Reverse-Mode Differentiable Ideal-Ballooning Stability Solver

[rahulgaur104]

Infinite-n ideal MHD ballooning modes are of significant interest to both the tokamak and the stellarator community.
These instabilities are also related to smaller-scale kinetic instabilities, which cause significant heat loss from fusion reactors.
This commit adds the ability to both analyze and optimize MHD equilibria against the ideal ballooning mode.

An adjoint implementation of an ideal ballooning solver has only been successfully demonstrated previously on a much smaller scale. If this commit works, it would be at least an order of magnitude faster than the linked code.

Here are the tasks:

• Add geometry coefficients
• Test geometric coefficients. Maybe compare it with Patrick's fork in DESC. Add a test
• Compare results with each other (ideal_ball_gamma1, ideal_ball_gamma2, Newcomb_metric) and with my older finite-difference solver
• Eigendecomposition and adjoint of the matrices. Wrap the routine in DESC magic.
• Compare results for the HELIOTRON case with COBRAVMEC
• Write a test for HELIOTRON comparison with COBRAVMEC
• Write a test for the Newcomb metric
• Add a tutorial notebook explaining ideal ballooning and Newcomb calculations

[dpanici]

some very small changes. I will review again once re-requested

[dpanici]

I second this, it would also match the paper notation better

[rahulgaur104]

Merging this branch as I have two approvals.