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\title{Precision Drift-Tube Chambers for the ATLAS Muon Spectrometer at Super-LHC}

%\author{A.~Engl,~R.~Hertenberger,~O.~Kortner,~H.~Kroha,~F.~Legger,~R.~Richter,~F.~Rauscher% <-this % stops a space
%\thanks{Manuscript received November xx, 2008.}% <-this % stops a space
%\thanks{O.~K.,~H.~K.,~F.~L.,~R.~R. are with the Max-Planck-Institut f\"ur Physik, M\"unchen, Germany (corresponding author e-mail: federica.legger@mppmu.mpg.de).}% <-this % stops a space
%\thanks{A.~E.,~R.~H., F. R. are with Ludwig-Maximilians Universit\"at, M\"unchen, Germany.}
%}

\author{J.~Dubbert,~O.~Kortner,~H.~Kroha,~F.~Legger,~R.~Richter,\\
\emph{Max-Planck-Institut f\"ur Physik, F\"ohringer Ring 6, D-80805, M\"unchen, Germany,} \\
A.~Engl,~R.~Hertenberger,~F.~Rauscher, \\
\emph{Ludwig-Maximilians-Universit\"at M\"unchen, Am Coulombwall 1, D-85748, Garching, Germany,}% <-this % stops a space
\thanks{Manuscript received November 14, 2008.}% <-this % stops a space
}

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\begin{abstract}
The precise measurement of muon momenta up to 1~TeV/$c$ is one of the most
challenging aspects of the ATLAS experiment at the Large Hadron Collider (LHC) at CERN. The ATLAS muon
spectrometer is equipped with three layers of Monitored Drift Tube (MDT) chambers in a magnetic field generated by a
superconducting air-core magnet system which are designed to cope with neutron background counting rates of up to 500~cm$^{-2}$s$^{-1}$.
However, 10 times higher background rates are to be expected at Super-LHC, the high-luminosity upgrade of the LHC.
We investigate the possibility of increasing the rate capability of the drift tube detectors 
by reducing the tubes diameter from the current value of 30~mm to 15~mm. Cosmic ray test results of
a prototype detector with 15~mm diameter drift tubes
in the presence of $\gamma$ ray fluxes of up to 2000~cm$^{-2}$s$^{-1}$ are discussed.\end{abstract}


\section{Introduction}

\IEEEPARstart{I}{n} the muon spectrometer of the ATLAS detector at the Large Hadron Collider (LHC) at CERN\cite{ATLAStp}
large Monitored Drift-Tube (MDT) chambers are used for precision tracking 
in a toroidal magnetic field of superconducting air-core magnets.
The MDT chambers are equipped with two triple or quadruple layers of pressurized
aluminum drift tubes of 30~mm diameter and 0.4~mm wall thickness, filled with Ar:CO$_2$ (93:7) gas mixture at an
absolute pressure of 3~bar. An operating voltage of 3080~V, corresponding to a gas gain of 2~x~10$^4$, is applied between the 
tube wall and the gold-plated 50~$\mu$m diameter tungsten-rhenium wire which is positioned at the center of the tube with an
accuracy of 20~$\mu$m. The spatial resolution of individual drift tubes is 80~$\mu$m, which
translates into a position resolution of 30~$\mu$m for a 6-layer chamber. This allows for a momentum resolution of better than %10\%$
for muon momenta of up to 1~TeV/$c$\cite{MuonTDR}.

The ATLAS muon spectrometer will be exposed to high background fluxes of neutrons and $\gamma$ rays
with energies in the 1 MeV range, originating from interactions of the LHC collision products 
in the beam pipe, the shielding material, the calorimeters and accelerator elements.
Detection efficiencies of the MDT chambers for these neutrons and photons are about $0.1\%
and $1\%, respectively\cite{aleksa-phd}. Monte Carlo simulations\cite{baranov} predict the
highest background rates in the ATLAS muon spectrometer in the inner layers of the endcap regions closest to the beam pipe.
Due to uncertainties in the cross section and particle multiplicities in proton-proton collisions at a center-of-mass energy of
$\sqrt{s} = 14$~TeV and limited knowledge of the showering processes in the shielding material and of the chamber sensitivities,
a safety factor of 5 has been taken into account in the background rate estimates for the design of the ATLAS muon spectrometer.
Hence, the MDT chambers are designed to cope with particle fluxes up to 500~cm$^{-2}$s$^{-1}$ at the nominal LHC luminosity
of 10$^{34}$cm$^2$s$^{-1}$ which corresponds to a maximum counting rate per tube of 300 kHz in drift tubes of 2~m length.

The LHC upgrade schedule foresees a stepwise increase of the luminosity by up to an order of magnitude beyond the
nominal value\cite{slhc}. The background rates are expected to roughly scale with the luminosity. With 
luminosity increasing beyond the nominal value, muon chambers in the endcap regions of the ATLAS muon spectrometer 
will reach the limits of their rate capability.
We investigate the possibility of using drift-tube chambers with reduced tube diameter
up to the highest background rates expected at Super-LHC.

