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\title {Performance of PHENIX Muon CSCs with Different Chamber Gases}
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\author{Melynda Brooks (LANL)}
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\date{May, 1997}
\maketitle
\section{Introduction}

The performance of a prototype PHENIX muon cathode
strip chamber (CSC) with different chamber gases has been studied.  
Since the muon tracking chambers will reside inside a
magnet during operation, it is preferable to have a chamber
gas which has a small Lorentz angle to minimize the resolution
degradation caused by the Lorentz angle.  A search of the
literature was performed to see what gases would give us
our desired small Lorentz angle ~\cite{dinesh}. Several
recommendations were given for $CF_{4}$ mixtures which would give
a relatively small Lorentz angle in our magnetic fields.  To
understand the performance of our chambers with these gas
mixtures, the resolution, efficiency, and charge distributions
were studied for gas mixtures of $CF_{4}$:isobutane (50:50),
$CF_{4}$:isobutane (20:80), $CF_{4}$:$CO_{2}$:isobutane (20:60:20),
$CO_{2}$:$CF_{4}$ (50:50) and Ar:isobutane (70:30) bubbled through
isopropyl alcohol.  The last gas was used as a reference gas
that has been well studied, to which we could 
compare the faster gas mixtures.


\section{The Prototype Cathode Strip Chamber and Readout System}

The chamber that was used for the gas studies was a full-size
Station 2 prototype cathode strip chamber that contained one
gap.  A full description of the chamber can be found in ~\cite{lee}.
The chamber half-gap was 0.32 cm, the anode wire spacing was 1 cm,
and the cathode strip spacing was 0.5 cm, with 1 cm readout.

Sixteen cathode strips were instrumented with NMS
preamplifiers (ref), which went to an 11-bit FERA ADC and was
read out using a CODA ~\cite{coda} data acquisition system.  The
NMS amplifiers are not the amplifiers that will be used in the
final PHENIX system, and are known to be noisier than the specifications
that have been given for the PHENIX electronics.  A calibration of the
amplifier-ADC system found that the noise in the system is
approximately 14600 electrons/channel or 2.3 fC.  Because of this
large noise (our PHENIX noise specification is 3000 electrons/channel),
our resolution is limited by noise and can be expected to meet our
100 $\mu$m specification only at the highest gains of the chamber.

\section{Cosmic-Ray Test Stand and Analysis Methods}

\subsection{Test-Stand}
A cosmic-ray test stand was assembled to test the CSC (see Figure
~\ref{fig:cosmic}).  The test stand consisted of two scintillators 
for triggering
on cosmic rays and four drift chambers for tracking the
cosmic rays to the prototype chamber.  Each drift chamber had
two x planes and two y planes, giving a total of eight x and 
eight y planes for tracking.

\begin{figure}
  \centerline{\psfig{height=3.0in,figure=cosmic.eps}}
  \caption{A schematic of the cosmic-ray test stand that was
   used to study the performance of the prototype CSC.
   \label{fig:cosmic}}
\end{figure}

The acceptance of the cosmic ray test stand covered approximately
(0,11) degrees with respect to a track that would be normal to
the anode wires, and the angular distribution was centered 
around approximately 5 degrees because of the alignment of the
chambers, the instrumented area of the CSC, and the position
of the scintillators.

The resolution of each drift chamber plane was approximately 
100 $\mu$m, giving a pointing resolution of approximately
80 $\mu$m if a
chi-square cut of 1.0 was placed on a fit to straight tracks
passing through the chambers.  The resolutions that were measured
were therefore a quadrature sum of an 80 $\mu$m projection error
plus the intrinsic resolution of the CSC.  Cosmic rays were
used to align the drift chambers and CSC, and the error in the
alignment is somewhat uncertain but is expected to be small 
compared to the 80 $\mu$m projection error.

\subsection{Calibrations}
The sixteen cathode strip electronics channels were calibrated
by putting a square pulse of known duration and voltage
through a resistor pack into the preamplifier.  This gave us a known
charge that went through the amplifier into the charge-integrating
ADC, allowing us to calculate the number of channels/fC in the
amplifier-ADC chain.  The resistors were matched to about 1\%,
and no correction was made for the difference in resistor values,
so some calibration error may also be contributing to our 
resolutions.

The position of a track in the CSC was extracted from the pulse-
height distribution measured on the cathode strips.  The position 
was extracted from $Q_{m}/Q_{tot}$ where $Q_{m}$ is the charge
measured on the peak strip and $Q_{tot}$ is the sum of charges
measured on all strips in a cluster.  A cluster is defined to be 
a contiguous set of strips which are above a threshold cut.

The calibration of hit position versus $Q_{m}/Q_{tot}$ was
determined using cosmic rays which are assumed to uniformly
populate the instrumented area of the chamber.  If the
distribution is uniform then one can write:

\begin{equation}
\frac{dN}{dx} = \frac{dN}{dq}\frac{dq}{dx} = c
\end{equation}

where q = $Q_{m}/Q_{tot}$ and x is the position on the strip
$Q_{m}$.  If you invert $\frac{dq}{dx}$ and integrate:

\begin{equation}
\int\frac{dN}{dq}dq = c\int\frac{dx}{dq}dq
\end{equation}
\begin{equation}
x \propto \int\frac{dN}{dq}dq
\end{equation}

showing that x is proportional to the integral $\int\frac{dN}{dq}dq$
integrated up to q.  A table of $\int\frac{dN}{dq}dq$ is taken from
the uniformly distributed cosmic ray data and is normalized by 
requiring that the integral from 0 to infinity is equal to the distance
between readout strips. This provides a look-up table for converting
$Q_{m}/Q_{tot}$ into x.

