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Tracks through a zero length multipole to simulate space charge effects
Parallel capable? : yes
Parameter Name |
Units |
Type |
Default |
Description |
This element simulates transverse space charge (SC) kick using
K.Y. Ng's formula ( K.Y. Ng, FNAL, private communication).
The linear SC force is given by:
 |
(30) |
where
,
is the integrating length,
are rms beam size.
The non-linear SC force is given by:
![\begin{displaymath}
\Delta y'=\frac{K_{sc}Le^{-z^2/(2\sigma_z^2)}}{2\sigma_z\sqr...
...x}{\sigma_y}}
{\sqrt{2(\sigma_x^2-\sigma_y^2)}}\right)\right ]
\end{displaymath}](img255.gif) |
(31) |
where
is the complex error function
![\begin{displaymath}
w(z)=e^{-z^2}\left [ 1+\frac{2i}{\sqrt{\pi}}\int\limits_0^z e^{\zeta^2}d\zeta\right ]
\end{displaymath}](img257.gif) |
(32) |
Equation 31 appear to diverge when
. In fact, this is not
true, because the expressions inside the square brackets will provide zero too at
to cancel the poles outside. In our code, we calculate this equation
at
and
, and average the total effects.
To invoke the calculation, one must use set up command
``insert_sceffects'' proceed ``run_setup'' and ``Twiss_output''
command proceed ``track''.
Next: SCRAPER
Up: Element Dictionary
Previous: SCATTER
Michael Borland
2007-09-07