Commit 809b2b50 authored by snuverink_j's avatar snuverink_j
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replace \milli

parent 3dfed95a
......@@ -44,7 +44,7 @@ In TRACE 3D, the input beam is described by the following set of parameters:
\item \textbf{ER}: particle rest mass [{MeV/\squarec}];
\item \textbf{Q}: charge state (+1 for protons);
\item \textbf{W}: beam kinetic energy [{MeV}]
\item \textbf{XI}: beam current [{\milliA}]
\item \textbf{XI}: beam current [{mA}]
\item \textbf{BEAMI}: array with initial Twiss parameters in the three phase planes
\begin{center}
BEAMI = $\alpha_x , \beta_x, \alpha_y, \beta_y, \alpha_{\phi}, \beta_{\phi} $ \\
......@@ -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
particles is $N_{\text{p}} = 10^{5}$.
\subsection{\textit{OPAL} Input}
......
......@@ -426,15 +426,15 @@ Name:DISTRIBUTION, TYPE = GAUSS,
OFFSETPZ = 1200.0
USEEV = TRUE;
\end{verbatim}
This creates a Gaussian shaped distribution with zero transverse emittance, zero energy spread, $\sigma_{x} = {1.0}{\millim}$,
$\sigma_{y} = {3.0}{\millim}$, $\sigma_{z} = {2.0}{\millim}$ and an average energy of:
This creates a Gaussian shaped distribution with zero transverse emittance, zero energy spread, $\sigma_{x} = {1.0}{mm}$,
$\sigma_{y} = {3.0}{mm}$, $\sigma_{z} = {2.0}{mm}$ and an average energy of:
\begin{equation*}
W = {1.2}{MeV}
\end{equation*}
In the $x$ direction, the Gaussian distribution is cutoff at $x = 2.0 \times \sigma_{x} = {2.0}{\millim}$. In the $y$
direction it is cutoff at $y = 2.0 \times \sigma_{y} = {6.0}{\millim}$. This distribution is \emph{injected} into the simulation
at an average position of $(\bar{x},\bar{y},\bar{z})=({1.0}{\millim}, {-2.0}{\millim}, {10.0}{\millim})$.
In the $x$ direction, the Gaussian distribution is cutoff at $x = 2.0 \times \sigma_{x} = {2.0}{mm}$. In the $y$
direction it is cutoff at $y = 2.0 \times \sigma_{y} = {6.0}{mm}$. This distribution is \emph{injected} into the simulation
at an average position of $(\bar{x},\bar{y},\bar{z})=({1.0}{mm}, {-2.0}{mm}, {10.0}{mm})$.
......@@ -694,7 +694,7 @@ The attributes of an \emph{emitted} \texttt{FLATTOP} distribution are defined in
The \texttt{FLATTOP} distribution was really intended for this mode of operation in order to mimic
common laser pulses in photoinjectors. The basic characteristic of a \texttt{FLATTOP} is a uniform, elliptical transverse distribution
and a longitudinal (time) distribution with a Gaussian rise and fall time as described in Section~\ref{gaussdisttypephotoinjector}.
Below we show an example of a \texttt{FLATTOP} distribution command with an elliptical cross section of {1}{\millim} by {2}{\millim} and a flat top,
Below we show an example of a \texttt{FLATTOP} distribution command with an elliptical cross section of {1}{mm} by {2}{mm} and a flat top,
in time, {10}{ps} long with a {0.5}{ps} rise and fall time as defined in Figure~\ref{flattop}.
\begin{verbatim}
......
......@@ -1373,7 +1373,7 @@ Azimuthal symmetry of the ring. Ring elements will be placed repeatedly
Set to \texttt{FALSE} to disable checking for ring closure.
\item[LAT\_RINIT]
Radius of the first element placement in the lattice [{\millim}].
Radius of the first element placement in the lattice [{mm}].
\item[LAT\_PHIINIT]
Azimuthal angle of the first element placed in the lattice [degree].
