^2\rangle}$:

$<1/R> = 2\pi \frac{\partial A}{\partial V}$ (JETTO vs TORAX, same eqdsk):

Note <1/R> is not expected to be constant for STs.

[jcitrin]

On the first example, as discussed in #1371, I think that may be an issue with the near-axis smoothing, exasperated by using an EQDSK file.

[jcitrin]

On the second example, the issue is probably that we need to decouple the area and volume calculations. dA/dV = 1/(2piR) by construct in TORAX. e.g. in from_eqdsk , and in build_standard_geometry

[theo-brown]

Yep, agree on the second. For the first, I could test loading the same geometry from some other sources? I agree it looks like an interpolation/smoothing issue rather than something more serious. I think I can dig out a CHEASE STEP geometry and can easily get an IMAS one

[jcitrin]

For the first, I could test loading the same geometry from some other sources? I agree it looks like an interpolation/smoothing issue rather than something more serious. I think I can dog out a CHEASE STEP geometry and can easily get an IMAS one

That sounds good

[theo-brown]

Regarding the point you mentioned about it being surprising how much the approximation <1/R> ≈ 1/R breaks down when we spoke in person.

I think the Shafranov shift is just big in STs like STEP, increasing by ~10x over the radius - see a comparison below between something STEPish and something JETish.

This in turn breaks the V ≈ A × 2πR₀ approximation, as the real relationship is dV = ⟨2πR⟩dA.

If it's ok, I'd like to make a PR to add the true relationship (with <1/R>) to all the TORAX geometry loaders.

[theo-brown]

Note that this will also mean that the current density profiles are off as well (at least for the first timestep), because they are computed from Ip_profile_face / spr.

[jcitrin]

Note that this will also mean that the current density profiles are off as well (at least for the first timestep), because they are computed from Ip_profile_face / spr.

No problem. The expectation is that the existing (standard shaping) sim test results will change by a relatively small fraction.

Note (if you aren't already aware) of the existing scripts for generating new sim tests and comparing results to existing cases.
https://torax.readthedocs.io/en/v1.0.3/contribution_tips.html#contribution-tips

[theo-brown]

I could test loading the same geometry from some other sources

I'm working on this offline, as I'm not sure I can share the plots due to STEP IP restrictions.
That said, the linked PR #1413 does resolve the <1/R> problem and leads to a match of geo.spr profiles.