[MAP] Fw: Liouville'?s theorem, kinematic invariants?, and dynamic invariants

[Kirk T McDonald]

Folks,

I am taking the liberty of forwarding this email from Moses Chung to the whole MAP list in hopes that some or you can comment on his paper better than I can.

--Kirk


From: Moses Chung 
Sent: Tuesday, March 15, 2011 11:54 AM
To: Kirk T McDonald 
Subject: [MAP] Liouville'?s theorem, kinematic invariants?, and dynamic invariants



Dear Prof. McDonald,

This is Moses Chung, one of the MAP collaborators in Korea,
a former Fermilab postdoc, and a former Princeton grad. (plasma physics program).
Indeed, I took your E&M course to prepare the prelim. long time ago. :)
I'm really enjoying the recent discussion on emittance, invariants, and Liouville' theorem etc.
I have a couple of comments.

As an experimentalist, I've had difficulty in following the Lebedev-Bogacz's paper and 
Lie algebra papers and book by Alex. Probably, it is mainly due to my ignorance in math.
On the other hand, it is also true that those formulations are quite different or at least not 
straight-forward compared to the well-known Courant-Snyder formalism in 1D.

To cope with this problem, I wrote a paper as attached thanks to the
recent theoretical work by Dr. Hong Qin and Prof. Davidson in PPPL.
Since our formulation does not explicitly show two eigen-emittances as other theories have,
we had some criticism from theorist.
However, for the long cooling channel, which is intrinsically nonlinear and stochastic,
I believe emittances in two eigenplanes (using the theorists' term) should become nearly equal.
In this case, our formulation may give very useful and easy guideline for the 
rms properties of the beam with keeping very similar structure to the 1D Courant-Snyder formalism.

I would be very glad to hear opinion in the context of the recent discussion.

Sincerely,
Moses









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