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MAD-X PTC and MAD-NG Normal Form matters
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MAD-X PTC and MAD-NG Normal Form matters
Frank Schmidt, Normal Form issues and validation techniques
Frank presents various tools to reconstruct Hamiltonian (H) and Generating Function terms (F) from tracking and from maps. These tools are very valuable to validate MADX-PTC or MAD-NG output. He has an example set up at:
https://cernbox.cern.ch/index.php/s/UGIdU0YzTdT0xiy
Lattice: fivecell.seq
MAD-X runs: take one of the fivecell_XXX.madx files
Frank observes a discrepancy in the F terms when running MADX-PTC for both sextupolar and octupolar order (asking for single order gives correct results). For Piotr this 'bug' was fixed in a recent version in MADX. Due some limitations in the sound of the zoom meeting it was not fully clear the configuration. The proposal is for Frank to distribute a simple example and to compare Sussix, MADX-PTC and MAD-NG, maybe sitting together with Piotr and Laurent to fully understand the configuration.
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Laurent, MAD-NG Normal Form
Laurent reports that he has developed a new NF in MAD-NG based on the Log^{-1} that gives different results than his previous implementation based on the extraction of H terms. He connects this to the problem that Frank sees supporting the Log approach (same as PTC). The proposed general check seems very needed at this point.
A small summary sent by Frank after the meeting:
1) When the NormalForm is conducted while pushing the F3 to the pseudo Hamiltonian H3 the results are:
a) The H3 terms are correct.
b) But: the F4 terms are modified
c) Even worse the detuning with amplitude is quite different even changing sign.
d) Therefore pushing the F4 to the pseudo Hamiltonian H4 must fail by definition since the F/H relation is fixed.
2) The similarity transformation with A(1-3) such that the lowest order of the map is 4 and all is fine!
3) I have tried the newer versions after Piotr's changes and I am getting the rough approximation always and that is not the one stop solution! I am afraid that one needs to follow the recommendations as outlined in my talk, which essentially means that one will need a order by order approach or deal with more complex Poisson brackets.
If Piotr has a simple MAD-X example that I could check please provide it!
4) Fortunately we now have support by the simulations to sort this out!
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