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\begin{document}


% this will be Mucool Note #

\vspace{1 in}
\title{RF Induced Backgrounds in MICE}
\author{J. Norem\\ HEP Division, Argonne National Laboratory, 
Argonne IL 60439}
\author{D. Li\\ Lawrence Berkeley National Laboratory, Berkeley, 
CA 94720}
\author{A. Bross, A. Moretti\\ Fermi National 
Accelerator Laboratory, Batavia IL 60510}
\author{Y. Torun\\ Illinois Institute of Technology, 
Chicago, IL 60616}
\author{E. McKigney\\ Imperial College, London, England}

\date{June 30, 2002}   
\maketitle
 
\section{MICE Overview}
%Mice Description
%	Plan  How many synchrotron periods?
%	Detector + rf problems
%	Ring + linear
%	Detector options
%		Silicon fiber
%		TPG
%		TOF

The goal of the Muon Ionization Cooling Experiment (MICE) is to 
demonstrate measurable muon cooling effects with realistic hardware, to 
show that neutrino factories, and eventually muon colliders 
can be built\cite{mice}\cite{nufact}.  A proposal for this experiment will be sent to 
Rutherford Appleton Lab at the end of 2002.  The apparatus will consist of 
a particle diffuser, an initial spectrometer, rf and absorbers to
cool the muons and a final spectrometer and TOF system.  This is 
shown in Fig. 1a.  A variety of cooling modules could be used, 
including curved sections which should provide longitudinal cooling.
We have been using an 805 MHz cavity in Lab G of Fermilab to measure 
dark currents and radiation levels at high rf accelerating fields in 
the presence of solenoidal magnetic fields.  This apparatus is shown 
in Fig. 1b.


\begin{figure}
\psfig{file=MICErf12.eps,scale=0.9}  
\caption{The MICE experiment, and the test cell used to evaluate rf 
backgrounds.}
\end{figure} 


%       In order to measure the channel performance, it is necessary
%to measure the beam emmitance both before and after the section
%of channel under test.  This will be done using two solenoidal
%spectrometers.  The strategy for the measurement is to measure the
%position and momentum of individual particles entering and leaving
%the channel, and then reconstruct a synthetic beam.  Although this
%does not provide information about collective effects, it does allow
%a direct evaluation of the performance of the channel, and comparison
%with Monte Carlo simulations.

        The MICE spectrometers will consist of solenoids 
capable of achieving
at least 5 Tesla. These will be matched to the channel under test, to
avoid emittance growth at the interface.  Two types of tracking detector
systems are proposed; one based on scintillating fiber and one based on
a Time Projection Chamber read out with a Gaseous Electron Multiplier,
which is referred to as a TPG. 

        The scintillating fiber tracker design (SFT) is based on experience
with the D0 detector at Fermilab and the tracker for the MuScat experiment.
The SFT would have four planes of three layer crossed fiber doublets in each
solenoid, with a total of about 24000 electronics channels.  The fibers
are round doubly clad plastic scintillating fibers with a polystyrene core.  
Each detector
plane presents about 0.4\% of a radiation length to the beam.   The light from
the scintillating fibers will be coupled into clear fibers and transported
out of the solenoid to readout electronics based on Visible Light Photon
Counters (VLPCs).  The advantages of this system are the ability to operate
in a vacuum and a fast response time, and that the electronics can be
located away from the experiment and shielded from magnetic fields and RF
pickup.  

        The fiber produces a signal pulse with a time width  on
the order of 10 nS, and the VLPC can be operated at a rate of 100 MHz.
By using timing information to reject hits which do not fall into
a trigger window, the SFT can tolerate single hit background 
rates up to 0.3 MHz, with a probability of overlap with an event of 
$\leq 1\%$.  The conversion efficiency for the background gammas 
from the cavity in the detector elements is between 1\% and 0.1\%, 
depending on energy.  

        The TPG option is based on experience with the HARP TPC.  The
idea is to minimize the mass presented to the beam during the measurement
process by using only a thin window at the inside end of the channel, 
and putting the
readout at the other end of the chamber.  The two sources of background
for this tracker are gammas and electrons from the cavity which ionize the
tracking gas, and pick-up of the RF in the front-end electronics.  Because
the TPG is active for the entire spill, these backgrounds will have to be
removed using pattern recognition software which reconstructs the helices
from individual hits, and rejects noise hits.  The rate of background hits
which can be tolerated is not known at this time.


