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\begin{document}
\title[805 MHz and 201 MHz RF Cavity Development for MUCOOL]{805 MHz and 201 MHz RF Cavity Development for MUCOOL}
\author{Derun Li, J. Corlett, A. Ladran, R. MacGill, J. Wallig, M. Zisman \dag;
\ A. Moretti, A. Rowe, Z.B. Qian, V. Wu \ddag ; 
R.~A. Rimmer $\opensquare$; \ J. Norem $\star$; D. Summers 
$\bullet$ ; and Y. Torun $\diamond$
\footnote[3]{To whom correspondence should be addressed: DLi@lbl.gov}}
\address{\dag\ Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA}
\address{\ddag\ Fermi National Accelerator Laboratory, Batavia, IL 60510, USA} 
\address{$\opensquare$ Jefferson Lab, Newport News, VA 23606, USA} 
\address{$\star$ Argonne National Laboratory, Argonne, IL 60439, USA} 
\address{$\bullet$ The University of Mississippi at Oxford, MS 38677, USA} 
\address{$\diamond$  Illinois Institute of Technology, Chicago, IL 60616, USA} 
\begin{abstract}
A muon cooling channel calls for very high accelerating gradient RF
structures to restore the energy lost by muons in the absorbers.  The
RF structures have to be operated in a strong magnetic field and thus
the use of superconducting RF cavities is excluded.  To achieve a high
shunt impedance while maintaining a large enough aperture to
accommodate a large transverse emittance muon beam, the cavity design
adopted is a pillbox-like geometry with thin Be foils to terminate the
electromagnetic field at the cavity iris.  The possibility of using
grids of thin-walled metallic tubes for the termination is also being
explored.  Many of the RF-related issues for muon cooling channels are
being studied both theoretically and experimentally using an 805 MHz
cavity that has a pillbox-like geometry with thin Be windows to
terminate the cavity aperture.  The design and performance of this
cavity are reported here.  High-power RF tests of the 805 MHz cavity
are in progress at Lab G in Fermilab.  The cavity has exceeded its
design gradient of 30 MV/m, reaching 34 MV/m without external magnetic
field.  No surface damage was observed at this gradient.  The cavity
is currently under conditioning at Lab G with an external magnetic
field of 2.5 T.  We also present here a 201 MHz cavity design for muon
cooling channels. The proposed cavity design is also suitable for use
in a proof-of-principle Muon Ionization Cooling Experiment (MICE).
\end{abstract}
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\section{Introduction}
Designs of muon ionization cooling channels for a Neutrino Factory, a
Muon Collider or the Muon Ionization Cooling Experiment (MICE) call
for very high gradient RF accelerating structures. Depending on which
cooling stage is considered, high-gradient RF cavities are needed at
frequencies in the range of 201 MHz to 805 MHz, with peak accelerating
gradients of 16 MV/m to 30 MV/m, respectively.  Detailed information
on muon cooling research can be found on the Web at \cite{web}.
Taking advantage of the muon's penetration property, an RF cavity with
its beam irises covered by thin Be windows was proposed to achieve a
higher gradient or shunt impedance.  This is due to electric field
enhancement on axis resulting from metallic windows used to terminate
the cavity.  Ideal windows for RF cavities used in a cooling channel
should be thin and mechanically strong, be made of a low-$Z$ material,
and have good electrical and thermal conductivities.  Low-$Z$ and thin
material is needed to minimize multiple scattering in the windows.
Good electrical conductivity is needed to minimize RF power
dissipation on the windows.  Good thermal conductivity is needed to
conduct away the RF-induced heat efficiently.  Mechanical strength is
needed to ensure that the cavity is not detuned by the deformation of
the windows resulting from the RF heating.  Our studies have shown
that beryllium is the best candidate for the windows in all the above
respects.
