LinkingCurrent objective

[ddudt]

This is a nonlinear form of the existing linear objective FixSumCoilCurrent. It ensures the total current through the coils matches the poloidal current of the equilibrium. This is necessary for single-stage optimization where the equilibrium and coils are changing simultaneously.

[github-actions]

|             benchmark_name             |         dt(%)          |         dt(s)          |        t_new(s)        |        t_old(s)        | 
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
 test_build_transform_fft_lowres         |     +4.34 +/- 5.58     | +2.39e-02 +/- 3.07e-02 |  5.75e-01 +/- 2.3e-02  |  5.51e-01 +/- 2.0e-02  |
 test_equilibrium_init_medres            |     -1.56 +/- 6.66     | -7.21e-02 +/- 3.07e-01 |  4.54e+00 +/- 1.5e-01  |  4.61e+00 +/- 2.7e-01  |
 test_equilibrium_init_highres           |     +0.53 +/- 2.86     | +3.13e-02 +/- 1.68e-01 |  5.92e+00 +/- 1.2e-01  |  5.89e+00 +/- 1.2e-01  |
 test_objective_compile_dshape_current   |     +0.01 +/- 2.44     | +2.90e-04 +/- 1.01e-01 |  4.13e+00 +/- 9.0e-02  |  4.13e+00 +/- 4.6e-02  |
 test_objective_compute_dshape_current   |     +2.30 +/- 6.92     | +1.24e-04 +/- 3.73e-04 |  5.51e-03 +/- 3.5e-04  |  5.38e-03 +/- 1.2e-04  |
 test_objective_jac_dshape_current       |     +0.72 +/- 7.17     | +3.22e-04 +/- 3.20e-03 |  4.49e-02 +/- 2.0e-03  |  4.46e-02 +/- 2.5e-03  |
 test_perturb_2                          |     -2.85 +/- 2.58     | -6.05e-01 +/- 5.47e-01 |  2.06e+01 +/- 4.7e-01  |  2.12e+01 +/- 2.8e-01  |
 test_proximal_freeb_jac                 |     -0.95 +/- 2.34     | -7.29e-02 +/- 1.79e-01 |  7.57e+00 +/- 1.1e-01  |  7.64e+00 +/- 1.4e-01  |
 test_solve_fixed_iter                   |     -2.25 +/- 2.46     | -7.96e-01 +/- 8.71e-01 |  3.46e+01 +/- 7.0e-01  |  3.54e+01 +/- 5.2e-01  |
 test_LinearConstraintProjection_build   |     -1.22 +/- 3.60     | -1.35e-01 +/- 4.00e-01 |  1.10e+01 +/- 3.5e-01  |  1.11e+01 +/- 1.9e-01  |
 test_build_transform_fft_midres         |     -2.52 +/- 4.89     | -1.66e-02 +/- 3.22e-02 |  6.42e-01 +/- 2.0e-02  |  6.58e-01 +/- 2.5e-02  |
 test_build_transform_fft_highres        |     -2.57 +/- 2.63     | -2.66e-02 +/- 2.72e-02 |  1.01e+00 +/- 1.7e-02  |  1.03e+00 +/- 2.1e-02  |
 test_equilibrium_init_lowres            |     -1.45 +/- 3.02     | -6.21e-02 +/- 1.29e-01 |  4.22e+00 +/- 9.2e-02  |  4.28e+00 +/- 9.0e-02  |
 test_objective_compile_atf              |     -3.45 +/- 4.64     | -2.97e-01 +/- 4.00e-01 |  8.31e+00 +/- 3.0e-01  |  8.61e+00 +/- 2.6e-01  |
 test_objective_compute_atf              |     -4.15 +/- 5.51     | -7.36e-04 +/- 9.78e-04 |  1.70e-02 +/- 9.0e-04  |  1.77e-02 +/- 3.9e-04  |
 test_objective_jac_atf                  |     -1.42 +/- 2.70     | -2.89e-02 +/- 5.49e-02 |  2.01e+00 +/- 3.9e-02  |  2.04e+00 +/- 3.8e-02  |
 test_perturb_1                          |     -3.70 +/- 1.61     | -5.97e-01 +/- 2.60e-01 |  1.55e+01 +/- 1.6e-01  |  1.61e+01 +/- 2.0e-01  |
 test_proximal_jac_atf                   |     -0.78 +/- 1.06     | -6.57e-02 +/- 8.93e-02 |  8.34e+00 +/- 4.2e-02  |  8.40e+00 +/- 7.9e-02  |
 test_proximal_freeb_compute             |     -2.01 +/- 1.42     | -4.15e-03 +/- 2.93e-03 |  2.02e-01 +/- 2.1e-03  |  2.07e-01 +/- 2.1e-03  |
 test_solve_fixed_iter_compiled          |     -0.56 +/- 2.46     | -1.28e-01 +/- 5.62e-01 |  2.27e+01 +/- 3.8e-01  |  2.28e+01 +/- 4.2e-01  |

[dpanici]

do #1231

[dpanici]

Any progress on this @daniel-dudt ?

[dpanici]

Use Linking number calc for linear objective for sum coil currents as well, to use as weights for sum

[dpanici]

I think an equivalent sort of objective to ensure that the coils are creating the necessary current, without needing the linking number calculation (though I'd still like that in sometime), is to directly calculate $\int_{o}^{2\pi/NFP} \mathbf{B}{coil} \cdot \mathbf{e}{\zeta} d\zeta - \int_{o}^{2\pi/NFP} \mathbf{B}{DESC} \cdot \mathbf{e}{\zeta} d\zeta$ which is the relation that Ampere's law tells us (the second term here is $G(\rho=1)$, possibly sans a $2\pi$ factor).

This being zero means the coils are consistent with Ampere's law and avoids needing to worry about the linking currents (though this is a bit more expensive, as it relies on biot-savart integration over the coils to get $\mathbf{B}_{coil}$

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.62%. Comparing base (4bfa728) to head (ab74f48).
Report is 38 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1222      +/-   ##
==========================================
+ Coverage   95.60%   95.62%   +0.02%     
==========================================
  Files          98       98              
  Lines       25300    25374      +74     
==========================================
+ Hits        24188    24264      +76     
+ Misses       1112     1110       -2     

Files with missing lines	Coverage Δ
desc/coils.py	97.98% <100.00%> (+0.20%)	⬆️
desc/objectives/__init__.py	100.00% <ø> (ø)
desc/objectives/_coils.py	99.34% <100.00%> (+0.06%)	⬆️

... and 1 file with indirect coverage changes

[ddudt]

I can't officially approve, but it looks good.

[ddudt]

this could be 1 line instead of 4

[dpanici]

techincally just a single float but not a big deal

[dpanici]

I think the name could be changed to LinkingCurrentConsistency or something, or the docstring should make it clearer that target should be zero, and NOT the targeted linking current G

[ddudt]

Do we understand why this constraint is being flagged as "incompatible"? This is like the simplest possible linear constraint, so I'm worried if this doesn't work without warnings.

[f0uriest]

The error is like 1e-9 which is about what we'd expect given the currents are ~MA