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\begin{document}
%\marginpar{ \vspace*{0cm} \hspace*{10.0cm}Internal Report}
%\title{PREPARATION OF PAPERS FOR JACoW CONFERENCES\thanks{Work supported by ...}}
\title{OBSERVATIONS OF ELECTRON CLOUD PHENOMENA AT PETRA III}
\author{R.~Wanzenberg\thanks{rainer.wanzenberg@desy.de}, DESY, Hamburg, Germany}
\maketitle
\begin{abstract}
PETRA III is a third generation synchrotron radiation
facility at DESY, which is presently operated with
positron beams. Regular user operation started in mid 2010
after a commissioning phase which began in April 2009.
The design current of 100 mA has been achieved but with
different number of bunches and bunch to bunch distances
than originally foreseen since a strong vertical emittance
growth was observed for the design bunch filling pattern
with 960 bunches. During machine studies different bunch
filling patterns have been tested. In 2012 two scrubbing
runs with 480 bunches and a bunch to bunch spacing of 16 ns
have been done. The recent measurements indicate that
the scrubbing runs have mitigated the emittance growth.
Furthermore conditioning effects have been observed during
the user runs in 2011. The results from the measured
emittances and tune spectra are reported.
\end{abstract}
\section{INTRODUCTION}
PETRA III \cite{TDRPETRAIII} is a third generation synchrotron radiation facility at DESY.
The PETRA ring was built in 1976 as an electron and positron collider and used
as a preaccelerator for the HERA lepton hadron collider ring from 1988 until 2007.
During the conversion to a synchrotron radiation facility from 2007 to 2009 one
octant of the PETRA ring has been completely redesigned to provide space for 14 undulators.
The new experimental hall is shown in Fig.~\ref{NewHall}. The commissioning
with beam started in April 2009 and user runs have been started
in 2010 \cite{Balewski:2010zz}. PETRA III is presently running in a top up operation mode
with {\em positrons} since PETRA III is sharing the same preaccelerator
chain with the synchrotron source DORIS, which is running with positrons
to avoid problems with ionized dust particles.
\begin{figure}[hbbb]
\centering
\includegraphics*[width=70mm]{./Figures/PETRAIIInewhall.eps}
\caption{Aerial view of the new experimental hall of PETRA III
which was build from 2007 to 2008.}
\label{NewHall}
\end{figure}
%%
%%================================================================
%%
\subsection{Beam parameters}
A summary of the PETRA III design parameters can be found in
Table~\ref{PIIIparameter} \cite{TDRPETRAIII}.
The very low emittance of 1~nm~rad has been achieved with
the help of 20 damping wigglers with a length of 4~m each
and a peak magnetic field of $1.5$~T and a period length
of $0.2$~m \cite{Tischer:2008zz}.
\begin{table}[hhhtb]
\centering
\caption{PETRA III design parameters}
\begin{tabular}{lcc}
\toprule
\textbf{Parameter} & \multicolumn{2}{c}{\textbf{PETRA III}} \\
\midrule
\hline
Energy /GeV & 6 & \\
Circumference /m & 2304.0 & \\
Revolution & & \\
frequency /kHz & 130.1 & \\
harmonic number & 3840 & \\
RF frequency /MHz & 500 & \\
\hline
Total current /mA & 100 & 100 \\
Bunch & & \\
Population $N_0$/$10^{10}$ & 0.5 & 12.0 \\
Number of bunches & 960 & 40 \\
Bunch separation & & \\
$\Delta t$ /ns & 8 & 192 \\
\hline
Emittance & & \\
$\epsilon_{x}$/nm & 1 & \\
$\epsilon_{y}$/nm & 0.01 & \\
Bunch length /mm & 12 & \\
\hline
Tune $Q_x$ & 36.13 & \\
\phantom{Tune} $Q_y$ & 30.29 & \\
\phantom{Tune} $Q_s$ & 0.049 & \\
Momentum & & \\
compaction /$10^{-3}$ & 1.2 & \\
\hline
\bottomrule
\end{tabular}
\label{PIIIparameter}
\end{table}
The design current of 100~mA has been
achieved but with a different filling scheme than originally foreseen
since a vertical emittance blow-up has been observed for a filling scheme
with equidistantly spaced bunches with a bunch to bunch spacing of 8~ns
and 16~ns. First observations of the instability are reported in
\cite{Wanzenberg:EC10}. There were indications already in 2009 that
the vertical emittance increase is related to electron cloud effects
\cite{Ohmi:1995,Zimmermann:2001ax}.
