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_midres         |     +5.82 +/- 4.75     | +3.48e-02 +/- 2.84e-02 |  6.33e-01 +/- 1.8e-02  |  5.99e-01 +/- 2.2e-02  |
 test_build_transform_fft_highres        |     +2.85 +/- 5.18     | +2.75e-02 +/- 5.00e-02 |  9.92e-01 +/- 4.4e-02  |  9.64e-01 +/- 2.4e-02  |
 test_equilibrium_init_lowres            |     +7.16 +/- 7.23     | +2.78e-01 +/- 2.80e-01 |  4.16e+00 +/- 4.0e-02  |  3.88e+00 +/- 2.8e-01  |
 test_objective_compile_atf              |     +2.79 +/- 3.71     | +2.19e-01 +/- 2.92e-01 |  8.09e+00 +/- 2.2e-01  |  7.87e+00 +/- 1.9e-01  |
 test_objective_compute_atf              |     +3.80 +/- 1.76     | +3.98e-04 +/- 1.84e-04 |  1.09e-02 +/- 1.5e-04  |  1.05e-02 +/- 1.0e-04  |
 test_objective_jac_atf                  |     +3.37 +/- 1.61     | +6.30e-02 +/- 3.01e-02 |  1.93e+00 +/- 2.4e-02  |  1.87e+00 +/- 1.8e-02  |
-test_perturb_1                          |     +7.24 +/- 2.34     | +1.02e+00 +/- 3.29e-01 |  1.51e+01 +/- 6.1e-02  |  1.40e+01 +/- 3.2e-01  |
 test_proximal_jac_atf                   |     +0.76 +/- 1.18     | +6.16e-02 +/- 9.52e-02 |  8.15e+00 +/- 7.9e-02  |  8.09e+00 +/- 5.4e-02  |
 test_proximal_freeb_compute             |     -0.78 +/- 0.76     | -1.53e-03 +/- 1.48e-03 |  1.94e-01 +/- 1.1e-03  |  1.96e-01 +/- 1.0e-03  |
 test_solve_fixed_iter_compiled          |     -0.37 +/- 2.13     | -6.30e-02 +/- 3.58e-01 |  1.68e+01 +/- 1.6e-01  |  1.68e+01 +/- 3.2e-01  |
 test_build_transform_fft_lowres         |     -0.90 +/- 5.43     | -5.04e-03 +/- 3.06e-02 |  5.57e-01 +/- 2.1e-02  |  5.62e-01 +/- 2.2e-02  |
 test_equilibrium_init_medres            |     -0.79 +/- 6.99     | -3.49e-02 +/- 3.10e-01 |  4.40e+00 +/- 2.2e-01  |  4.44e+00 +/- 2.2e-01  |
 test_equilibrium_init_highres           |     +2.46 +/- 5.34     | +1.37e-01 +/- 2.97e-01 |  5.71e+00 +/- 1.9e-01  |  5.57e+00 +/- 2.3e-01  |
 test_objective_compile_dshape_current   |     -1.12 +/- 6.91     | -4.43e-02 +/- 2.73e-01 |  3.91e+00 +/- 2.2e-01  |  3.95e+00 +/- 1.6e-01  |
 test_objective_compute_dshape_current   |     +0.68 +/- 2.37     | +2.46e-05 +/- 8.54e-05 |  3.63e-03 +/- 5.1e-05  |  3.60e-03 +/- 6.8e-05  |
 test_objective_jac_dshape_current       |     -0.27 +/- 7.72     | -1.14e-04 +/- 3.22e-03 |  4.16e-02 +/- 1.5e-03  |  4.17e-02 +/- 2.8e-03  |
 test_perturb_2                          |     +0.11 +/- 3.42     | +2.21e-02 +/- 6.85e-01 |  2.01e+01 +/- 3.1e-01  |  2.01e+01 +/- 6.1e-01  |
 test_proximal_freeb_jac                 |     -0.30 +/- 2.06     | -2.33e-02 +/- 1.57e-01 |  7.64e+00 +/- 9.3e-02  |  7.66e+00 +/- 1.3e-01  |
 test_solve_fixed_iter                   |     -0.37 +/- 3.61     | -1.07e-01 +/- 1.05e+00 |  2.90e+01 +/- 8.9e-01  |  2.91e+01 +/- 5.5e-01  |
 test_LinearConstraintProjection_build   |     -0.50 +/- 1.99     | -1.16e-01 +/- 4.62e-01 |  2.30e+01 +/- 2.9e-01  |  2.32e+01 +/- 3.6e-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 95.63%. Comparing base (005c4f8) to head (815ad41).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1222      +/-   ##
==========================================
+ Coverage   95.59%   95.63%   +0.03%     
==========================================
  Files          96       96              
  Lines       24601    24675      +74     
==========================================
+ Hits        23518    23597      +79     
+ Misses       1083     1078       -5     

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 2 files with indirect coverage changes

[f0uriest]

We had talked about adding the linking number stuff to FixSumCoilCurrents, but it might be easier to just add an eq_fixed option to this, in which case we precompute G and set self._linear = True