Change Cheetah particle coordinate to Canonical variables

[cr-xu]

Description

Rename coordinate s to tau

To avoid confusion and make space for the variable s denoting the position of reference particle along a beamline,
the 5-th component of the particle phase space coordinate is renamed to tau.

Rename xp, yp to px, py to be consistent with other codes

Remove trailing s in retrieving phase space coordinates from ParticleBeam

Change the documentations to explicitly state that Cheetah is using the canonical phase space coordinates $(x,px,y,py,\tau,\delta)$

• $px = P_x / P_0$
• $\tau = c\Delta t$, bunch head has negative $\tau$
• $\delta = \frac{\Delta E}{P_0 c}$ is the relative energy deviation from the reference particle

This is merely a documentation change at this point becasue all the calculations are valid. The conversions from/to ASTRA and OCELOT are indeed done in the correct way.

There is now a new page documenting the coordinate system in readthedocs: https://cheetah-accelerator--163.org.readthedocs.build/en/163/coordinate_system.html

Also: Fixes #162 and other places where dtype is listed as parameter but not actually used.

Motivation and Context

• I have raised an issue to propose this change (required for new features and bug fixes)

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation (update in the documentation)

Checklist

• I have updated the changelog accordingly (required).
• My change requires a change to the documentation.
• I have updated the tests accordingly (required for a bug fix or a new feature).
• I have updated the documentation accordingly.
• I have reformatted the code and checked that formatting passes (required).
• I have have fixed all issues found by flake8 (required).
• I have ensured that all pytest tests pass (required).
• I have run pytest on a machine with a CUDA GPU and made sure all tests pass (required).
• I have checked that the documentation builds (required).

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[roussel-ryan]

A question and a comment, Q: the beam coordinate properties all have "s" appended to their names ie. "xs", "xps", is it possible to remove the "s"? Comment: instead of using Tau I would suggest using "z" instead to abide by Bmad convention https://www.classe.cornell.edu/bmad/manual.html. We can discuss during our meeting tomorrow

[cr-xu]

• I don't have a problem with removing the trailing s for the coordinates of the macroparticles.
• Regarding $\tau$: the point is to make a distinction to bmad's $z$ as they are different. However, mad-x also uses $z$... (I hope this page explains this clearly https://cheetah-accelerator--163.org.readthedocs.build/en/163/coordinate_system.html) At this point I also don't know which way will be less confusing for users.
  @jank324 What's your opinion?

[jank324]

• Tye original motivation for the trailing s was a convention from functional programming, where a single element would be x and a collection of multiple x would be xs. As a computer scientist, I like this, but we should of course make sure it doesn't cause confusion, for example with the longitudinal s (?)
• I'm not sure about tau vs z. But I am sure that at this point I definitely am confused. 😄

[jank324]

@cr-xu that last commit means this is now properly ready for review and merging, right?

[cr-xu]

@cr-xu that last commit means this is now properly ready for review and merging, right?

I was just resolving merge conflicts. Now it should be ready for review.