In 2010 filling schemes with short trains of 4 bunches and different
spacings between the bunch trains (144~ns and 80~ns) have been used,
see Fig.~11 in \cite{Wanzenberg:EC10}.
During the user runs in 2011 and 2012 three
different filling scheme have been mainly used with a bunch spacing of 32~ns,
128~ns and 192~ns, see Table \ref{PIIIpara2011} and
Fig.~\ref{BunchCurr2011}. The filling schemes with 60 and 40 bunches
are used for time resolved measurements. No emittance growth related
to electron cloud effects is observed for these two schemes.
\begin{table}[hhhbt]
\centering
\caption{PETRA III parameters 2011/2012}
\begin{tabular}{lccc}
\toprule
\textbf{Parameter} & \multicolumn{3}{c}{\textbf{User runs}} \\
\midrule
\hline
Total current /mA & 100 & 100 & 80 \\
Bunch & & & \\
Population $N_0$/$10^{10}$ & 2.0 & 8.9 & 9.6 \\
Number of bunches & 240 & 60 & 40 \\
Bunch separation & & & \\
$\Delta t$ /ns & 32 & 128 & 192 \\
\hline
\bottomrule
\end{tabular}
\label{PIIIpara2011}
\end{table}
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/P3bunch_pattern_user.eps}
\caption{Filling schemes for the user runs in 2012. The smallest bunch to
bunch spacing is 32 ns.}
\label{BunchCurr2011}
\end{figure}
%%
%%================================================================
%%
\subsection{Instability threshold}
The threshold density $\rho_{e, th}$ for the onset of electron cloud
effects can be estimated
from an approach by K.~Ohmi \cite{Ohmi:2004zg} which is based on a combination of a
broad band resonator model for the impedance \cite{Ohmi:2002} and
a coasting beam model for the instability:
\begin{equation} \label{eq:rho_eth}
\rho_{e, th} = \frac{2 \, \gamma \, Q_s \, \omega_{e,y} \, \sigma_z / c}
{K \, Q_{res} \, \sqrt{3} \, r_e \, \langle \beta_y \rangle \, C},
\end{equation}
where $Q_s$ is the synchrotron tune, $Q_{res} \approx 5$ is the Q-value of the
broad band impedance model, $K$ is a factor to take into account the pinch effect
and $\omega_{e,y}$ is the oscillation frequency of the electrons in the bunch potential.
$C$ is the circumference of the ring, $\gamma$ the relativistic $\gamma$-factor, $r_e$ the
classical electron radius and $\langle \beta \rangle$ the average betatron function
and $\sigma_z$ is the bunch length.
Assuming that $K \approx \omega_{e,y} \,\sigma_z / c $ one
obtains the following threshold density (see Table~\ref{PIIIthreshold_density}):
\begin{table}[hhhbt]
\centering
\caption{PETRA III threshold density}
\begin{tabular}{lc}
\toprule
\textbf{PETRA III} & $K = \omega_{e,y} \,\sigma_z / c $ \\
\midrule
\hline
$\rho_{e, th}$ & $1.4 \, \cdot \, 10^{12} \,{\rm m}^{-3}$ \\
\hline
\bottomrule
\end{tabular}
\label{PIIIthreshold_density}
\end{table}
%%
%%================================================================
%%
\subsection{Vacuum system}
The vacuum chamber, which is installed in the PETRA III dipole magnets,
is shown in Fig.~\ref{DipoleChamber} \cite{Seidel:2005hz, Boespflug:2008}.
An integrated vacuum pump with NEG strip is integrated in an ante chamber,
which is placed on the inner side of the PETRA ring.
Synchrotron radiation hits the outer side of the vacuum chamber which is water cooled.
\begin{figure}[htb]
\centering
\includegraphics*[width=65mm]{./Figures/DipoleChamber.eps}
\caption{Vacuum chamber of the PETRA III dipole magnet.
The dimension of the ellipse are 80 $\times$ 40~mm.}
\label{DipoleChamber}
\end{figure}
The chamber is made from aluminum and had initially (as received) a
maximum secondary emission yield (SEY) of $\delta_{\rm max} = 2.7$ \cite{Grosso:IPAC2011}.
After an electron dose of $1.2 \cdot 10^{-2} \,\,{\rm C/mm^2}$ the maximum SEY is reduced
to $1.5$ to $1.8$ depending on the vacuum conditions in the laboratory measurements
\cite{Grosso:IPAC2011}.
