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20 hours ago •
PlasmaControl
PlasmaControl
How to handle NAE O(rho) stellarator symmetry, but O(rho^2) asymmetric solutions with NAE constraints
When the NAE equilibrium is stellarator asymmetric bc of O(r^2) effects, the DESC equilibrium fit is also asymmetric. BUT, the NAE O(r) constraints are stellarator symmetric.
This leads to the first problem, which is that the constraints will be setting the stellarator asymmetric parts of the equilibrium's O(r) coefficients to roughly 0, which can cause some weirdness when solving
To allevaite the issue I thought to drop any NAE constraints whose target was below a threshold value (of like 1e-12 or so). However, this means when solving, the equilibrium's stellarator asymmetric coefficients are free to move as they wish, and this results in a completely different looking equilibrium than the NAE equilibrium (as expected I guess, since there is so much more freedom that we are not constraining).
Check out this pull request on 
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iota is off near-axis, so the non-stell-sym O(r) constraints seem to be off somehow
| benchmark_name | dt(%) | dt(s) | t_new(s) | t_old(s) |
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
test_build_transform_fft_lowres | -5.15 +/- 6.60 | -6.81e-04 +/- 8.72e-04 | 1.25e-02 +/- 1.3e-04 | 1.32e-02 +/- 8.6e-04 |
test_build_transform_fft_midres | -0.89 +/- 0.95 | -8.25e-04 +/- 8.84e-04 | 9.24e-02 +/- 6.3e-04 | 9.32e-02 +/- 6.2e-04 |
test_build_transform_fft_highres | -0.77 +/- 0.93 | -3.60e-03 +/- 4.34e-03 | 4.63e-01 +/- 3.0e-03 | 4.66e-01 +/- 3.1e-03 |
test_equilibrium_init_lowres | +0.37 +/- 4.35 | +2.98e-03 +/- 3.54e-02 | 8.17e-01 +/- 2.3e-02 | 8.14e-01 +/- 2.7e-02 |
test_equilibrium_init_medres | +0.47 +/- 0.90 | +6.62e-03 +/- 1.28e-02 | 1.43e+00 +/- 8.0e-03 | 1.42e+00 +/- 1.0e-02 |
test_equilibrium_init_highres | +0.29 +/- 0.74 | +1.23e-02 +/- 3.08e-02 | 4.20e+00 +/- 1.6e-02 | 4.19e+00 +/- 2.6e-02 |
test_objective_compile_dshape_current | +0.50 +/- 7.72 | +2.19e-02 +/- 3.38e-01 | 4.40e+00 +/- 2.3e-01 | 4.37e+00 +/- 2.5e-01 |
test_objective_compile_atf | +1.09 +/- 7.66 | +9.99e-02 +/- 7.04e-01 | 9.29e+00 +/- 5.9e-01 | 9.19e+00 +/- 3.9e-01 |
test_objective_compute_dshape_current | +0.32 +/- 2.15 | +6.83e-06 +/- 4.53e-05 | 2.12e-03 +/- 2.6e-05 | 2.11e-03 +/- 3.7e-05 |
test_objective_compute_atf | +2.20 +/- 0.97 | +1.63e-04 +/- 7.16e-05 | 7.56e-03 +/- 4.8e-05 | 7.39e-03 +/- 5.3e-05 |
test_objective_jac_dshape_current | -0.70 +/- 14.82 | -3.28e-04 +/- 6.92e-03 | 4.63e-02 +/- 3.1e-03 | 4.67e-02 +/- 6.2e-03 |
test_objective_jac_atf | -6.02 +/- 5.26 | -1.40e-01 +/- 1.23e-01 | 2.19e+00 +/- 1.0e-01 | 2.33e+00 +/- 6.4e-02 |
test_perturb_1 | -0.08 +/- 14.14 | -7.32e-03 +/- 1.22e+00 | 8.63e+00 +/- 8.7e-01 | 8.64e+00 +/- 8.5e-01 |
test_perturb_2 | +4.12 +/- 4.27 | +6.03e-01 +/- 6.24e-01 | 1.52e+01 +/- 3.6e-01 | 1.46e+01 +/- 5.1e-01 |
