@@ -163,7 +163,7 @@ In that case the approach is identical to the Hockney method \ref{hockney, eastw

%When the free space Green function is a symmetric function of $\mathbf{x}-\mathbf{x'}$, a circular shift of the Green function array, moving $\mathbf{x}-\mathbf{x'}=0$ from the

%center of the grid to the corner corresponding to the origin of grid points, produces a periodic Green function that is identical to the

%periodic Green function used in the Hockney method. Viewed this way, the only difference between an ``ordinary" FFT-based convolution

%periodic Green function used in the Hockney method. Viewed this way, the only difference between an "ordinary" FFT-based convolution

%and one described by Hockney is a circular shift of the Green function. The usual description of the Hockney approach involves making the Green function periodic and symmetric,

%but that is because the Green function for the free space potential is symmetric; if the Hockney approach were used to directly compute the electric fields

%by convolving the charge density with the electric field Green functions, then the Green functions would have to be anti-symmetrized.

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@@ -208,7 +208,7 @@ and $\text{FFT}^{-1}\{ . \}$ denotes a backward FFT in all 3 dimensions.

%subject to open boundary conditions in all spatial directions: $\phi (\mathbf{q}) \rightarrow 0$ as $|\mathbf{q}| \rightarrow \infty$ or

%imposing periodic boundary conditions in longitudinal directions. The assumption of using an ``isolated system`` is physically

%imposing periodic boundary conditions in longitudinal directions. The assumption of using an "isolated system" is physically

%motivated by observing the ratio of the beam size to vacuum vessel domensions. It has the computational advantages that one can use cyclic convolution in Equation~\ref{FourierPoisson}.

%The computational domain $\Omega \subset \R^3$ is simply connected and has a cylindrical

Before starting to track, a beam line see~Section~\ref{line}\ifthenelse{\boolean{ShowMap}}{or

sequence see~Section~\ref{sequence}}{} and a beam see~Chapter~\ref{beam} must be selected.

The time step (\texttt{DT}) and the maximal steps to track (\texttt{MAXSTEPS}) or \texttt{ZSTOP} should be set. This command causes \textit{OPAL} to enter ``tracking mode'',

The time step (\texttt{DT}) and the maximal steps to track (\texttt{MAXSTEPS}) or \texttt{ZSTOP} should be set. This command causes \textit{OPAL} to enter "tracking mode",

in which it accepts only the track commands see~Table~\ref{trackcmd}. In order to preform several tracks, specify arrays of parameter

in \texttt{DT}, \texttt{MAXSTEPS} and \texttt{ZSTOP}. This can be used to change the time step manually.