......@@ -1383,7 +1383,7 @@ Angle in the mid-plane relative to the ring tangent for placement of the first
element [degree].
\item[BEAM\_RINIT]
Initial radius of the reference trajectory [{\millim}].
Initial radius of the reference trajectory [{mm}].
\item[BEAM\_PHIINIT]
Initial azimuthal angle of the reference trajectory [degree].
......@@ -1406,9 +1406,9 @@ arbitrary position in the coordinate system of the preceding element. This
enables drift spaces and placement of overlapping elements.
\begin{kdescription}
\item[END\_POSITION\_X] x position of the next element start in the
coordinate system of the preceding element [{\millim}].
coordinate system of the preceding element [{mm}].
\item[END\_POSITION\_Y] y position of the next element start in the
coordinate system of the preceding element [{\millim}].
coordinate system of the preceding element [{mm}].
\item[END\_NORMAL\_X] x component of the normal vector defining the placement of
the next element in the coordinate system of the preceding element.
\item[END\_NORMAL\_Y] y component of the normal vector defining the placement of
......@@ -1539,11 +1539,11 @@ placed using the \texttt{RingDefinition} element.
\item[PHASE\_MODEL]
String naming the time dependence model of the cavity phase offset, $\phi$.
\item[WIDTH]
Full width of the cavity [{\millim}].
Full width of the cavity [{mm}].
\item[HEIGHT]
Full height of the cavity [{\millim}].
Full height of the cavity [{mm}].
\item[L]
Full length of the cavity [{\millim}].
Full length of the cavity [{mm}].
\end{kdescription}
The field inside the cavity is given by
\begin{equation}
......@@ -1811,19 +1811,19 @@ If this particle leave the bunch, it will be removed during the integration afte
\begin{kdescription}
\item[XSTART]
The x coordinate of the start point. [{\millim}]
The x coordinate of the start point. [{mm}]
\item[XEND]
The x coordinate of the end point. [{\millim}]
The x coordinate of the end point. [{mm}]
\item[YSTART]
The y coordinate of the start point. [{\millim}]
The y coordinate of the start point. [{mm}]
\item[YEND]
The y coordinate of the end point. [{\millim}]
The y coordinate of the end point. [{mm}]
\item[ZSTART]
The vertical coordinate of the start point [{\millim}]. Default value is {-100}{\millim}.
The vertical coordinate of the start point [{mm}]. Default value is {-100}{mm}.
\item[ZEND]
The vertical coordinate of the end point. [{\millim}]. Default value is {-100}{\millim}.
The vertical coordinate of the end point. [{mm}]. Default value is {-100}{mm}.
\item[WIDTH]
The width of the septum. [{\millim}]
The width of the septum. [{mm}]
\item[PARTICLEMATTERINTERACTION]
\texttt{PARTICLEMATTERINTERACTION} is an attribute of the element. Collimator physics is only a kind of particlematterinteraction.
It can be applied to any element. If the type of \texttt{PARTICLEMATTERINTERACTION} is \texttt{COLLIMATOR}, the material is defined here.
......@@ -1875,15 +1875,15 @@ This is a restricted feature: \texttt{DOPAL-t}.
The particles hitting on the septum is removed from the bunch. There are 5 parameters to describe a septum.
\begin{kdescription}
\item[XSTART]
The x coordinate of the start point. [{\millim}]
The x coordinate of the start point. [{mm}]
\item[XEND]
The x coordinate of the end point. [{\millim}]
The x coordinate of the end point. [{mm}]
\item[YSTART]
The y coordinate of the start point. [{\millim}]
The y coordinate of the start point. [{mm}]
\item[YEND]
The y coordinate of the end point. [{\millim}]
The y coordinate of the end point. [{mm}]
\item[WIDTH]
The width of the septum. [{\millim}]
The width of the septum. [{mm}]
\end{kdescription}
\begin{tikzpicture}[scale=1.5,axis/.style={very thick, ->, >=stealth'}]
......@@ -1915,13 +1915,13 @@ The particles lost on the SEPTUM are recorded in the ASCII file \textit{\textles
The particles hitting on the probe is recorded. There are 5 parameters to describe a probe.
