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

[alex dragt]

Dear Kirk,

      If you employ (1.5.29) and (1.5.30) in my book, you will find that

H=\gamma mc^2+q\psi.

Then. from (1.6.5), it follows that

p_t=-H=-\gamma mc^2-q\psi,

in agreement with Rob's slide 16.

Best,

Alex

If you

On Mar 11, 2011, at 8:10 PM, Kirk T McDonald wrote:

> 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
>
>

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