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\begin{document}

\title{
RECENT DEVELOPMENTS IN MODELING TIME-RESOLVED SHIELDED-PICKUP MEASUREMENTS OF ELECTRON CLOUD BUILDUP AT CESRTA
}
\author{J.A.~Crittenden, Y.~Li, X.~Liu, M.A.~Palmer, J.P.~Sikora\\ 
CLASSE\thanks{Work supported by the US National Science Foundation 
\mbox{PHY-0734867}, \mbox{PHY-1002467}, and the U.S. Department of Energy \mbox{DE-FC02-08ER41538}},
Cornell University, Ithaca, NY 14850, USA\\*[2mm]
S.~Calatroni, G.~Rumolo\\
CERN, Geneva, Switzerland\\*[2mm]
S.~Kato\\
KEK, Oho, Tsukuba, Ibaraki 305-0801, Japan\\*[2mm]
R.P.~Badman\\
Syracuse University, Syracuse, NY 13244, USA
\\*[5mm]}

\maketitle

\begin{abstract}
The Cornell Electron Storage Ring Test Accelerator program includes 
investigations into the mitigation of electron cloud buildup using 
a variety of techniques in custom vacuum chambers. 
The CESR ring accommodates two such chambers equipped with BPM-style pickup detectors shielded against
the direct beam-induced signal. 
The signals recorded by a digitizing oscilloscope provide time-resolved information 
on cloud development. 
Results for diamond-like carbon, amorphous carbon, and titanium-nitride coatings
have been obtained and compared to those for an uncoated aluminum chamber.
Here we report on extensions to the ECLOUD modeling code which refine its description
of a variety of new types of {\it in situ} vacuum chamber comparisons.
Our results highlight the sensitivity
afforded by these measurements to the modeled
quantum efficiency for producing photoelectrons, 
their production location and energy distributions,
as well as to the secondary yield and production kinematics.
We use this sensitivity to draw conclusions comparing the photoelectron and secondary
yield properties of the various vacuum chamber coatings, including conditioning effects
as a function of synchrotron radiation dose. We find substantial conditioning effects
in both the quantum efficiency for producing photoelectrons and in the secondary yield.

\end{abstract}


\section{Introduction}
The Cornell Electron Storage Ring Test Accelerator ({\cesrta}) program~\cite{ref:icfa50} 
includes the installation of custom vacuum chambers
with retarding-field-analyzer (RFA) ports and shielded-pickup (SPU)
detectors~\cite{ref:pac11jps, ref:ecloud10jac}.
The time-resolved measurements from the SPU detectors 
provide time structure information
on electron cloud (EC) development, in contrast to the time-integrated 
RFA measurements~\cite{ref:ipac11jrc}.
The SPU measurements began in early 2010 and include a wide variety of electron
and positron bunch spacings and populations for beam energies from 2.1~{\gev} to 5.3~{\gev}.
This report concentrates on two-bunch studies at 5.3~{\gev}, where a witness bunch
drives the EC formed by the passage of the leading bunch.
The EC development results from the photoelectron production, the EC dynamics,
and the secondary yield (SEY) properties of the vacuum chamber. The EC buildup
simulation code ECLOUD~\cite{ref:icfazim} has been extended to model the SPU detector response, and generalized
to provide the additional flexibility required to adequately model the SPU signals. 
This report employs the ECLOUD model to interpret SPU measurements and draw conclusions
on the conditioning properties of TiN, amorphous carbon (a-C)~\cite{ref:prstabcyv} and diamond-like (DL)
carbon~\cite{ref:ecloud10sk} coatings on aluminum vacuum chambers.

\section{Shielded-pickup Detectors}
Three SPU electrodes biased at 50~V collect charge migrating 
through ports in the top of the vacuum chamber.
The centers of the electrodes are 0 and ${\pm 14}$~mm from the
horizontal center of the chamber, with the central electrode offset longitudinally.
Each port comprises 169 vertical holes of 0.76~mm diameter arranged in concentric circles
up to a diameter of 18~mm. 
The transparency factor for vertical trajectories is~27\%. The
approximate 3:1 depth-to-diameter ratio is chosen to shield
the detectors from the signal induced directly by the beam.
The front-end readout electronics utilize RF amplifiers
with $50~{\Omega}$ input impedance and a total voltage gain of 100.
Digitized oscilloscope traces are recorded with 0.1~ns step size.
The SPU measurements discussed in this paper were recorded with the central electrode.