Significant efforts have been devoted to the design of a high-gradient
RF cavity with thin Be windows.  An 805 MHz low-power test cavity with
Be windows was built and tested to study the Be windows' thermal and
mechanical properties when heated by a halogen lamp under different
cavity temperatures~\cite{derun}. A high-power 805 MHz test cavity,
designed and built recently, is currently under test in Lab G at
Fermilab, where a high-power RF test facility has been dedicated for
the 805 MHz muon RF cavity research.  A superconducting magnet is also
available in Lab G for tests with strong magnetic fields.  In
principle, grids consisting of thin-walled metallic tubes can also be
used to terminate the cavity irises electromagnetically.  Thin walled
tubes are mechanically stronger than thin foils.  Engineering efforts
have been initiated to study how to model, design, and fabricate a
cavity with such grids.
This paper reports on the 805 MHz cavity design and recent progress on
high-power tests of the cavity.  In addition, a 201 MHz cavity design
that could be used for muon cooling channels and/or the MICE
experiment is presented.
\section{805 MHz High-Power Test Cavity Design}
The 805 MHz cavity design adopts a cylindrically symmetrical pillbox
geometry with conventional beam irises covered by metallic windows,
either Cu plates or thin Be foil.  Detailed information on the cavity
design and fabrication have been reported in~\cite{derun2}.  RF power
is fed through a coupler that has a kidney-shaped coupling slot in one
end-plate of the cavity and is attached to a transition waveguide to a
standard WR975 waveguide. Figure~\ref{cavity} is a mechanical drawing
showing a cross section of the cavity geometry and the coupler.
\begin{figure}[htb]
\centerline{\psfig{figure=cavity.eps,width=120mm}}
\caption{Cross section of the 805 MHz high power test cavity.}
\label{cavity}
\end{figure}
Main cavity parameters are listed in Table~\ref{para}.  The cavity
design allows for demountable windows to be installed.  As shown in
Figure~\ref{cavity}, RF probes, view ports and thermocouple ports are
available for measuring peak RF power inside the cavity, for visual
inspections of the windows using a bore-scope, and for monitoring
window temperatures.
\begin{center}
\begin{table}[h]
\begin{center}
\caption{\label{para} Main design parameters of the 805 MHz cavity.
The shunt impedance used here is defined as ${V_{0,T}^2}/{P}$}
\begin{tabular}{lcc|lcc}
Parameter & Value & Unit & Parameter & Value & Unit \\
Cavity radius & 15.62 & cm  & Shunt impedance $Z_0$ & 38 & M$\Omega$ \\
%\mr
Cavity length & 8.1 & cm & Shunt impedance $ZT^2$ & 32 & M$\Omega$ \\
%\mr
Coupling slot span & 50 & degree  & Quality factor & 18,800 & \\
%\mr
Be window diameter & 16.0 & cm & Coupling constant & 1.0 & \\
%\mr
Be window thickness & 127 & $\mu$m & Gradient $E_0$ & 30 & MV/m \\
\end{tabular}
\end{center}
\end{table}
\end{center}
The cavity design was performed using the MAFIA code in both the
frequency and the time domains~\cite{derun3}.  The cavity was
fabricated at the University of Mississippi, and brazed at
Alpha-Braze, a company in Fremont, California.  Cavity and coupler
tuning were conducted at the University of Mississippi as well. Final
cavity integration and assembly were carried out at LBNL.  Microwave
measurements performed at LBNL and at Lab G (before high-power
testing) showed good agreement between design and measured values.
\section{High Power Testing of the 805 MHz Cavity}
High power RF tests have been conducted in Lab G.  A 12 MW peak power
klystron and a superconducting solenoid are available for the tests to
permit studying the cavity with Be windows both with and without
magnetic fields.  Previous experience from a Fermilab 805 MHz
open-iris structure indicated that severe surface damage could occur,
especially in the presence of a strong solenoidal magnetic
field. Large dark currents and x-ray intensities were measured during
the test. Analysis of these measurements is in progress and our
preliminary understanding has been presented
recently~\cite{Norem}. Recognizing that surface damage might occur in
the 805 MHz cavity with the Be windows, we started high power tests
with copper windows (plates) instead.
