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

[Kirk T McDonald]

Rick,

Thanks for this.

It sounds to me like ECALC9 only includes a vector potential for DC magnets.

For rf cavities, it sounds like neither the vector nor scalar potential are considered.

This is inconsistent with the nominal rules of Hamiltonian dynamics.

I am still trying to clarify whether we can get away with such apparent inconsistencies.

--Kirk

From: Fernow, Richard C 
Sent: Monday, March 14, 2011 1:51 PM
To: MAP-l at lists.bnl.gov 
Subject: Re: [MAP] Use of x,y,t as Hamiltonian coordinates.

Kirk,

 

First let me say that the physics content of ECALC9 is entirely the work of Gregg Penn. I made a modified version ECALC9F that took its input from an input file instead of the keyboard and have tried to maintain it as problems arose over the years. I also wrote the Mucool note 280 to help me understand what Gregg was doing. Sometimes this isn’t very clear in the code. I don’t think FORTRAN was Gregg’s native language. Anyway looking over the code again this morning

 

1.      Greg calculates em6, emT, and emL using three different matrices.

2.      The variables for em6 are {x, y, t, px, py, E}. The momenta appear to be mechanical, i.e. the correction for Bz is not applied here.

3.      The variables for emT are {x, y, px, py}. The momenta also appear to be mechanical in this matrix. The statement I made about this at JLAB was apparently wrong.

4.      The variables for emL are {t, E, AT2}. The third variable is the square of the transverse amplitude.

5.      The only place where the on-axis field appears to be used is in calculating the canonical angular momentum and the transverse amplitude.

 

Rick

 

 

It is my understanding the ICOOL/ECALC presently uses the first of these transformations, I.e., it uses coordinates

(x, y, t, p_mech_x+qA_x/c, p_mech_y+qA_y/c, E_mech)

 

[Rick Fernow: Can you comment on this?]

 

It now seems to me that this is actually OK in principle (although perhaps a somewhat "ugly" transformation)

 



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