\begin{kdescription}
\item[XSTART]
The x coordinate of the start point. [{\millim}]
The x coordinate of the start point. [{mm}]
\item[XEND]
The x coordinate of the end point. [{\millim}]
The x coordinate of the end point. [{mm}]
\item[YSTART]
The y coordinate of the start point. [{\millim}]
The y coordinate of the start point. [{mm}]
\item[YEND]
The y coordinate of the end point. [{\millim}]
The y coordinate of the end point. [{mm}]
\item[WIDTH]
The width of the probe, NOT used yet.
\end{kdescription}
......@@ -1960,13 +1960,13 @@ Please note that the stripping physics in not included yet.
There are 9 parameters to describe a stripper.
\begin{kdescription}
\item[XSTART]
The x coordinate of the start point. [{\millim}]
The x coordinate of the start point. [{mm}]
\item[XEND]
The x coordinate of the end point. [{\millim}]
The x coordinate of the end point. [{mm}]
\item[YSTART]
The y coordinate of the start point. [{\millim}]
The y coordinate of the start point. [{mm}]
\item[YEND]
The y coordinate of the end point. [{\millim}]
The y coordinate of the end point. [{mm}]
\item[WIDTH]
The width of the probe, NOT used yet.
\item[OPCHARGE]
......
......@@ -119,14 +119,14 @@ Both the Furman-Pivi's model and Vaughan's model have been carefully benchmarked
\begin{figure}[ht]
\begin{center}
\includegraphics[width=1\linewidth,angle=0]{figures/Multipacting/const_particle_benchmark_FurmanPivi.pdf}
\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 $f={200}{MHz}$, $V_0={120}{V}$, $d={5}{mm}$}
\label{fig:PPFurman-Pivi}
\end{center}
\end{figure}
\begin{figure}[ht]
\begin{center}
\includegraphics[width=1\linewidth,angle=0]{figures/Multipacting/const_particle_benchmark.pdf}
\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 $f={1640}{MHz}$, $V_0={120}{V}$, $d={1}{mm}$.}
\label{fig:PPVaughan}
\end{center}
\end{figure}
......
......@@ -113,7 +113,7 @@ The independent variable is: \textbf{t} [{s}].
\subsubsection{NOTE: unit conversion of momentum in \textit{OPAL-t} and \textit{OPAL-cycl}}
Convert $\beta_x \gamma$ [dimensionless] to [{\millirad}],
Convert $\beta_x \gamma$ [dimensionless] to [{mrad}],
\begin{equation}
\label{eq:betagamma1}
......@@ -121,7 +121,7 @@ Convert $\beta_x \gamma$ [dimensionless] to [{\millirad}],
\end{equation}
\begin{equation}
\label{eq:betagamma2}
P_x[{\millirad}]=1000\times\frac{(\beta_x\gamma)}{(\beta\gamma)_{\text{ref}}}.
P_x[{mrad}]=1000\times\frac{(\beta_x\gamma)}{(\beta\gamma)_{\text{ref}}}.
\end{equation}
Convert from [{eV/c}] to $\beta_x\gamma$ [dimensionless],
......@@ -199,7 +199,7 @@ If \texttt{TYPE=CARBONCYCL}, the program requires the $B_z$ data which is store
\end{center}
\end{figure}
We need to add 6 parameters at the header of a plain $B_z$ [{k\gauss}] data file, namely,
$r_{min}$ [{\millim}], $\Delta r$ [{\millim}], $\theta_{min}$ [{^{\circ}}], $\Delta \theta$ [{^{\circ}}],
$r_{min}$ [{mm}], $\Delta r$ [{mm}], $\theta_{min}$ [{^{\circ}}], $\Delta \theta$ [{^{\circ}}],
$N_\theta$ (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:
......@@ -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,
$r_{min}$ [{\millim}], $\Delta r$ [{\millim}], $\theta_{min}$[{^{\circ}}], $\Delta \theta$[{^{\circ}}],
$r_{min}$ [{mm}], $\Delta r$ [{mm}], $\theta_{min}$[{^{\circ}}], $\Delta \theta$[{^{\circ}}],
$N_\theta$(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.
