Ku/available energy for turbulence transport

[unalmis]

adds my spectrally accurate implementation of @RalfMackenbach 's available energy

NCSX

W7-X

[github-actions]

Memory benchmark result

|               Test Name                |      %Δ      |    Master (MB)     |      PR (MB)       |    Δ (MB)    |    Time PR (s)     |  Time Master (s)   |
| -------------------------------------- | ------------ | ------------------ | ------------------ | ------------ | ------------------ | ------------------ |
  test_objective_jac_w7x                 |    3.75 %    |     3.933e+03      |     4.081e+03      |    147.37    |       31.44        |       29.94        |
  test_proximal_jac_w7x_with_eq_update   |    2.10 %    |     6.444e+03      |     6.579e+03      |    135.29    |       156.00       |       156.48       |
  test_proximal_freeb_jac                |    0.55 %    |     1.331e+04      |     1.338e+04      |    73.48     |       80.62        |       81.13        |
  test_proximal_freeb_jac_blocked        |    1.05 %    |     7.662e+03      |     7.742e+03      |    80.77     |       70.18        |       69.88        |
  test_proximal_freeb_jac_batched        |   -0.34 %    |     7.627e+03      |     7.601e+03      |    -25.87    |       69.19        |       70.10        |
  test_proximal_jac_ripple               |   -1.75 %    |     3.545e+03      |     3.483e+03      |    -61.98    |       56.26        |       55.76        |
  test_proximal_jac_ripple_bounce1d      |    4.51 %    |     2.042e+02      |     2.134e+02      |     9.21     |        4.41        |        4.51        |
  test_eq_solve                          |    0.16 %    |     2.053e+03      |     2.056e+03      |     3.18     |       88.54        |       89.03        |

For the memory plots, go to the summary of Memory Benchmarks workflow and download the artifact.

[rahulgaur104]

Are there benchmarks comparing the AE values with the ones in Mackenbach paper or from a TEM simulation?

[RalfMackenbach]

Perhaps we can do a benchmark tokamak-case and compare my output to these. With multiple wells, boundary conditions and singularity become a nuisance. @unalmis, is there a simple tokamak case you have?

[unalmis]

yes we can chat more over on unalmis#27 later. The implementation in unalmis#27 is better than the chain of PR's on this repo.