The cavity was conditioned to reach 34 MV/m rather quickly, with a low
sparking rate. After this initial test, the cavity was taken apart and
a new thinner Cu window was installed to permit better x-ray
measurements.  No surface damage was observed after careful
inspection.  The cavity is currently being tested with the
superconducting magnet on. The magnet is operated in its solenoidal
mode, at a magnetic field of 2.5 T.  More multipacting zones were
observed and a much higher radiation level was measured during this
conditioning compared with the no-magnetic-field case. The
conditioning process has been slow; a gradient of $\sim$10 MV/m was
reached after two and a half weeks of conditioning.  More measurements
and data analysis are under way, and will be reported later.
\section{201 MHz Cavity Design}
The cavity uses a slightly reentrant rounded profile with a large beam
aperture, as shown in Figure~\ref{201}, covered either by thin flat Be
windows or grids of thin-walled aluminum tubes~\cite{Bob}.  Based on
experiments with pre-stressed Be foils in the 805 MHz cavity, the
thickness of the foils was chosen so that the temperature rise at the
center is below that at which the foils buckle. Table~\ref{para2}
lists main parameters of the cavity.
\begin{figure}[htb]
\centerline{\psfig{figure=cavity201.eps,width=120mm}}
\caption{Conceptual design of the 201 MHz cavity.} 
\label{201}
\end{figure}
The cavity design was performed using the MAFIA code; thermal analysis
was done with ANSYS.  The grid design is still under investigation to
find the optimal size and spacing of the tubes. RF heating on the
tubes needs to be further studied.
\begin{center}
\begin{table}[htb]
\caption{Main RF design parameters of the 201 MHz cavity}
\label{para2}
\begin{center}
\begin{tabular}{cccccc}
Radius & Length & $E_0$ & $E_{\rm peak}$ on surface & Be diameter & 
Be thickness \\
(cm) & (cm) & (MV/m) & (MV/m) & (cm) & (mm)\\
61 & 43 & 16.2 & 26.5 & 21 & 1.15 \\
\end{tabular}
\end{center}
\end{table}
\end{center}
\section{Conclusion}
The 805 MHz cavity has been successfully tested and reached 34 MV/m
without magnetic fields.  High power RF testing with magnetic fields
is ongoing.  Possible surface damage and the radiation level from dark
currents will be studied carefully.  The 201 MHz cavity design is
nearly completed and ready for fabrication.
\section*{Reference}
\begin{thebibliography}{99}
\bibitem{web}   \underline{{http://www.fnal.gov/projects/muoni$_{-}$collider/cool.html}}
\bibitem{derun} Derun Li, et al., "Mechanical and Thermal Analysis of 
                Beryllium Windows for RF Cavities in a Muon Cooling 
                Channel", EPAC'2002, Paris, France (June 2002)
\bibitem{derun2} Derun Li, et al., "High Power RF Test of An 805 MHz RF
                Cavity for a Muon Cooling Channel", EPAC'2002, Paris, France
                (June 2002)
\bibitem{derun3} Derun Li, et al., "Design and Fabrication of an 805 MHz
                RF Cavity with Be Windows for a High Power RF Testing for
                a Muon Cooling Experiment", PAC'2001, Chicago, IL, USA (2001)
\bibitem{Norem} J. Norem, et al., "Lab G Results: X-Ray and Dark Current",
                Presentation at MUCOOL Collaboration Meeting, Shelter Island,
                New York, USA (May 2002); J. Norem, et al, "RF Induced 
                Background in MICE", This conference (July 2002)
\bibitem{Bob}   R.~A. Rimmer, et al., "Closed-Cell 201.25 MHz RF Structures 
                for a Muon Ionization Cooling Experiment", EPAC'2002, Paris,
                France (June 2002)
\end{thebibliography}
\end{document}