%\section{Development of the ECLOUD electron cloud buildup simulation program}
\section{ECLOUD simulation code}
The ECLOUD EC buildup simulation code consists of a photoelectron generation model, the time-sliced
EC dynamics driven by space-charge, beam-kick, and magnetic forces, and a detailed model for secondary
electrons produced by EC electrons striking the vacuum chamber wall. 
The calculation of EC kinematics
determines arrival times, momentum vectors and charges of the macroparticles reaching the 
upper surface of the chamber at the positions of the pickups. A model for
the acceptance of the SPU detectors has been added, as has an option to use
the output of the synchrotron radiation photon tracking code SYNRAD3D~\cite{ref:ecloud10gfd} for the 
photoelectron production azimuthal distribution. Recent modifications to the ECLOUD
code have included generalizing the photoelectron model to allow independent quantum
efficiencies and energy distributions for photoelectrons produced by direct and reflected
photons. Previous work has shown the sensitivity of these studies to photoelectron production
parameters and the ability to discriminate between various processes contributing to the secondary 
yield model~\cite{ref:furmanpivi}. For example, the elastic yield determining the 
EC lifetime was found to be much smaller than the 75\% value found for
uncoated aluminum, reaching about 5\% for the TiN and a-C
coatings~\cite{ref:ecloud10jac,ref:pac11jac}.
Such an analysis for the DL-carbon-coated vacuum chamber installed in January 2011,
has determined a similarly low value for the elastic yield.


\section{In situ comparisons of custom vacuum chambers}
One fruitful analysis strategy has proved to be the comparison of SPU signals in chambers which
have been swapped into the same location in the CESR ring and studied under
identical beam conditions. The two 
regions in CESR equipped with SPU detectors 
%placed symmetrically in the CESR ring
differ in radiation environment, since the dominant source points are in dipole magnets of differing
strengths. At 5.3~{\gev}, for example, the source dipole field is 3~kG (2~kG) in the west (east) region
for a positron beam, resulting in a critical energy of 5.6~{\kev} (3.8~{\kev}). In addition, the situation 
with regard to reflected radiation is different. By comparing SPU signals recorded at the same place
in the ring with the same beam energy, bunch spacing and bunch population, many systematic contributions to
the comparisons are avoided, and relatively simple changes to the modeling suffice to quantify the different
properties of the vacuum chambers. 

Figure~\ref{fig:carbon} shows such a comparison for an a-C-coated chamber
in May and December 2010 for two 5.3~{\gev} 28-ns-spaced bunches each carrying $4.8\times10^{10}$ 
positrons, corresponding to a bunch current of 3~mA. 
\begin{figure}[tb]
    \centering
%    \includegraphics*[width=0.95\columnwidth]{comp_105_0_2.eps}
    \includegraphics*[width=0.99\columnwidth]{WEPC135_f1.eps}
    \caption{Shielded pickup signals measured in an a-C-coated chamber in May (blue dotted line) 
and December (red dotted line) of 2010 for two 5.3~{\gev}, 28-ns-spaced bunches each
carrying $4.8\times10^{10}$ 
positrons. The ECLOUD model 
optimized for the May data is shown as blue circles, the error bars showing the 
signal macroparticle statistical uncertainties. 
%The conditioning effect due to an exposure to synchrotron radiation 
%increased by a factor of about twenty is reproduced by a 50\% decrease in the modeled 
%quantum efficiency for photoelectron production(red boxes). A reduction in the secondary 
%yield of 25\% (green triangles) is inconsistent with the observed effect.
}
   \vspace{-5pt}
    \label{fig:carbon}
\end{figure}
During the intervening time interval, 
CESR had operated at high current as an X-ray research facility, with the consequence that synchrotron 
radiation dose on the chamber had increased by a factor of about 20, from 
$8.1{\times}10^{23}$ to  $1.8{\times}10^{25}$~$\gamma$/m. 
Also shown is the ECLOUD model optimized to reproduce the May measurement. Since the signal from the 
leading bunch arises from photoelectrons produced on the bottom of the vacuum chamber~\cite{ref:ecloud10jac,ref:pac11jac}, 
careful 
tuning of the energy distribution and quantum efficiency (QE) for photoelectrons produced by reflected 
photons is required to reproduce the size and shape of the signal. The signal from the 
witness bunch includes additionally the contribution from secondary EC electrons accelerated into the 
SPU detector by the witness-bunch kick. The modeled witness signal is therefore
crucially dependent on the SEY and  production kinematics. 
Since conditioning affects both signals similarly, we can conclude that the 
change is in the QE rather than in the SEY. The December measurement is 
reproduced by a 50\% decrease in the modeled QE for photoelectron production. 
A reduction in the SEY of 25\% is inconsistent with the observed effect, since
the modeled leading bunch signal remains unchanged.