In 2012 the measured average vacuum pressure in PETRA III without beam is
$5.0 \cdot 10^{-10}$~mb and about $1.5 \cdot 10^{-8}$~mb with beam (100~mA).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{MEASUREMENTS}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The commissioning of PETRA III \cite{Balewski:2010zz} with beam started in April 2009.
The damping wigglers have been installed on a step by step basis from May 20 to June 25, 2009.
After the installation of the damping wigglers
the horizontal design emittance of 1 nm has been achieved. The vertical emittance
was about 20~pm corresponding to an emittance coupling of about 2\%.
But for some filling schemes with many bunches a mainly vertical emittance blow-up was observed,
correlated with additional lines (sidebands) in the tune spectra.
For the user runs in Aug.~2010 short trains of 4 bunches and different
spacings between the bunch trains have been used to avoid an emittance growth \cite{Wanzenberg:EC10}.
In 2011 it was possible to use a filling scheme with 240 equally spaced bunches
(bunch spacing of 32~ns), see Fig.~\ref{BunchCurr2011}, which clearly indicates
a conditioning effect. At the end of the user runs in 2011 the integrated beam
current was nearly 1000~Ah. In March 2012 two dedicated scrubbing runs were
performed. After the scrubbing runs the emittance has been measured for
different bunch filling schemes. The main results of the studies are summarized
in this section of this report.
%%
%%================================================================
%%
\subsection{Emittance diagnostic}
At PETRA III a special diagnostic beam line is used to measure the
horizontal and vertical spot size of
the synchrotron light of a bending magnet \cite{Kube:2010zz}.
From the spot size the emittance is calculated. A measurement from
a user run with 240 bunches and a total bunch current of 100~mA
is shown in Fig.~\ref{DBL2012}. The beam size corresponds to an
average which includes all 240 bunches. From the spot size a horizontal
emittance of 1.18~nm was calculated. Due to an aberration in the optical
beamline it is not possible to measure a vertical emittance smaller
than 35~pm. For the example in Fig.~\ref{DBL2012} the calculated and
displayed vertical emittance was 37~pm.
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/DBLEmittance240Bunche.eps}
\caption{Measured photon spot size from the diagnostic beam line
of PETRA III. From the rms spot size a horizontal emittance
of 1.18~nm is calculated. The total beam current of 100~mA
was stored in 240 bunches (32 ns bunch spacing).}
\label{DBL2012}
\end{figure}
Since 2012 an interferometric vertical beam size measurement
\cite{Naito:2006zs,Hayano:1999cw,Kube:2008zza,Baleski:DIPAC09} is used to obtain
a more accurate measurement of the vertical emittance.
The principle of the measurement is shown in Fig.~\ref{interference}.
Synchrotron light from a bending magnet is sent through a double slit and
generates an interference pattern. The beam size is calculated from the
visibility of the interferogram, which indicates the degree of spatial
coherence of the photons. A measurement of the vertical beam size at PETRA~III
is shown in Fig.~\ref{InterferBL}. From the beam size a vertical emittance
of about 5~pm was calculated for this measurement (March 8, 2012), which corresponds
to an emittance coupling of $0.5$~\%.
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/interference.eps}
\caption{Principle of the interferometric vertical beam size measurement.}
\label{interference}
\end{figure}
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/InterferBeamLine.eps}
\caption{Measured interference pattern to determine the vertical
emittance. From the beam size a vertical emittance
of about 5~pm was calculated (March 8, 2012).}
\label{InterferBL}
\end{figure}
%%
%%================================================================
%%
\subsection{Scrubbing runs}
In 2012 two dedicated scrubbing runs with a total time period
of four days (two weekends, March 3-4 and March 10-11, 2012)
have been performed with a filling scheme of 480 equally spaced
bunches and a total beam current of 100~mA,
see Fig.~\ref{pattern_scrub}. The integrated beam was about 10~Ah.
The photoelectron dose $d_{ch}$ on the dipole chamber wall
can be estimated from the mean number of emitted photons per length:
\begin{equation}
\frac{dN_{\gamma}}{dz} = \frac{5}{2\sqrt{3}} \, \frac{1}{137} \,
\frac{E}{m_0 \, c^2} \, \frac{1}{\rho} = 0.065 \, \frac{1}{\rm m},
\end{equation}
and integrated beam current $\int I \,dt$:
\begin{equation}
d_{ch} = Y \, \frac{dN_{\gamma}}{dz} \, \frac{1}{C_{ch}} \int I \,dt
= 1.2 \, 10^{-2} \, {\rm C/mm^2},
\end{equation}
where $\rho \approx 190 \, {\rm m}$ is the bending radius of the
dipole magnet in the arc, $Y \approx 0.1$ is the primary photoelectron emission
yield and $C_{ch} = 194 {\rm mm}$ is the inner circumference of the
vacuum chamber (Fig.~\ref{DipoleChamber}). The estimated photoelectron
dose during the scrubbing runs is similar to the dose applied to the
Al samples in the laboratory \cite{Grosso:IPAC2011}. In the laboratory
the measured maximum secondary emission yield $\delta_{max}$ was reduced to about $1.8$
for vacuum conditions similar to those in the PETRA III vacuum system.
