Rc/toroidal angle

[f0uriest]

• near axis constraints with omega
• constant offset surface
• Proximal projection
• Add stuff for spectral condensation / optimal fitting
• Default to fixing zeta==phi?
• to_FourierRZCurve methods should now be possible?
• Fix calculation of A, a_major/a_minor, other stuff that needs to be computed at const phi, not const zeta
• changing continuation/perturbation to work with the new coordinates (changing regularization)

Resolves #465

[unalmis]

Are you sure that DSHAPE should have non positive curvature? tests/test_objective_funs.py::test_mean_curvature is failing

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     +0.44 +/- 5.26     | +2.33e-03 +/- 2.81e-02 |  5.37e-01 +/- 2.0e-02  |  5.35e-01 +/- 1.9e-02  |
 test_build_transform_fft_midres         |     -0.36 +/- 4.18     | -2.25e-03 +/- 2.58e-02 |  6.16e-01 +/- 2.2e-02  |  6.18e-01 +/- 1.4e-02  |
 test_build_transform_fft_highres        |     +0.43 +/- 3.38     | +4.39e-03 +/- 3.41e-02 |  1.01e+00 +/- 2.9e-02  |  1.01e+00 +/- 1.7e-02  |
 test_equilibrium_init_lowres            |     -0.58 +/- 2.92     | -2.26e-02 +/- 1.13e-01 |  3.86e+00 +/- 5.7e-02  |  3.88e+00 +/- 9.8e-02  |
 test_equilibrium_init_medres            |     +0.20 +/- 3.63     | +8.58e-03 +/- 1.59e-01 |  4.37e+00 +/- 9.0e-02  |  4.37e+00 +/- 1.3e-01  |
 test_equilibrium_init_highres           |     +1.96 +/- 2.08     | +1.12e-01 +/- 1.19e-01 |  5.84e+00 +/- 9.9e-02  |  5.73e+00 +/- 6.5e-02  |
-test_objective_compile_dshape_current   |     +9.36 +/- 1.41     | +3.61e-01 +/- 5.44e-02 |  4.21e+00 +/- 4.7e-02  |  3.85e+00 +/- 2.8e-02  |
-test_objective_compile_atf              |    +37.31 +/- 1.25     | +3.12e+00 +/- 1.05e-01 |  1.15e+01 +/- 9.0e-02  |  8.36e+00 +/- 5.4e-02  |
 test_objective_compute_dshape_current   |    +19.74 +/- 6.98     | +2.62e-04 +/- 9.26e-05 |  1.59e-03 +/- 4.7e-05  |  1.33e-03 +/- 8.0e-05  |
-test_objective_compute_atf              |    +41.36 +/- 6.77     | +1.77e-03 +/- 2.90e-04 |  6.06e-03 +/- 2.4e-04  |  4.29e-03 +/- 1.6e-04  |
-test_objective_jac_dshape_current       |    +88.80 +/- 15.22    | +3.24e-02 +/- 5.56e-03 |  6.89e-02 +/- 4.3e-03  |  3.65e-02 +/- 3.5e-03  |
-test_objective_jac_atf                  |    +76.56 +/- 2.48     | +1.46e+00 +/- 4.72e-02 |  3.37e+00 +/- 4.2e-02  |  1.91e+00 +/- 2.2e-02  |
-test_perturb_1                          |     +9.63 +/- 2.33     | +1.32e+00 +/- 3.19e-01 |  1.50e+01 +/- 1.8e-01  |  1.37e+01 +/- 2.6e-01  |
-test_perturb_2                          |    +11.95 +/- 1.54     | +2.26e+00 +/- 2.90e-01 |  2.12e+01 +/- 1.7e-01  |  1.89e+01 +/- 2.4e-01  |
-test_proximal_jac_atf                   |    +123.23 +/- 2.37    | +9.97e+00 +/- 1.92e-01 |  1.81e+01 +/- 1.8e-01  |  8.09e+00 +/- 5.8e-02  |
-test_proximal_freeb_compute             |     +9.17 +/- 0.91     | +1.64e-02 +/- 1.62e-03 |  1.95e-01 +/- 1.4e-03  |  1.79e-01 +/- 8.1e-04  |
-test_proximal_freeb_jac                 |    +313.17 +/- 5.85    | +2.31e+01 +/- 4.31e-01 |  3.05e+01 +/- 4.2e-01  |  7.37e+00 +/- 7.4e-02  |
-test_solve_fixed_iter                   |    +76.09 +/- 19.61    | +1.37e+01 +/- 3.54e+00 |  3.18e+01 +/- 3.1e+00  |  1.81e+01 +/- 1.7e+00  |

[dpanici]

test_compute_everything try also with omega nonzero or something

[dpanici]

just load and resave all the eqs after merge, dont resolve as there is not consistnecy to set omega to zero yet on this branch

[unalmis]

Note to self:

• in bounce integrals you used d zeta / B dot grad zeta for field line differential length where the zeta in dzeta denotes the field line zeta, and the zeta in B dot grad zeta denotes DESC's coordinate zeta. this is fine currently, but work through the math when desc zeta is generalized with stream function. nothing changes with bounce/field line stuff.
• and check for any 2d divergence theorems in zeta surface. Edit: The integration over boundaries we do (2d divergence theorems etc.) no longer work. I have done the math to fix them. Once this gets up to date with master, feel free to ping me and I'll push the update

[unalmis]

alpha_t should be corrected to
data["alpha_t"] = data["theta_PEST_t"] - data["iota"] * data["phi_t"]

[unalmis]

Also the formula for alpha uses zeta while its derivatives use phi.

[dpanici]

@unalmis I merged master, gonna see which tests fail but I think there needs to be some extra logic added to "A" and "A(z)" to prevent ZernikeRZToroidalSection objects from getting an error when they try to compute "A", or at least there is a test failing due to that. They have no W_lmn attribute but somewhere we try to access it when computing with those objects

[unalmis]

@unalmis I merged master, gonna see which tests fail but I think there needs to be some extra logic added to "A" and "A(z)" to prevent ZernikeRZToroidalSection objects from getting an error when they try to compute "A", or at least there is a test failing due to that. They have no W_lmn attribute but somewhere we try to access it when computing with those objects

Note they aren't computed correctly here yet because you need to use source grids to do coordinate mapping. I think the error you see is due to #1127 . Also A(z) and A` compute functions will change in #1094 .

[dpanici]

couple omega to theta pest somehow?