\subsection{Efficiency Calculations}

Efficiencies were measured by selecting tracks from the drift
chambers which pointed to the instrumented area of the CSC and
requiring that the CSC:

\begin{itemize}
\item Have one cluster in the active area of the chamber.
\item Have at least two cathode strips in the cluster above threshold 
so that it is possible to fit the position of the track.
\item The resulting fit position must be within 0.5 cm of the
projected position of the drift chambers.
\end{itemize}

If more than two clusters were found in the instrumented section
then the CSC was recorded as being inefficient, so it is quite
possible that the efficiencies that will be listed below are
somewhat smaller than they will be when more sophisticated 
tracking software is used.

\section{Performance of CSC with Different Gases}

As stated in the introduction, the resolution, efficiency, and
charge distributions were studied for each gas mixture.  Results will
be given for Ar:isobutane (70:30), $CF_{4}$:isobutane (50:50),
$CF_{4}$:isobutane (20:80), and $CF_{4}$:$CO_{2}$:isobutane (20:60:20).
A mixture of $CO_{2}$:$CF_{4}$ was also tried, but we were unable
to get stable performance from the chamber except over a very 
limited voltage range at low gain.  It is uncertain whether this was 
because of the gas mixture or a problem with our gas system, so it 
will be studied some more in the future.

\subsection{Charge Distributions}

For each of the gas mixtures, data were taken from the cosmic-ray
test stand chambers and the CSC at several voltages of the CSC
covering the efficiency plateau.  For each of these voltages,
cathode strip clusters were found and the voltage of the peak
strip in the cluster was recorded.  The mean value of this peak
strip versus chamber voltage for the four gas mixtures is shown
in Figure ~\ref{fig:chargevsgas}.  As can be seen in the figure,
the $CF_{4}$ mixtures tend to require higher operating voltages to
reach the efficiency plateau, but they also tend to produce 
larger signals on the cathode strips across the plateau.  This
latter feature may be an advantage since it should be easier to
meet our signal-to-noise requirements if we have larger signals
in the chamber.  However, we must also make sure that our ADC
gives us the needed range to cover the expected cathode strip
pulse heights if we are to use a $CF_{4}$ mixture.

\begin{figure}
  \centerline{\psfig{height=6.0in,figure=chargevsgas.eps}}
  \caption{The average charge of the peak cathode strip (converted
   into fC) versus
   chamber voltage for the four gas mixtures studied.
   \label{fig:chargevsgas}}
\end{figure}

\subsection{Efficiency Plateaus}

For each gas mixture, the efficiency of the CSC was measured
for several voltages.  The efficiency was determined in the way
that was described in the Analysis Methods section and the voltages
were selected to try to cover the efficiency plateau from the low
efficiencies up to break-down voltage.  For some of the mixtures,
the data points do not go all the way down to the low efficiency
region, but are close.  The data are shown in Figure ~\ref{fig:eff_all}.

\begin{figure}
  \centerline{\psfig{height=6.0in,figure=eff_all.eps}}
  \caption{The efficiency of the CSC versus chamber voltage for
   the four gas mixtures studied.
   \label{fig:eff_all}}
\end{figure}

All gas mixtures showed a reasonably broad plateau with the 
$CF_{4}$:isobutane (20:80) giving the largest plateau of approximately
500 V.

\subsection{Chamber Resolution}

All gas mixtures achieved a resolution of approximately 100 $\mu$m
at the high end of the efficiency plateaus, where the signal-to-noise
ratio should have been close to what we hope to achieve with the
PHENIX electronics.  An example resolution distribution, averaged
over all accepted tracks, pulse-heights, etc. is shown in Figure
~\ref{fig:cscres} for the $CF_{4}$:isobutane (20:80) mixture, at
2650 volts.

\begin{figure}
  \centerline{\psfig{height=6.0in,figure=cscres_cf4iso_2080.eps}}
  \caption{The residuals of the projection of the cosmic ray
   test-stand fitted track minus the fitted position in the CSC.
   The residuals include all tracks in the active area that pass
   a chi-square cut in the drift-chamber fit of less than 1.0.
   \label{fig:cscres}}
\end{figure}

If the expected projection error of 80 $\mu$m is subtracted from 
the residual, we obtain a resolution of approximately 85 $\mu$m
for the chamber with this gas and voltage setting.

\section{Conclusions}

All the gas mixtures studied in this paper will give good chamber
resolutions and have a broad operating plateau.  However, the 
$CF_{4}$ mixtures have significantly smaller Lorentz angles, and
they also appear to provide a better possibility for maintaining
good signal:noise ratios because they give larger pulse-heights
on the cathode strips across the plateau.  The $CF_{4}$:isobutane,
(20:80) mixture appears to be the best of the $CF_{4}$ mixtures
because it has the largest operating plateau, larger cathode
signals, and according to the literature has one of the smallest
Lorentz angles (approximately 8.5 degrees at 1 Tesla).

\begin{thebibliography}{99}
\bibitem{dinesh}B. V. Dinesh, "Lorentz Angle Effect in Gas Mixtures," 
http://phnxmu.lanl.gov/Files/muon/notes/phenix-muon-95-22/dinesh.html.
\bibitem{lee}D. M. Lee, et al, "Large CSC Chamber for the PHENIX
Muon Detector with Ultra Thin Cathode Foils," 1996 IEEE Nuclear
Science Symposium Conference Record, Vol. 1, 274.
\bibitem{coda} CEBAF On Line Data Acquisition, http://alcor.cebaf.gov/coda/.
\end{thebibliography}
\end{document}

