[MAP] Use of x,y,t as Hamiltonian coordinates.

[Kirk T McDonald]

Rob,

Thanks for this comment.

Your slide 16 seems to imply that the canonical momentum associated with coordinate t, when using (x,y,t) as coordinates, is
p_t = - (E_mech + q V).

This does not quite match what I infer from Alex Dragt that

p_t = - H
= - { sqrt[ m^2 c^4 + (p_mech - q A / c)^2 ] + q V }

How did you arrive at your simplification?

Your result matches Dragt's if the vector potential is zero.....

Are you saying that we can ignore the vector potential, but not the scalar potential?

--Kirk


From: Robert D Ryne 
Sent: Saturday, March 12, 2011 12:07 AM
To: Kirk T McDonald 
Cc: alex dragt ; MAP List 
Subject: Re: [MAP] Use of x,y,t as Hamiltonian coordinates.


Kirk, 


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.


Rob



-------------- next part --------------
An HTML attachment was scrubbed...
URL: https://lists.bnl.gov/mailman/private/map-l/attachments/20110312/6e75a2b6/attachment.html