Implement TBMT model for beam spin tracking about hipace

[pots007]

Hey guys!
This'd be awesome! The algorithm for the implementation in FBPIC is detailed in the appendix of this paper. I think the only difficulty in FBPIC was with storing the 'old' momentum.
For FBPIC we have written a test to compare the spin evolution to the plane wave case, not sure if something similar would be applicable here.

[AlexanderSinn]

Hello @pots007,
I am looking into adding this to HiPACE++ and I have a few questions regarding what is needed:

• Do you need openpmd input for sx sy and sz? If so, should they be multiplied by h bar?
• Do you need openpmd output for sx sy and sz?
• Should there be a standalone initialization option (no openpmd) for sx, sy and sz? Should this be uniform or random on a sphere surface or both? Would this be dependent on the beam particle positions?
• Should there be support for in-situ diagnostics with sx, sy and sz? If so what kind of moments should be collected?
• Is sx^2 + sy^2 + sz^2 always equal to 1, or another constant value that is the same for all particles?  

[pots007]

Hey @AlexanderSinn ,
awesome, thanks for working on this! My thoughts would be:

• Do you need openpmd input for sx sy and sz? If so, should they be multiplied by h bar? -> no, they are all normalised so just the 'raw' value is OK.
• Do you need openpmd output for sx sy and sz? -> Yes, I've implemented them in FBPIC under 'spin/x' etc, similarly to momentum.
• Should there be a standalone initialization option (no openpmd) for sx, sy and sz? Should this be uniform or random on a sphere surface or both? Would this be dependent on the beam particle positions? -> this is a tricky one. I think in the first instance, fixed values (eg sz=1 ) are fine - as long as the user-inputted values are normalised. We can think of more complex values later, what I did here may be a good starting point for discussions.
• Should there be support for in-situ diagnostics with sx, sy and sz? If so what kind of moments should be collected? -> I am not sure what you mean here. I think OpenPMD output is fine.
• Is sx^2 + sy^2 + sz^2 always equal to 1, or another constant value that is the same for all particles? -> it's always 1 for all particles.

Cheers!