TPSA in Xsuite Matching (Interface to MAD-NG)

[babreufig]

Description

Implements MAD-NG TPSA Action to use MAD-NG tracked damaps to acquire optical parameters.

This pull request requires at least MAD-NG version 1.1.8. There is a discrepancy in the chromaticity calculation between MAD-NG version 1.1.7 and 1.1.8, where the phix is by a factor 2 smaller in the new version. This seems to be a different convention(?). Needs a follow-up because this affects Ax/Bx/Ay/By functions which are then different between Xsuite and MAD-NG. For reference: MethodicalAcceleratorDesign/MAD-NG@5c87e03

Given the revert from the chromaticity bug, this pull request should be shipped with MAD-NG version 1.1.9!

Important: Depends on xsuite/xdeps#106

• Supports ranged settings with initial conditions
• Supports full-lattice settings with and without initial conditions
• Supports Beta functions, Alpha functions, Dispersions and Phase Advances as Targets
• Phase Advances uses faster Twiss and TPSA as well
• Interchangability between Xsuite ('betx', 'bety') and MAD-NG ('beta11_ng', 'beta22_ng') target names
• Orbit targets supported (x, px, ...)
• Changed twiss function to put coupling and chromaticities as optional flags
• Support R-Matrix matching
• Conversion between zeta/t and delta/pt

Mandatory:

• I have added tests to cover my changes
• All the tests are passing, including my new ones
• I described my changes in this PR description

[babreufig]

Functionality is ready. Needs follow-up because new MAD-NG version breaks two tests that rely on calculating chromaticities, as phix/phiy in MAD-NG 1.1.8 changed by a factor 2. This can be found in this commit (MethodicalAcceleratorDesign/MAD-NG@5c87e03) @giadarol

[szymonlopaciuk]

Good job, it's quite well structured and readable!

Some requests/comments/questions/suggestions for your consideration.

[szymonlopaciuk]

Good for me, just the little comment.

[babreufig]

New MAD-NG Version has been released, the related tests pass now! We could now pin the new version and this is then mergeable @szymonlopaciuk