......@@ -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,
$r_{min}$ [{\millim}], $\Delta r$ [{\millim}], $\theta_{min}$[{^{\circ}}], $\Delta \theta$[{^{\circ}}],
$r_{min}$ [{mm}], $\Delta r$ [{mm}], $\theta_{min}$[{^{\circ}}], $\Delta \theta$[{^{\circ}}],
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.
......@@ -430,13 +430,13 @@ The neighboring bunches problem is motivated by the fact that for high intensity
separation, single bunch space charge effects are not the only contribution. Along with the increment of beam
current, the mutual interaction of neighboring bunches in radial direction becomes more and more important,
especially at large radius where the distances between neighboring bunches get increasingly small and even they
can overlap each other. One good example is PSI {590}{MeV} Ring cyclotron with a current of about {2}{\milliA} in
can overlap each other. One good example is PSI {590}{MeV} Ring cyclotron with a current of about {2}{mA} in
CW operation and the beam power amounts to {1.2}{MW}. An upgrade project for Ring is in process with
the goal of {1.8}{MW} CW on target by replacing four old aluminum resonators by four new copper cavities with peak
voltage increasing from about {0.7}{MW} to above {0.9}{MW}. After upgrade, the total turn
number is reduced from 200 turns to less than 170 turns.
Turn separation is increased a little bit, but still are at the same order
of magnitude as the radial size of the bunches. Hence once the beam current increases from {2}{\milliA} to {3}{\milliA}, the mutual space
of magnitude as the radial size of the bunches. Hence once the beam current increases from {2}{mA} to {3}{mA}, the mutual space
charge effects between radially neighboring bunches can have significant impact on beam dynamics.
In consequence, it is important to cover neighboring bunch effects in the simulation to quantitatively study its impact on the beam dynamics.
......@@ -468,7 +468,7 @@ For the {\bfseries Tune Calculation mode}, one additional auxiliary file with t
84.000 2278.0 0.025
\end{verbatim}
In each line the three values represent energy $E$, radius $r$ and $P_r$ for the SEO (Static Equilibrium Orbit)
at starting point respectively and their units are {MeV}, {\millim} and {\millirad}.
at starting point respectively and their units are {MeV}, {mm} and {mrad}.
A bash script \textit{tuning.sh} is shown on the next page, to execute \textit{OPAL-cycl} for tune calculations.
\examplefromfile{examples/tuning.sh}
......@@ -516,7 +516,7 @@ The frequency of the data output can be set using the \texttt{SPTDUMPFREQ} optio
\section{Matched Distribution}
In order to run matched distribution simulation one has to specify a periodic accelerator. The function call also needs
the symmetry of the machine as well as a field map. The user then specifies the emittance $\pi{\millim\millirad}$.
the symmetry of the machine as well as a field map. The user then specifies the emittance $\pi{mmmrad}$.
\begin{verbatim}
/*
* specify periodic accelerator
......@@ -530,7 +530,7 @@ Dist1:DISTRIBUTION, TYPE=GAUSSMATCHED, LINE=l1, FMAPFN=...,
MAGSYM=..., EX = ..., EY = ..., ET = ...;
\end{verbatim}
\subsection{Example}
Simulation of the PSI Ring Cyclotron at {580}{MeV} and current {2.2}{\milliA}. The program finds a matched
Simulation of the PSI Ring Cyclotron at {580}{MeV} and current {2.2}{mA}. The program finds a matched
distribution followed by a bunch initialization according to the matched covariance matrix.\\
The matched distribution algorithm works with normalized emittances, i.e. normalized by the lowest energy of the
machine. The printed emittances, however, are the geometric emittances. In addition, it has to
......
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