emit.tex

%%\title{EMIT}
%  Changed by: Chris ISELIN, 27-Jan-1997 
%  Changed by: Hans Grote, 15-Oct-2002 
%  Changed by: Ralph Assmann, 02-Sep-2003 

\chapter{EMIT: Equilibrium emittances} 
\label{chap:emit}
%Fully Coupled Motion and Radiation}

\texttt{EMIT} calculates the equilibrium emittances: 

\madbox{
EMIT, DELTAP=real, TOL=real;
}\vspace{5mm}

The attributes for the \texttt{EMIT} command are: 

\begin{madlist}
  \ttitem{DELTAP} the average energy error. \\
  \texttt{EMIT} adjusts the RF frequencies in order to obtain this
  average energy error: the revolution frequency $f_0$
  is determined for a fictitious particle with constant momentum error  
  %DELTAP = delta$_\textit{s}$ = delta(\textit{E}) / \textit{p$_s$ c}
  $\mathtt{DELTAP} = \delta_s = \delta(E) / p_s c$ travelling along the
  design orbit. The RF frequencies are then set to   
  %\textit{f$_{RF}$ = h f$_0$}. 
  $f_{RF} = h f_0$. 

  \ttitem{TOL} The tolerance attribute is for the distinction between
  static and dynamic cases: \\
  if for the eigenvalues of the one-turn matrix, $|$e\_val\_5$|$ \textless
  tol and $|$e\_val\_6$|$ \textless tol, then the longitudinal motion is
  not considered, otherwise it is. \\
  (Default:~1.000001)  
\end{madlist}


If the machine contains at least one RF cavity, and if synchrotron
radiation is enabled with \hyperref[sec:beam]{\texttt{BEAM,
    RADIATE=true;}}, the 
\texttt{EMIT} command computes the equilibrium emittances and other
electron beam parameters using the method in \cite{chao1979}.

In this calculation the effects of quadrupoles, sextupoles and
octupoles along the closed orbit are also considered. Thin multipoles are
used only if they have a fictitious length \texttt{LRAD} different from zero.  

If the machine does not contain any RF cavity, if synchrotron radiation is
turned off (\hyperref[sec:beam]{\texttt{BEAM, RADIATE=false;}}, or if the longitudinal
motion is not stable, \texttt{EMIT} only computes the parameters that
are not related to radiation and does not update the \texttt{BEAM} values.

If synchrotron radiation is enabled (\hyperref[sec:beam]{\texttt{BEAM, RADIATE=true;}}, 
and the \texttt{DELTAP} attribute is zero, and the longitudinal motion is stable, 
\texttt{EMIT} calculates and updates the following values for the \texttt{BEAM} attached 
to the current sequence: both geometric and normalized transverse emittances, 
longitudinal emittance and beam sizes ($\sigma_E$ and $\sigma_t$), 
damping partition numbers, energy loss per turn and synchrotron tune.


\textbf{Example:}
\madxmp{
RFC: RFCAVITY, HARMON..., VOLT=...; \\
\ldots \\
BEAM, ENERGY = 100.0, RADIATE=true; \\
EMIT, DELTAP = 0.01;
}

\textbf{Remark:}\\
This module assumes nearly constant lattice functions
inside elements. This assumption works for many machines, like LEP
%(\href{http://cern.ch/frs/mad-X_examples/emit/LEP/}{see example}),
but it fails when the lattice functions largely vary inside single
elements. In the later case it is advised to slice the elements.
%as shown in the example pertaining to
%\href{http://cern.ch/frs/mad-X_examples/emit/ALBA/}{ALBA}.     

% \href{Rogelio HREF=http://consult.cern.ch/xwho/people/69118}{R.Tom\'as} 
% \textbf{Last updated:} 03/13/2013 13:47:20