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/P3bunch_pattern_scrub.eps}
\caption{Bunch filling patterns for the scrubbing runs with
480 bunches and a bunch to bunch distance of 16~ns.}
\label{pattern_scrub}
\end{figure}
During the scrubbing runs the beam emittance was monitored at the
diagnostic beam line. In Fig.~\ref{scrub_run} a screen shot of the
archive data viewer is shown. The horizontal scale covers a time
range of 100 h from March 9, $00\!:\!00$~h to March 13, $04\!:\!00$~h.
On the vertical scale the beam current (green line), the number of
bunches (blue line), the vertical emittance (red line) and the
horizontal emittance (black line) are shown in normalized units.
The beam current was always 100~mA. The number of bunches was 480
during the scrubbing run and 240 before the scrubbing run.
PETRA III was set-up in the 240 bunch mode with an horizontal
emittance of about 1~nm. During the scrubbing run
the horizontal emittance increased from initially 2~nm to 4~nm.
The vertical emittance decreased from 104~pm to 33~pm (red line).
The increased emittance is an evidence for effects due to electron
clouds although the beam dynamics is not understood.
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/scrubbing_run.eps}
\caption{Screen shot of the archive data viewer, showing the
the beam current (green line), the number of
bunches (blue line), the vertical emittance (red line) and the
horizontal emittance (black line)}
\label{scrub_run}
\end{figure}
%%
%%================================================================
%%
\subsection{Benefits from scrubbing}
The conditioning of the vacuum chamber surface due to beam operation
with a total integrated beam current of about 1000~Ah at the end of 2011
and the two dedicated scrubbing runs in March 2012 resulted in
extended possibilities for the filling schemes without emittances
growth, see Fig.~\ref{pattern_benefits}. In 2012 it was possible
to fill 320 bunches with a bunch to
bunch spacing of 24~ns and a total beam current of 100~mA without a
vertical emittance degradation while in 2011 this was only possible
with a bunch spacing of 32~ns. Furthermore it is now possible to
use a filling scheme with 60 bunch trains with 5 bunches while
in 2011 it was only possible to use trains with 4 bunches without
an emittance increase.
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/P3bunch_pattern_benefits.eps}
\caption{Bunch filling schemes without emittance growth in 2012.
The total beam current is always 100~mA.}
\label{pattern_benefits}
\end{figure}
But a filling pattern with 60 bunch trains with 6 bunches still showed
a significant vertical emittance increase. Also the filling scheme with
480 bunches (Fig.~\ref{pattern_scrub}), which was used during the
scrubbing runs, is not suitable for user operation.
Nevertheless the influence of the scrubbing runs on the
instability threshold is a strong evidence that the observed emittance
growth results from electron clouds.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{SIMULATIONS}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Simulations of the build-up of an electron cloud in dipole vacuum
chambers have been made with version 4.0 of the computer code ECLOUD
\cite{Rumolo:2002ti, ECLOUDmanual}. The vacuum chamber in the dipole
magnets is modeled as an ellipse with a width of 80~mm and a height of 40~mm,
see Fig.~\ref{DipoleChamber}. The dipole field strength is $0.104$~T.
To solve the equation of motion the Runge-Kutta integration method was
chosen within the ECLOUD code. Simulation results for the filling
schemes with 60 short bunch trains with 4 and 6 bunches are shown in
Fig.~\ref{SimuM60xn} for SEY of $\delta_{max} =2.0$. The filling
sequence of the bunch trains is clearly visible in the electron cloud
intensity.
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/SimuM60xn.eps}
\caption{Simulation of the electron cloud for 60x4 (blue line) and 60x6 (red line) bunches
for a total beam current of 100~mA and a SEY of $\delta_{max} =2.0$.}
\label{SimuM60xn}
\end{figure}
From the measurements it is known that the filling scheme with 60
bunch trains with 4 is not suffering from electron cloud effects
while the scheme with 60 trains with 6 bunches shows a strong
vertical emittance increase. Therefore it is expected that the
cloud density for the filling scheme with 60 times 6 bunches
should be above the estimated threshold density of
$1.4 \, \cdot \, 10^{12} \,{\rm m}^{-3}$ (see Eqn.~\ref{eq:rho_eth}
and Table~\ref{PIIIthreshold_density}), while the
cloud density for the filling scheme with 60 times 4 bunches
should be below this density. The simulated central density for the
two filling schemes is shown in Fig.~\ref{SimuC60xn}.