% No room for this
%\begin{figure*}[htbp]
%    \centering
%    \includegraphics*[height=52.5mm]{comp_104_0_2.eps}
%    \includegraphics*[height=52.5mm]{comp_103_0_2.eps}
%    \includegraphics*[height=52.5mm]{comp_102_0_2.eps}
%    \caption{Vacuum chamber comparisons}
%   \vspace{-5pt}
%    \label{fig:vccomp}
%\end{figure*}

Guided by the above comparisons, we can assess conditioning effects in the TiN- and 
DL-carbon-coated chambers in similar fashion. Figure~\ref{fig:tin} compares 
the SPU signals for two $8\times10^{10}~e^+$ bunches
in the TiN-coated chamber in April and June 2011, 
with accumulated synchrotron radiation doses of 
$5.9{\times}10^{24}$ and $1.1{\times}10^{25}$~$\gamma$/m, corresponding to integrated
beam currents up to more than 730 amp-hours.
\begin{figure}[tb]
    \centering
%    \includegraphics*[width=0.99\columnwidth]{comp_107_0_2.eps}
    \includegraphics*[width=0.99\columnwidth]{WEPC135_f2.eps}
    \caption{
SPU signals showing conditioning effects in the TiN-coated aluminum vacuum chamber
%Conditioning effects in the TiN-coated vacuum chamber for synchrotron radiation doses of 
%$5.9{\times}10^{24}$ and $1.1{\times}10^{25}$~$\gamma$/m
%, corresponding to integrated
%beam currents of 370 and 730 amp-hours. 
%Changes in the QE and SEY are less than a few percent.
}
   \vspace{-5pt}
    \label{fig:tin}
\end{figure}
Changes in the QE and SEY are less than a few percent.
The conditioning effects in the DL-carbon-coated
vacuum chamber are quite different, as shown in Fig.~\ref{fig:dlc}. 
\begin{figure}[tb]
    \centering
%    \includegraphics*[width=0.99\columnwidth]{comp_106_0_2.eps}
    \includegraphics*[width=0.99\columnwidth]{WEPC135_f3.eps}
    \caption{
SPU signals showing conditioning effects in the aluminum vacuum chamber coated with DL carbon
%SPU signals recorded in April and June 2011 in the DL-carbon-coated chamber 
%showing conditioning effects for radiation doses $6.6{\times}10^{24}$ to $1.3{\times}10^{25}$~$\gamma$/m
%Unlike the a-C and TiN coatings, the conditioning in this range results in 
%an increase in photoelectron production. Since the witness bunch signal is smaller despite the 
%increase in photoelectron production, one can conclude that the SEY in the 
%conditioned chamber is significantly lower.
}
   \vspace{-5pt}
    \label{fig:dlc}
\end{figure}
Conditioning effects are clearly observed for
a radiation dose increasing from $6.6{\times}10^{24}$ to $1.3{\times}10^{25}$~$\gamma$/m, corresponding to
370 and 730~amp-hours. Remarkably, the size and risetime of the signal from the leading bunch increased,
indicating that the QE for photoelectrons produced by reflected photons increased
somewhat, and that more photoelectrons were produced at higher kinetic energies. Despite the increase in 
photoelectron production, the signal from the witness bunch decreased, showing that the
conditioned SEY is significantly lower. Future modeling efforts will provide
quantitative estimates for these changes.

