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<DIV><FONT size=2 face=Arial>Folks,</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>--Kirk</FONT></DIV>
<DIV style="FONT: 10pt Tahoma">
<DIV><BR></DIV>
<DIV style="BACKGROUND: #f5f5f5">
<DIV style="font-color: black"><B>From:</B> <A title=mchung@fnal.gov
href="mailto:mchung@fnal.gov">Moses Chung</A> </DIV>
<DIV><B>Sent:</B> Tuesday, March 15, 2011 11:54 AM</DIV>
<DIV><B>To:</B> <A title=kirkmcd@Princeton.EDU
href="mailto:kirkmcd@Princeton.EDU">Kirk T McDonald</A> </DIV>
<DIV><B>Subject:</B> [MAP] Liouville'​s theorem, kinematic invariants​, and
dynamic invariants</DIV></DIV></DIV>
<DIV><BR></DIV>
<DIV> </DIV>
<DIV>Dear Prof. McDonald,</DIV>
<DIV> </DIV>
<DIV>This is Moses Chung, one of the MAP collaborators in Korea,</DIV>
<DIV>a former Fermilab postdoc, and a former Princeton grad. (plasma physics
program).</DIV>
<DIV>Indeed, I took your E&M course to prepare the prelim. long time ago.
:)</DIV>
<DIV>I'm really enjoying the recent discussion on emittance, invariants, and
Liouville' theorem etc.</DIV>
<DIV>I have a couple of comments.</DIV>
<DIV> </DIV>
<DIV>As an experimentalist, I've had difficulty in following the
Lebedev-Bogacz's paper and </DIV>
<DIV>Lie algebra papers and book by Alex. Probably, it is mainly due to my
ignorance in math.</DIV>
<DIV>On the other hand, it is also true that those formulations are quite
different or at least not </DIV>
<DIV>straight-forward compared to the well-known Courant-Snyder formalism
in 1D.</DIV>
<DIV> </DIV>
<DIV>To cope with this problem, I wrote a paper as attached thanks to the</DIV>
<DIV>recent theoretical work by Dr. Hong Qin and Prof. Davidson in PPPL.</DIV>
<DIV>Since our formulation does not explicitly show two
eigen-emittances as other theories have,</DIV>
<DIV>we had some criticism from theorist.</DIV>
<DIV>However, for the long cooling channel, which is intrinsically nonlinear and
stochastic,</DIV>
<DIV>I believe emittances in two eigenplanes (using the theorists'
term) should become nearly equal.</DIV>
<DIV>In this case, our formulation may give very useful and easy guideline for
the </DIV>
<DIV>rms properties of the beam with keeping very similar structure to the 1D
Courant-Snyder formalism.</DIV>
<DIV> </DIV>
<DIV>I would be very glad to hear opinion in the context of the recent
discussion.</DIV>
<DIV> </DIV>
<DIV>Sincerely,</DIV>
<DIV>Moses</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
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