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         |     +0.10 +/- 4.32     | +5.16e-04 +/- 2.27e-02 |  5.26e-01 +/- 1.9e-02  |  5.26e-01 +/- 1.2e-02  |
 test_build_transform_fft_midres         |     -1.25 +/- 2.01     | -7.67e-03 +/- 1.24e-02 |  6.08e-01 +/- 1.1e-02  |  6.16e-01 +/- 6.1e-03  |
 test_build_transform_fft_highres        |     +0.40 +/- 4.47     | +4.13e-03 +/- 4.60e-02 |  1.03e+00 +/- 2.6e-02  |  1.03e+00 +/- 3.8e-02  |
 test_equilibrium_init_lowres            |     -0.68 +/- 0.72     | -2.65e-02 +/- 2.81e-02 |  3.85e+00 +/- 2.1e-02  |  3.88e+00 +/- 1.9e-02  |
 test_equilibrium_init_medres            |     -0.98 +/- 1.13     | -4.14e-02 +/- 4.74e-02 |  4.16e+00 +/- 3.2e-02  |  4.21e+00 +/- 3.5e-02  |
 test_equilibrium_init_highres           |     -0.47 +/- 0.94     | -2.61e-02 +/- 5.24e-02 |  5.53e+00 +/- 4.0e-02  |  5.56e+00 +/- 3.4e-02  |
 test_objective_compile_dshape_current   |     -0.88 +/- 0.78     | -3.41e-02 +/- 3.04e-02 |  3.84e+00 +/- 2.1e-02  |  3.88e+00 +/- 2.2e-02  |
 test_objective_compile_atf              |     -0.84 +/- 2.43     | -6.67e-02 +/- 1.94e-01 |  7.91e+00 +/- 1.3e-01  |  7.97e+00 +/- 1.4e-01  |
 test_objective_compute_dshape_current   |     -0.38 +/- 1.37     | -1.32e-05 +/- 4.75e-05 |  3.45e-03 +/- 3.2e-05  |  3.46e-03 +/- 3.5e-05  |
 test_objective_compute_atf              |     +0.37 +/- 2.36     | +3.76e-05 +/- 2.42e-04 |  1.03e-02 +/- 1.6e-04  |  1.03e-02 +/- 1.8e-04  |
 test_objective_jac_dshape_current       |     +0.28 +/- 6.18     | +1.15e-04 +/- 2.52e-03 |  4.09e-02 +/- 2.1e-03  |  4.08e-02 +/- 1.4e-03  |
 test_objective_jac_atf                  |     +0.48 +/- 3.07     | +9.26e-03 +/- 5.96e-02 |  1.95e+00 +/- 3.6e-02  |  1.94e+00 +/- 4.8e-02  |
 test_perturb_1                          |     -0.50 +/- 0.98     | -6.27e-02 +/- 1.22e-01 |  1.24e+01 +/- 7.3e-02  |  1.25e+01 +/- 9.8e-02  |
 test_perturb_2                          |     -0.04 +/- 0.99     | -6.94e-03 +/- 1.73e-01 |  1.75e+01 +/- 1.3e-01  |  1.75e+01 +/- 1.1e-01  |
 test_proximal_jac_atf                   |     +0.53 +/- 0.74     | +4.29e-02 +/- 6.05e-02 |  8.19e+00 +/- 4.6e-02  |  8.15e+00 +/- 3.9e-02  |
 test_proximal_freeb_compute             |     +0.62 +/- 0.90     | +1.13e-03 +/- 1.64e-03 |  1.84e-01 +/- 1.1e-03  |  1.83e-01 +/- 1.2e-03  |
 test_proximal_freeb_jac                 |     -0.58 +/- 0.84     | -4.39e-02 +/- 6.29e-02 |  7.47e+00 +/- 5.7e-02  |  7.51e+00 +/- 2.8e-02  |
 test_solve_fixed_iter                   |     -1.00 +/- 60.24    | -5.04e-02 +/- 3.05e+00 |  5.01e+00 +/- 2.2e+00  |  5.06e+00 +/- 2.2e+00  |

[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