Feature/real space plot 3d

[bpatel2107]

A simple script to plot 3D visualisation of a flux tube. We do the fourier transform to real space and make the flux tube go from $-\pi$ to $\pi$ by appending on the end of the theta grid a phase shifted first value in theta. This makes the interpolation done for the mapping from field aligned to cartesian a lot easier.

The code currently plots at $\theta=0$, then a flux 3D torus of the data and then finally at a fixed toroidal angle $\zeta=0$ by interpolating onto that surface.

This does a simple mapping from the code's $y$ -> $\alpha$ -> $\zeta$ (at a given $\theta$) via

$\alpha = q \theta - \zeta$

However we currently don't account for the radial variation of $\alpha(r)$, $q(r)$ and the flux surface mapping with $\partial R/\partial r$ and $\partial Z/\partial r$. That is likely the only thing that is really missing. Essentially for each $x$ we need to expand the above expression to cover this. We do have $\partial \alpha/\partial r$ and $\partial \alpha/\partial \theta$ so it is possible.

Essentially the mapping from field aligned $(x,y,\theta)$ to cartesian $(X,Y,Z)$ is mostly right but could be improved

• Append data with final theta point (data doesn't include info +pi because its periodic)
• Fourier transform into real space using xrft $(k_x,k_y,\theta) \rightarrow (x, y, \theta)$
• Append $+L_y/2$ onto real space data (IFFT doesnt include final point back in)
• Map from $(x,\theta)$ to $(R,Z)$ or each radius $x$ - doesn't include radial variation of flux surfaces
• Map $y$ to corresponding toroidal angle $\zeta$ - doesn't include radial variation of $\alpha$
• Interpolate onto requested points (using periodicity in $y$ to get any toroidal angle)

Added a ChatGPT generated docs on this. Accidentally branched from the wrong branch though so a kinetics doc is in there...

[d7919]

0.005 being a placeholder rho* value?

[bpatel2107]

Yes, could clarify this or set it as an input

[bpatel2107]

Will merge for now and fix problems later on!