\section{Data}
%	Fowler Nordheim field emission,  f dependence, chemistry
%		Other complicating processes
%	Bremsstrahlung
%	Compton scattering / detectors
%	Multipactoring
%	Magnetic field effects
%	Breakdown
%	Damage
%		Copper
%		Burned spots

It seems important to understand the sources of radiation produced
in rf cavities, since there is some degree of extrapolation involved 
in the construction of high gradient, 200 MHz, rf cavities.
There is a variety of information on the processes producing dark 
currents and radiation in cavities, some of it comparatively recent.
This information implies local surface anomalies are the cause, and 
the model argues against significant frequency dependence, as 
parametrized by Kilpatrick.  These conclusions are in agreement with a
very slow dependence of rf gradient on frequency in superconducting 
cavities.  Recent developments in superconducting
rf also imply that breakdown and dark current emission can be 
improved by well understood techniques, primarily electropolishing 
and high pressure water rinsing.

%\subsection{Fowler Nordheim Field Emission}
%Fowler Nordheim field emission is well understood both theoretically 
%and experimentally.  Recent experiments in Lab G showed that all data 
%were consistant with field emission from a number of sharp points.  
%A variety of saturation effects which were seen were not fully 
%understood\cite{LabG}.

%\subsection{Bremsstrahlung}
%Bremsstrahlung has been understood for a long time, but the low 
%energy electrons produced in dark currents produce spectra somewhat 
%different from those at high energies\cite{B}.  The difference in 
%spectra is shown in Fig. 2.

\begin{figure}
\begin{center} 
\psfig{file=MICErf34.eps,scale=0.7}  
\end{center}
\caption{Data from the open cell(a), and pillbox cavity(b), showing 
the Fowler Nordheim emission at high fields 
and low field, presumably multipactor,
phenomena.  These data were taken with the solenoidal field off.}
\end{figure} 

%\subsection{Compton scattering}
%Compton scattering is the dominant interaction mechanism for the  
%approximately 1 MeV photons which will constitute most of the 
%background we are dealing with.  While these photons have an 
%attunuation length of approximately 10-20 g/cm$^{2}$, this attenuation 
%length is defined for a good geometry, in which any collision removes 
%the photon from the beam.  Unfortuneatly the situation we are dealing 
%with is not a good geometry, and we are also sensitive to photons 
%which have scattered.  The compton scattering process degrades the 
%photon energy somewhat, alters the photon direction significantly, 
%but does not reduce the number of photons at all.  Photons move 
%through copper like a gas.  This is shown by calculations of 
%effective differential dose albedo for bremsstrahlung beams in Fig. 3
%\cite{S}.

%\begin{figure}
%\begin{center} 
%\psfig{file=albedo.eps,scale=0.25}  
%\end{center}
%\caption{Albedo of low energy radiation.}
%\end{figure} 

%\subsection{Multipactoring}
Fig. 2a shows the results of the open cell studies with and without
magnetic field \cite{LabG}.  Fig. 2b
shows photomultiplier counts as a function of accelerating field.
Results with both the open cell and pillbox cavities seem to show a 
variety of multipactor 
phenomena at low gradients which we do not yet understand.   The 
slope at high field is field emission, but the counts at lower field, 
whose intensity changes with time and accelerating field do not seem
to be described in the literature.  The peak at the lowest field is 
very narrow.

%\begin{figure}
%\begin{center} 
%\psfig{file=Multipactor.eps,scale=0.30}  
%\end{center}
%\caption{PMT counts/250 pulses vs acceleration gradient.  Rate below
%10 MV/m seems to be multipactoring.}
%\end{figure} 

%\subsection{Breakdown}
%Cavity breakdown is one of the primary limitations of rf acceleration 
%and not completely understood.  We have developed a model which 
%considers the electrostatic stress applied to field emitters relitive 
%to the tensile strength of the material.  The argument can explain 
%breakdown events in copper cavities and quenches in superconducting rf.
%\cite{LabG}.

%\subsection{Magnetic field effects}
The magnetic field also strongly affects dark currents in an rf cavity.  
The electron orbits are changed, the cavity copper itself is altered 
by magnetoresisitance and the instrumentation is also affected.  
Measurements of the affects of the magnetic 
field have been imprecise, because of the sensitivity of the 
instrumentation to the field.  
 
