Add classes to represent analytical solutions for spheromaks #1995
Labels
feature request
Issues requesting a new feature or enhancement
priority: medium
Issues & PRs of moderate urgency and importance
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):
$$B_r = 2 B_0 \frac{a}{r} j_1(λr) \cos θ$$ $$B_θ = -B_0 \frac{a}{r} \frac{∂}{∂r} \left[ r j_1(λr) \right] \sin θ$$ $$B_ϕ = λa B_0 j_1(λr) \sin θ$$ $j_m$ 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.)
which are equations 4.42 in Spheromaks by Bellan. I believe
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.
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