\section{Summary}

The time-resolved shielded-pickup measurements of EC buildup at {\cesrta} provide
detailed information on photoelectron production and SEY characteristics of 
various mitigation techniques such as coatings of TiN, a-C and DL carbon. 
%Prior modeling work using extensions of the ECLOUD program has shown the sensitivity to 
%photoelectron production parameters and the ability to discriminate between the various processes 
%contributing to the SEY. 
Shielded-pickup witness bunch measurements for the same beam energy, bunch population 
and radiation environment have provided direct comparisons
for uncoated aluminum and TiN and a-C coatings. Such {\it in situ} comparisons 
also provide information on beam conditioning of the coatings.
The work presented here concentrates on comparisons of the three coatings
for various levels of accumulated synchrotron radiation dose, ranging up to $10^{25}$~$\gamma$/m
corresponding
to over 730 amp-hours at 5.3~{\gev}. The conditioning effect for the a-C coating was found
to be a factor of two reduction in QE for a factor of two increase in photon dose to
$1.8\times10^{25}$~$\gamma$/m. The change in SEY was less than a few percent. Based on the 
modeling result for the a-C-coated chamber, the SPU signals for various states of conditioning
were interpreted for the TiN and DL carbon coatings to provide information on conditioning
effects. 
The changes in QE and secondary
yield of the TiN coating
for doses between $5.9\times10^{24}$ and $1.1\times10^{25}$~$\gamma$/m were less than a few percent. 
In contrast to the reduction in
QE observed for a-C, the DL carbon coating
exhibited an increase in QE when the radiation dose increased by a factor of two up to 
$1.3{\times}10^{25}$~$\gamma$/m, while the SEY decreased significantly.

Development work in this modeling effort for the SPU measurements continues. In particular, work
to improve the reflectivity model in SYNRAD3D is underway~\cite{ref:ecloud10gfd,ref:ipac11lb}. 
Further understanding
of EC development and mitigation techniques will be obtained from the SPU measurements with
electron beams and solenoidal magnetic field scans. 


\section{Acknowledgments}
We wish to thank P.~Costa Pinto, G.~Dugan, M.~Furman, and K.~Harkay for useful discussions.

\begin{thebibliography}{9}   % Use for  1-9  references

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G.F.~Dugan, M.A.~Palmer, and D.L.~Rubin, 
%{\em ILC Damping Rings R\&D at \mbox{\cesrta}},
ICFA Beam Dynamics Newsletter No.~50, J.~Urakawa and W.~Chou (2009)

\bibitem{ref:pac11jps}
J.P.Sikora {\em et al.}, 
%{\em Time-Resolved Measurement of Electron ECs at {\cesrta} Using Shielded Pickups},
WEP195, proceedings of PAC2011
%, March 28 - April 1, 2011, New York City, NY, USA

\bibitem{ref:ecloud10jac}
J.A.Crittenden {\em et al.}, 
proceedings of the 49th ICFA Advanced Beam Dynamics Workshop
%, October 8-12, 2010, Cornell University

\bibitem{ref:ipac11jrc}
J.R.~Calvey {\em et al.}, 
%{\em Methods for Quantitative Interpretation of Retarding Field Analyzer Data},
MOPS083, these proceedings

\bibitem{ref:icfazim}
F.~Zimmermann, G.~Rumolo and K.~Ohmi, 
%\enquote{Electron Cloud Build Up in  Machines with Short Bunches,} in 
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  No. 33, p. 14--24 (Apr. 2004).

\bibitem{ref:prstabcyv}
C.~Yin~Vallgren {\em et al.}, 
%{\em Amorphous Carbon Coatings for the Mitigation of Electron Cloud in the CERN Super Proton Synchrotron}
Phys Rev ST-AB 14, 071001 (2011)

\bibitem{ref:ecloud10sk}
S.~Kato,
proceedings of the 49th ICFA Advanced Beam Dynamics Workshop
%, October 8-12, 2010, Cornell University

\bibitem{ref:ecloud10gfd}
G.~Dugan and D.~Sagan, 
%\enquote{Synrad3D Photon Propagation and Scattering  Simulation,} in 
proceedings of the 49th ICFA Advanced Beam Dynamics Workshop
%, October 8-12, 2010, Cornell University

\bibitem{ref:furmanpivi}
M.A.~Furman and M.T.F.~Pivi,
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Phys Rev ST-AB 5, 124404 (2002)

\bibitem{ref:pac11jac}
J.A.Crittenden {\em et al.}, 
WEP142, proceedings of PAC2011
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\bibitem{ref:ipac11lb}
L.~Boon {\em et al.}, 
MOPS083, these proceedings



\end{thebibliography}

\end{document}
