Add Shaing corrections to Angioni-Sauter model

[theo-brown]

Part of #1406.

Currently in draft form for development purposes. Before merging, will need to move many of the calculations to physics.collisions.

@fcasson @jcitrin for discussions.

Sources

Electrons: https://pubs.aip.org/aip/pop/article/4/5/1375/980556/Electron-transport-processes-close-to-magnetic
Ions: https://pubs.aip.org/aip/pop/article/4/3/771/263553/Ion-transport-process-around-magnetic-axis-in

[theo-brown]

In tandem with this PR I am producing a closer comparison of STEP-like plasmas in JETTO and TORAX; this is taking a while, so I thought I'd get the feature development under way as well.

Below is a plot of the initial state from a modified examples/step_flattop_bgb.py simulation comparing Shaing and Angioni-Sauter contributions for the full radius.

• Once I've got a more comparable JETTO run (requires turning off a bunch of models) I'll add JETTO NCLASS profiles as a reference.
• The chi produced by this model still don't seem to be looking like what we expect from NCLASS - namely, significant peaking in ion transport on the axis.
• However, there is an obvious improvement over Angioni-Sauter in that transport doesn't disappear on-axis.

I've added a smooth exponential transition between the two models, shown here:

[theo-brown]

Some notes from a discussion with Sarah Newton (neoclassical expert at UKAEA) and @fcasson

• NEO solves the force balance, solving for viscosities and transport simultaneously
• Anecdotally, NEO behaves similarly to NCLASS on axis in JET cases simulated in JETTO (chi neo i explodes at the axis)
• NCLASS uses fitted values for the viscosities as functions of collisionality (?), and then computes transport using those viscosities. The fit is not good everywhere.
• The Shaing 1997 model implemented here uses an asymptotic expansion for viscosity- effectively like evaluating NCLASS once and using that value always
• Angioni-Sauter is a fit to NEO data, but the fit is not good everywhere.

[theo-brown]

In integrated scenarios, the difference in value on-axis caused by this model actually makes a minimal difference, because the ion transport is still so tiny. Compare with the effect of adding in a patch to mimic NCLASS behaviour on the examples/step_flattop_bgb.py simulation:

(Solid=AS+Shaing, dashed=AS only)

(Solid=with on-axis patch, dashed=AS only)

(Solid=with on-axis patch, dashed=AS+Shaing)

As a recap of why we're interested in this, current holes at the core could be a huge problem for STEP. As you can see by comparing the q profiles, the ion transport in the core has a noticeable effect on the current hole.