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| benchmark_name | dt(%) | dt(s) | t_new(s) | t_old(s) |
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
test_build_transform_fft_lowres | +0.80 +/- 1.63 | +9.86e-05 +/- 2.01e-04 | 1.24e-02 +/- 1.5e-04 | 1.23e-02 +/- 1.3e-04 |
test_build_transform_fft_midres | +0.36 +/- 1.33 | +3.29e-04 +/- 1.21e-03 | 9.14e-02 +/- 7.9e-04 | 9.11e-02 +/- 9.2e-04 |
test_build_transform_fft_highres | -0.12 +/- 0.98 | -5.45e-04 +/- 4.47e-03 | 4.57e-01 +/- 3.8e-03 | 4.57e-01 +/- 2.3e-03 |
test_equilibrium_init_lowres | -1.03 +/- 2.05 | -8.26e-03 +/- 1.65e-02 | 7.95e-01 +/- 8.7e-03 | 8.03e-01 +/- 1.4e-02 |
test_equilibrium_init_medres | -2.28 +/- 1.49 | -3.29e-02 +/- 2.14e-02 | 1.41e+00 +/- 1.2e-02 | 1.44e+00 +/- 1.8e-02 |
test_equilibrium_init_highres | -0.62 +/- 0.95 | -2.61e-02 +/- 3.98e-02 | 4.17e+00 +/- 2.1e-02 | 4.20e+00 +/- 3.4e-02 |
test_objective_compile_dshape_current | -2.36 +/- 7.55 | -1.04e-01 +/- 3.33e-01 | 4.31e+00 +/- 2.3e-01 | 4.41e+00 +/- 2.4e-01 |
test_objective_compile_atf | -0.62 +/- 6.88 | -5.71e-02 +/- 6.35e-01 | 9.18e+00 +/- 5.4e-01 | 9.23e+00 +/- 3.4e-01 |
test_objective_compute_dshape_current | -4.13 +/- 3.81 | -9.13e-05 +/- 8.42e-05 | 2.12e-03 +/- 4.9e-05 | 2.21e-03 +/- 6.9e-05 |
test_objective_compute_atf | -1.36 +/- 2.03 | -1.04e-04 +/- 1.55e-04 | 7.53e-03 +/- 6.0e-05 | 7.64e-03 +/- 1.4e-04 |
test_objective_jac_dshape_current | -2.94 +/- 11.80 | -1.42e-03 +/- 5.71e-03 | 4.70e-02 +/- 2.4e-03 | 4.84e-02 +/- 5.2e-03 |
test_objective_jac_atf | -6.41 +/- 7.36 | -1.46e-01 +/- 1.68e-01 | 2.13e+00 +/- 1.4e-01 | 2.28e+00 +/- 9.6e-02 |
test_perturb_1 | -0.16 +/- 13.36 | -1.37e-02 +/- 1.16e+00 | 8.67e+00 +/- 8.2e-01 | 8.68e+00 +/- 8.2e-01 |
test_perturb_2 | +2.13 +/- 4.57 | +3.16e-01 +/- 6.77e-01 | 1.51e+01 +/- 6.3e-01 | 1.48e+01 +/- 2.6e-01 |
| benchmark_name | dt(%) | dt(s) | t_new(s) | t_old(s) |
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
test_build_transform_fft_lowres | -0.16 +/- 1.22 | -1.93e-05 +/- 1.53e-04 | 1.25e-02 +/- 1.0e-04 | 1.25e-02 +/- 1.1e-04 |
test_build_transform_fft_midres | +0.11 +/- 0.95 | +9.94e-05 +/- 8.68e-04 | 9.11e-02 +/- 7.0e-04 | 9.10e-02 +/- 5.1e-04 |
test_build_transform_fft_highres | +1.23 +/- 1.11 | +5.60e-03 +/- 5.07e-03 | 4.63e-01 +/- 3.3e-03 | 4.57e-01 +/- 3.8e-03 |
test_equilibrium_init_lowres | +1.96 +/- 1.80 | +1.53e-02 +/- 1.41e-02 | 7.99e-01 +/- 1.4e-02 | 7.83e-01 +/- 3.3e-03 |
test_equilibrium_init_medres | +0.56 +/- 1.63 | +7.96e-03 +/- 2.30e-02 | 1.42e+00 +/- 2.1e-02 | 1.41e+00 +/- 9.8e-03 |
test_equilibrium_init_highres | +0.88 +/- 0.79 | +3.66e-02 +/- 3.27e-02 | 4.19e+00 +/- 2.5e-02 | 4.15e+00 +/- 2.1e-02 |
test_objective_compile_dshape_current | +1.05 +/- 7.68 | +4.48e-02 +/- 3.29e-01 | 4.33e+00 +/- 2.5e-01 | 4.29e+00 +/- 2.2e-01 |
test_objective_compile_atf | +0.63 +/- 8.38 | +5.69e-02 +/- 7.59e-01 | 9.11e+00 +/- 6.1e-01 | 9.05e+00 +/- 4.5e-01 |
