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Add classes to represent analytical solutions for spheromaks #1995

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namurphy opened this issue Mar 7, 2023 · 0 comments · May be fixed by #2237
Open

Add classes to represent analytical solutions for spheromaks #1995

namurphy opened this issue Mar 7, 2023 · 0 comments · May be fixed by #2237
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feature request Issues requesting a new feature or enhancement priority: medium Issues & PRs of moderate urgency and importance

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@namurphy
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namurphy commented Mar 7, 2023

Feature description

We should add a class or classes to represent exact solutions for spheromak equilibria.

Motivation

There exist some exact solutions for spheromak equilibria, such as (for spherical geometry):
$$B_r = 2 B_0 \frac{a}{r} j_1(λr) \cos θ$$ $$B_θ = -B_0 \frac{a}{r} \frac{∂}{∂r} \left[ r j_1(λr) \right] \sin θ$$ $$B_ϕ = λa B_0 j_1(λr) \sin θ$$
which are equations 4.42 in Spheromaks by Bellan. I believe $j_m$ represents a spherical Bessel function, and $r=a$ is a surface where the radial magnetic field vanishes. We'll need to check the book for more details, and probably ask people who have a good understanding of spheromaks for help. (At this point I have only a superficial understanding, but will try to update this issue as I understand things better.)

Implementation strategy

This should be consistent with #1978, #1979, and #1980.

Additional context

For cylindrical geometry, there is probably some overlap with the Lundquist solution as described with #1980.

@namurphy namurphy added the feature request Issues requesting a new feature or enhancement label Mar 7, 2023
@github-actions github-actions bot added the Stale Dormant issues & PRs which will be automatically closed if the label is not removed. label May 7, 2023
@namurphy namurphy removed the Stale Dormant issues & PRs which will be automatically closed if the label is not removed. label May 12, 2023
@namurphy namurphy added the priority: medium Issues & PRs of moderate urgency and importance label May 23, 2023
@mohawk811 mohawk811 linked a pull request Jul 3, 2023 that will close this issue
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Labels
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