During the simulated time interval this
quantity fluctuates strongly between values below the
instability threshold and values which are 10 times above the
instability threshold. The strong fluctuations are most likely
not only caused by the interaction of the positron bunch with
the electron cloud but also due to the limited number of macro particles.
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/SimuC60xn.eps}
\caption{Simulation of the central volume density of the electron cloud
for 60x4 (blue line) and 60x6 (red line) bunches
for a total beam current of 100~mA and a SEY of $\delta_{max} =2.0$.
The green line corresponds to the threshold density of
$1.4 \, \cdot \, 10^{12} \,{\rm m}^{-3}$.}
\label{SimuC60xn}
\end{figure}
A detailed view of the simulated central volume density of the electron cloud
for the filling scheme with 60x4 bunches is shown in Fig.~\ref{SimuB60x4}.
In the same figure the number of electrons in the cloud (from Fig.~\ref{SimuM60xn})
is also plotted in arbitrary units. The central cloud density is below the
threshold density before the total number of electrons is increased from
the emitted primary photoelectrons generated from the synchrotron radiation
of each positron bunch. For the filling scheme with 60x6 bunches the
central volume density of the electron cloud does not drop below
the threshold density (see Fig.~\ref{SimuB60x6}). This indicates that the
measurements and the simulations are in agreement if one assumes that the
maximum SEY $\delta_{max}$ is about $2.0$.
\begin{figure}[htb]
\centering
\includegraphics*[width=70mm]{./Figures/SimuB60x4.eps}
\caption{Detailed view of the simulated central volume density of the electron cloud
for 60x4 bunches(blue line).
The green line corresponds to the threshold density of
$1.4 \, \cdot \, 10^{12} \,{\rm m}^{-3}$.
Furthermore the total number of electrons in the cloud is
shown in arbitrary units (red line).}
\label{SimuB60x4}
\end{figure}
\begin{figure}[hbt]
\centering
\includegraphics*[width=70mm]{./Figures/SimuB60x6.eps}
\caption{Detailed view of the simulated central volume density of the electron cloud
for 60x6 bunches(red line).
The green line corresponds to the threshold density of
$1.4 \, \cdot \, 10^{12} \,{\rm m}^{-3}$.
Furthermore the total number of electrons in the cloud is
shown in arbitrary units (blue line).}
\label{SimuB60x6}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{CONCLUSION}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
At PETRA III a strong vertical emittance increase
was observed in 2009 for bunch trains with 8~ns and 16~ns bunch to bunch
spacing. The vertical emittance increase was strongly dependent on the bunch
filling pattern and could be avoided if many short bunch trains with
only 4 bunches or larger bunch to bunch spacing were used.
A clear conditioning effect has been observed. While for the user
runs filling patterns with 40 and 60 bunch trains with 4 bunches were
used in 2010 it was possible to fill 240 equally space bunches with
a bunch spacing of 32~ns in 2011.
In March 2012 two dedicated scrubbing runs with a total integrated
beam current of about 10~Ah led to a further improvement of the situation.
It is now possible to fill 320 bunches with bunch spacing of 24~ns and
a total current of 100~mA without any significant emittance increase.
The influence of scrubbing runs on the instability threshold is a strong
evidence that the observed emittance growth is related to electron cloud
phenomena.
From measurements in the laboratory \cite{Grosso:IPAC2011}
the maximum SEY $\delta_{max}$ of the dipole chamber was
initially (as received) $2.7$.
Simulations with version 4.0 of the ECLOUD code for different filling
patterns indicate that maximum SEY is presently about $2.0$.
%\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{ACKNOWLEDGMENTS}
Thanks goes to my colleagues from DESY: K.~Balewski, M.~Bieler,
J.~Keil, A.~Kling, G.K.~Sahoo, for their support
with the machine operation and the monitoring of experimental data.
I also would like to thank K.~Balewski and A.~Kling for valuable discussions.
Last but not least I would like to thank M.~Lomperski for carefully
reading the manuscript.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%=================================================================================================
%thebibliography
%=================================================================================================
%\begin{thebibliography}{9} % Use for 1-9 references
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\end{document}