test_objective_compute_dshape_current | -0.84 +/- 2.01 | -1.77e-05 +/- 4.24e-05 | 2.10e-03 +/- 3.0e-05 | 2.11e-03 +/- 3.0e-05 |
test_objective_compute_atf | -3.27 +/- 1.26 | -2.51e-04 +/- 9.66e-05 | 7.43e-03 +/- 7.7e-05 | 7.68e-03 +/- 5.9e-05 |
test_objective_jac_dshape_current | -1.86 +/- 10.56 | -8.75e-04 +/- 4.97e-03 | 4.62e-02 +/- 3.1e-03 | 4.71e-02 +/- 3.9e-03 |
test_objective_jac_atf | +0.11 +/- 5.80 | +2.39e-03 +/- 1.30e-01 | 2.24e+00 +/- 5.9e-02 | 2.24e+00 +/- 1.2e-01 |
test_perturb_1 | +0.04 +/- 14.25 | +3.50e-03 +/- 1.21e+00 | 8.52e+00 +/- 9.1e-01 | 8.52e+00 +/- 8.0e-01 |
test_perturb_2 | +0.46 +/- 4.92 | +6.62e-02 +/- 7.11e-01 | 1.45e+01 +/- 5.8e-01 | 1.44e+01 +/- 4.2e-01 |
| benchmark_name | dt(%) | dt(s) | t_new(s) | t_old(s) |
| -------------------------------------- | ---------------------- | ---------------------- | ---------------------- | ---------------------- |
test_build_transform_fft_lowres | -1.80 +/- 1.01 | -2.30e-04 +/- 1.29e-04 | 1.26e-02 +/- 7.5e-05 | 1.28e-02 +/- 1.1e-04 |
test_build_transform_fft_midres | -0.63 +/- 1.62 | -5.86e-04 +/- 1.50e-03 | 9.20e-02 +/- 7.0e-04 | 9.26e-02 +/- 1.3e-03 |
+test_build_transform_fft_highres | -7.76 +/- 1.77 | -3.90e-02 +/- 8.87e-03 | 4.64e-01 +/- 3.0e-03 | 5.03e-01 +/- 8.4e-03 |
test_equilibrium_init_lowres | -0.61 +/- 1.44 | -2.53e-03 +/- 6.00e-03 | 4.16e-01 +/- 3.3e-03 | 4.18e-01 +/- 5.0e-03 |
test_equilibrium_init_medres | -0.25 +/- 2.13 | -1.91e-03 +/- 1.64e-02 | 7.65e-01 +/- 8.4e-03 | 7.67e-01 +/- 1.4e-02 |
test_equilibrium_init_highres | -0.62 +/- 1.54 | -1.46e-02 +/- 3.62e-02 | 2.33e+00 +/- 1.8e-02 | 2.35e+00 +/- 3.1e-02 |
test_objective_compile_dshape_current | +0.82 +/- 1.95 | +3.79e-02 +/- 8.99e-02 | 4.64e+00 +/- 2.9e-02 | 4.60e+00 +/- 8.5e-02 |
test_objective_compile_atf | +0.63 +/- 2.95 | +5.78e-02 +/- 2.72e-01 | 9.29e+00 +/- 1.7e-01 | 9.24e+00 +/- 2.1e-01 |
test_objective_compute_dshape_current | +0.06 +/- 1.64 | +3.93e-06 +/- 1.14e-04 | 6.94e-03 +/- 7.8e-05 | 6.94e-03 +/- 8.3e-05 |
test_objective_compute_atf | -1.11 +/- 2.47 | -1.53e-04 +/- 3.41e-04 | 1.36e-02 +/- 2.4e-04 | 1.38e-02 +/- 2.4e-04 |
test_objective_jac_dshape_current | +1.79 +/- 5.67 | +8.41e-04 +/- 2.67e-03 | 4.80e-02 +/- 1.6e-03 | 4.71e-02 +/- 2.2e-03 |
test_objective_jac_atf | -1.62 +/- 3.12 | -3.32e-02 +/- 6.38e-02 | 2.01e+00 +/- 4.4e-02 | 2.05e+00 +/- 4.6e-02 |
test_perturb_1 | -2.05 +/- 4.65 | -2.83e-01 +/- 6.40e-01 | 1.35e+01 +/- 1.2e-01 | 1.38e+01 +/- 6.3e-01 |
+test_perturb_2 | -3.66 +/- 1.21 | -7.35e-01 +/- 2.42e-01 | 1.94e+01 +/- 2.2e-01 | 2.01e+01 +/- 1.1e-01 |
test_proximal_jac_atf | -0.46 +/- 1.72 | -3.17e-02 +/- 1.18e-01 | 6.85e+00 +/- 7.7e-02 | 6.89e+00 +/- 9.0e-02 |
test_proximal_freeb_compute | -2.30 +/- 0.91 | -2.86e-03 +/- 1.14e-03 | 1.21e-01 +/- 7.2e-04 | 1.24e-01 +/- 8.8e-04 |
test_proximal_freeb_jac | +0.82 +/- 1.46 | +6.66e-02 +/- 1.18e-01 | 8.20e+00 +/- 1.0e-01 | 8.14e+00 +/- 6.3e-02 |