@@ -749,7 +749,7 @@ In the drift space following the bending magnet, the CSR effects are calculated

One important effect to notice is that in the drift space following the bending magnet, the normalized emittance $\epsilon_x(x, P_x)$ output by \textit{OPAL} keeps increasing while the trace-like emittance $\epsilon_x(x, x')$ calculated by ELEGANT does not. This can be explained by the fact that with a relatively large energy spread (about $3\%$ at the end of the dipole due to CSR), {\bf an correlation} between transverse position and energy can build up in a drift thereby induce emittance growth. However, this effect can only be observed in the normalized emittance calculated with $\epsilon_x(x, P_x)=\sqrt{\langle x^2\rangle\langle P_x^2\rangle-\langle xP_x \rangle^2}$ where $P_x =\beta\gamma x'$, not the trace-like emittance which is calculated as $\epsilon_x(x, x')=\beta\gamma\sqrt{\langle x^2\rangle\langle x'^2\rangle-\langle xx' \rangle^2}$\ref{prstab2003}. In Figure~\ref{plot-emit-csr-on}, a trace-like horizontal emittance is also calcualted for the \textit{OPAL} output beam distributions. Like the ELEGANT result, this trace-like emittance doesn't grow in the drift. However, their differences come from the ELEGANT's lack of CSR effect in the fringe field region.

\section{\textit{OPAL}\&\texttt{Impact-t}}

This benchmark compares rms quantities such as beam size and emittance of \textit{OPAL} and \texttt{Impact-t}\ref{qiang2005, qiang2006-1, qiang2006-2}. A {\bf cold}{10}{\milliA} H+ bunch is expanding in a {1}{m} drift space. A Gaussian distribution, with a cut at 4 $\sigma$ is used. The charge is computed by assuming a {1}{MHz} structure i.e. $Q_{\text{tot}}=\frac{I}{\nu_{\text{rf}}}$. For the simulation we use a grid with $16^{3}$ grid point and open boundary condition. The number of macro

This benchmark compares rms quantities such as beam size and emittance of \textit{OPAL} and \texttt{Impact-t}\ref{qiang2005, qiang2006-1, qiang2006-2}. A {\bf cold}{10}{mA} H+ bunch is expanding in a {1}{m} drift space. A Gaussian distribution, with a cut at 4 $\sigma$ is used. The charge is computed by assuming a {1}{MHz} structure i.e. $Q_{\text{tot}}=\frac{I}{\nu_{\text{rf}}}$. For the simulation we use a grid with $16^{3}$ grid point and open boundary condition. The number of macro

\caption{Time evolution of electron number predicted by theoretical model and \textit{OPAL} simulation using Furman-Pivi's secondary emission model with both constant simulation particle approach and real emission particle approach at $f={200}{MHz}$, $V_0={120}{V}$, $d={5}{\millim}$}

\caption{Time evolution of electron number predicted by theoretical model and \textit{OPAL} simulation using Furman-Pivi's secondary emission model with both constant simulation particle approach and real emission particle approach at $f={200}{MHz}$, $V_0={120}{V}$, $d={5}{mm}$}

\caption{Time evolution of electron number predicted by theoretical model and \textit{OPAL} simulation using Vaughan's secondary emission model with both constant simulation particle approach and real emission particle approach at $f={1640}{MHz}$, $V_0={120}{V}$, $d={1}{\millim}$.}

\caption{Time evolution of electron number predicted by theoretical model and \textit{OPAL} simulation using Vaughan's secondary emission model with both constant simulation particle approach and real emission particle approach at $f={1640}{MHz}$, $V_0={120}{V}$, $d={1}{mm}$.}

$N_\theta$ (total data number in each arc path of azimuthal direction) and $N_r$ (total path number along radial direction).

If $\Delta r$ or $\Delta\theta$ is decimal, one can set its negative opposite number. For instance, if $\Delta\theta=\frac{1}{3}{^{\circ}}$, the fourth line of the header should be set to -3.0.

Example showing the above explained format:

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@@ -258,7 +258,7 @@ finish

By running this in ANSYS, you can get a fields file with the name \textit{cyc100\_ANSYS.data}.

You need to put 6 parameters at the header of the file, namely,

$N_\theta$(total data number in each arc path of azimuthal direction) and $N_r$(total path number along radial direction).

If $\Delta r$ or $\Delta\theta$ is decimal,one can set its negative opposite number. This is useful is the decimal is unlimited.

For instance,if $\Delta\theta=\frac{1}{3}{^{\circ}}$, the fourth line of the header should be -3.0.

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@@ -301,7 +301,7 @@ For the detail about its usage, please see Section~\ref{cyclotron}.

\subsection{Default PSI format}

If the value of \texttt{TYPE} is other string rather than above mentioned, the program requires the data format like PSI format field file \textit{ZYKL9Z.NAR} and \textit{SO3AV.NAR}, which was given by the measurement.

We add 4 parameters at the header of the file, namely,