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<DIV><FONT size=2 face=Arial>Rob,</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>Thanks for this comment.</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>Your slide 16 seems to imply that the canonical
momentum associated with coordinate t, when using (x,y,t) as coordinates,
is</FONT></DIV>
<DIV><FONT size=2 face=Arial>p_t = - (E_mech + q V).</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>This does not quite match what I infer from Alex
Dragt that</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>p_t = - H</FONT></DIV>
<DIV><FONT size=2 face=Arial>= - { sqrt[ m^2 c^4 + (p_mech - q A / c)^2
] + q V }</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>How did you arrive at your
simplification?</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>Your result matches Dragt's if the vector potential
is zero.....</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>Are you saying that we can ignore the vector
potential, but not the scalar potential?</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="mailto:rdryne@lbl.gov CTRL + Click to follow link"
href="mailto:rdryne@lbl.gov">Robert D Ryne</A> </DIV>
<DIV><B>Sent:</B> Saturday, March 12, 2011 12:07 AM</DIV>
<DIV><B>To:</B> <A
title="mailto:kirkmcd@Princeton.EDU CTRL + Click to follow link"
href="mailto:kirkmcd@Princeton.EDU">Kirk T McDonald</A> </DIV>
<DIV><B>Cc:</B> <A
title="mailto:dragtnb@comcast.net CTRL + Click to follow link"
href="mailto:dragtnb@comcast.net">alex dragt</A> ; <A
title="mailto:map-l@lists.bnl.gov CTRL + Click to follow link"
href="mailto:map-l@lists.bnl.gov">MAP List</A> </DIV>
<DIV><B>Subject:</B> Re: [MAP] Use of x,y,t as Hamiltonian
coordinates.</DIV></DIV></DIV>
<DIV><BR></DIV><SPAN style="FONT-SIZE: 14px" class=Apple-style-span>Kirk,</SPAN>
<DIV style="FONT-SIZE: 14px"><BR></DIV>
<DIV style="FONT-SIZE: 14px">The 6-vector of canonical variables is shown on
slide 16 of my presentation at the MAP meeting. These are the variables that
should be used for eigen-emittance calculations. Of course this happens "for
free" in a code that uses canonical variables. When I calculate eigen-emittances
from a non-canonical code, the diagnostic subroutine does the conversion to
canonical variables.</DIV>
<DIV style="FONT-SIZE: 14px"><BR></DIV>
<DIV style="FONT-SIZE: 14px">Rob</DIV>
<DIV style="FONT-SIZE: 16px"><SPAN style="FONT-SIZE: medium"
class=Apple-style-span><FONT class=Apple-style-span size=4><SPAN
style="FONT-SIZE: 16px" class=Apple-style-span><BR></SPAN></FONT></SPAN></DIV>
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