%\subsection{Damage}
 
		

%	Acceleration
%		low frequency  (200 MHz)  =>  Stored energy,  frf dependence of Dark Currents (~f -1/4 Shepard?)
%		Block diagram,  ( -DE/2  +DE  -DE/2 )
%		rf cavity phase => e energy spectra at two ends  => Thinner pilbox cavities??
%		mu- or mu+ cooling.
%	Scattering and energy loss in windows and degraders
%	Electrons in Cusps
%		Br > Br	
%	Surface treatment
%		Be problems,  can it be cleaned?
%	Initial state
%		Chemistry, typography, vacuum
%	Breakdown and damage mechanisms
%		Copper, electron microbeam problems
%The acceleration of dark current electrons depends on the cavity 
%design.  Fig. 5 shows the acceleration gradient seen by electrons 
%going forward and backward relative to the muons.  Electrons moving 
%forward relative to the muons move faster and slowly slip out of time 
%as they move ahead, while electrons moving backward see a rapidly 
%changing phase which, with narrow cavities, can be made to average 
%out to zero, producing no acceleration.  This option would cost more
%because
%the thin cavities required would have a lower impedance, and thus 
%would require more power for the same gradient.  

%\begin{figure}
%\begin{center} 
%\psfig{file=Darkcurrentphase.eps,scale=0.30}  
%\end{center}
%\caption{Acceleration as a function of distance from muon.
%Electrons behind the muons are moving backward.}
%\end{figure} 

Scattering and energy loss will also reduce the flux of dark current 
and x rays from reaching the detectors. 
Low energy electrons will be attenuated by the absorbers 
and deflected by the cusp fields in the FOFO structure.   GEANT and ICOOL 
are being used to simulate this.

%\begin{figure}
%\begin{center} 
%\psfig{file=Cavitystoredenergy.eps,scale=0.30}  
%\end{center}
%\caption{Stored energy for the 200 and 805 MHz cavities.}
%\end{figure} 

%	Electrons
%		Fluxes  I(E)
%		Spatial Distributions
%		B field dependence
%		Time structure
%		Multipactoring
%	X rays
%		Spectrum
%		Fluxes
%	RF noise in electronics
%		HP meter to measure rf losses
%	How much power goes into the cavity after a breakdown event occurs?

\section{Limits to the Accelerating Field}
%	RF backgrounds
%		Lab G results, Open Cell / LBL cavity
%	RF power limits
The limit to the gradient that can be used in the rf cavities is 
determined by the accelerating gradient producing the maximum tolerable
rate of dark current electrons and x rays.  There is some uncertainty 
in this estimate due to lack of knowledge about the copper and Be 
surfaces in the 200 MHz cavities, transport of electrons and x rays 
through the system, and the detectors.  This section attempts to make 
conservative assumptions where information is unavailable.  The 
accuracy of these initial estimates should be expected to converge as
more information becomes available.

The background rates depend on the tracking technology.
The scintillating fiber tracker will consist of 4 planes with a 
resolving time of 20 ns.  We assume a maximum rate of 2-10 background 
hits in this window, giving rates for recoil Compton electrons of 
100 - 500 MHz / plane.
The TPG will be live for the entire spill. and will integrate the 
x rays seen in the fill time of the rf system.  We should determine the 
maximum number of compton recoil tracks in the chamber without 
additional trackfinding. 
We thus assume an overall background rate of 100 MHz, or 1 track in 10 ns, 
in about 0.01 radiation lengths, as the maximum tolerable rate for 
the spectrometers.
A rate of one electron /10 ns corresponds to 0.016 nA. 
Our data have shown that 10 primary electrons produce roughly one 
detectable
Compton electron when stopped in aluminum or plastic, using a thick 
scintillator for a detector.  Our detectors will be thin,
but there may be material nearby.

We can assume that most of the electrons will be diverted by the cusp 
fields and absorbers, and less than 0.1 of these will enter the 
spectrometers, about the same as the flux of Compton conversion 
electrons.  The Compton photons will be attenuated somewhat by their
angular divergence.
The maximum Compton x ray current is then $\sim$0.016 nA, divided 
by efficiency 
for x ray production/detection, which we estimate as 0.1, giving a 
maximum rate of $\sim$0.16 nA, or a maximum accelerating field of about 13 MV/m.
This field seems to be greater than the maximum that can be generated 
by our power supplies at the present time.  Nevertheless magnetic 
field effects, and changes in dark currents due to the use of Be have
not been tested with pillbox cavities.






 
\section{Conclusions}
%	Surface treatments
%   Required R&D priorities



The conclusions from almost a year operating cavities in Lab G are
fairly optimistic.  It seems possible to operate the MICE experiment up to 
gradients of $\sim$13 MV/m if pillbox geometries are used.  The primary 
complication is that the design we plan to use has strong magnetic 
field, with large, flat Be windows.  We are in the process of testing
these details.


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%multipactor