Neutral velocity space coordinates

[mrhardman]

Neutrals currently have support for 3V velocity space with the vz vr vzeta coordinates. This choice seems natural when using cylindrical coordinates, but with require interpolation when mapping from the charged particle vpa vperp gyrophase coordinates. There are currently no differential velocity space operators envisaged for the neutral pdf. This means that we could avoid costly 3V interpolation by using vpa vperp gyrophase coordinates for the neutral velocity space.

This change would require refactoring some loops, the mpi, and require some functions for mapping vpa vperp gyrophase to vz vr vzeta for the advection routines.

@johnomotani @mabarnes @LucasMontoya4 Would this rewrite be of interest for (or before) the generalisation from 1D1V to 1D2V moment kinetics?

[LucasMontoya4]

@mrhardman How difficult would it be to make these mapping functions? That sounds like a good idea to me..

[mrhardman]

For vpa, vperp, gyrophase -> vz, vr, vzeta, the transformation is written here

moment_kinetics/moment_kinetics/src/velocity_grid_transforms.jl

Lines 55 to 57 in 3038940

	vz_val = vpa.grid[ivpa]*bzed - vperp.grid[ivperp]*sin(gyrophase.grid[igyro])*bzeta
	vr_val = vperp.grid[ivperp]*cos(gyrophase.grid[igyro])
	vzeta_val = vpa.grid[ivpa]*bzeta + vperp.grid[ivperp]*sin(gyrophase.grid[igyro])*bzed

, for the inverse transformation, it is written here:

moment_kinetics/moment_kinetics/src/velocity_grid_transforms.jl

Lines 105 to 106 in 3038940

	vpa_val = bzed*vz.grid[ivz] + bzeta*vzeta.grid[ivzeta]
	vperp_val = sqrt( vr.grid[ivr]^2.0 + (bzed*vzeta.grid[ivzeta] - bzeta*vz.grid[ivz])^2.0)

.

@johnomotani @LucasMontoya4 Do moment-kinetic neutrals already have "acceleration" terms with velocity derivatives on the neutral pdf? (because of the change of variables).