\section{MDT chamber performance at high counting rates}

At high background rates, the MDT chambers are known to suffer from a degradation of the spatial resolution
due to space-charge fluctuations\cite{aleksa,deile} and of the muon
detection efficiency due to increased occupancy of the drift tubes\cite{sandra}.
Reducing the tube diameter from 30 to 15 mm while leaving all other parameters including the gas gain unchanged, leads
to a reduction of the maximum drift time by a factor of $\sim 3.5$ from about 700~ns to 200~ns\cite{ieee07} and
of the conversion rate of neutrons in the drift tube walls by a factor of two resulting in an occupancy
reduction by a factor of about 7.
In addition, the space-to-drift-time relationship becomes more linear
reducing the sensitivity to space charge effects.

%DO WE WANT A SHORT SENTENCE AND REF TO LAST YEAR PROCEEDINGS:
%OR A LONGER EXPLANATION?

%If one neglects electronics effects such as artificial dead time and signal shaping time, 
%the tube occupancy depends on the maximum drift time of the electrons. 
%The space-to-drift-time relationship for the Ar:CO$_2$ gas
%mixture used in the MDT chambers is shown in Fig. \ref{fig_rt_sim}. 
%The maximum drift time is about 700 (200) ns for 30 (15) mm diameter drift tubes, 
%therefore by halving the tube diameter the occupancy is reduced by a factor 3.5. 
%Converted $\gamma$ particles in the tube wall also contribute to increase the occupancy at high rates. 
%In 15 mm diameter tubes half the conversions take place at
%the same particle flux. Overall, 15 mm diameter drift tubes have the same occupancy as
%30 mm diameter tubes at 7 times higher rates. An additional advantage of the reduction of the tube 
%diameter from 30~mm to 15~mm is the increased redundancy in the
%track measurement since more tubes can be packed into the same
%volume, which would partly compensate the single-tube efficiency
%loss. The effect of multiple scattering on the spatial and momentum resolution 
%due to the presence of additional material will be the subject of future investigations - estimation???. 

%The space-charge distribution generated by the ion clouds drifting toward the tube wall changes the drift
%electric field, influencing both the drift velocity and the gas gain. By lowering the effective potential seen by the
%drift electrons, the gas gain decreases at high counting rates. The effective voltage drop grows with the third power
%of the drift tube radius \cite{riegler}, and is therefore 8 times smaller in 15 mm diameter tubes. 
%The change in the electric field leads to fluctuations of the space-to-drift time relationship,
%causing a deterioration of the spatial resolution especially in
% non linear gases, such as the Ar:CO$_2$ (93:7) mixture used in the ATLAS MDT chambers, since the
%drift velocity is strongly dependent on the electric field. This effect is not crucial in 15 mm 
%diameter tubes, since the gas response is more linear for drift radii smaller than 7.5 mm. 
%In general, a linear gas is desirable since it entices a lesser dependency on environmental
%parameters, such as temperature, magnetic field, gas pressure and
%background radiation. Mixtures other than Ar:CO$_2$, with fast and linear gas responses, are being investigated. 
%However up to now none has been found that has the same aging properties as Ar:CO$_2$ (93:7) - add
%reference??.

%\begin{figure}[!t]
%%\centering
%\includegraphics[width=3.2in]{rt_sim.eps}
%%\vspace{-1cm}
%\caption{Space-time relationship for the Ar:CO$_2$ (93:7) gas
%mixture at 3 bars currently used in the MDT chambers.}
%\label{fig_rt_sim}
%\end{figure}


\section{Design of 15 mm diameter drift tubes}


The 15~mm diameter drift tube design follows as much as possible the current ATLAS MDT design.
The aluminum tube wall is 400~$\mu$m thick, and a 50~$\mu$m tungsten-rhenium wire is placed at the center of
the tube. The drift tubes are filled with the same gas mixture Ar:CO$_2$ (93:7) as 30~mm diameter tubes, 
at 3~bar pressure.
The tube operating voltage
is set to 2730~V, which corresponds to a gas gain of 20000. 
The electric field being the same as in the current MDTs for
drift radii smaller than 7.5~mm, standard ATLAS MDT electronics can be used for the readout. A summary of the various
parameters used for 15~mm and 30~mm diameter drift tubes can be found in
Table \ref{tab_15vs30}.

%ADD MORE DETAILS ON ENDPLUG DESIGN AND GAS CONNECTIONS??

\begin{table}[h]
% increase table row spacing, adjust to taste
\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of \extrarowheight as needed to properly center the text within the cells
\caption{Comparison of operating parameters for 15~mm and 30~mm
diameter drift tubes.} \label{tab_15vs30} \centering
% Some packages, such as MDW tools, offer better commands for making tables
% than the plain LaTeX2e tabular which is used here.
\begin{tabular}{|l||c|c|}
\hline
Diameter &15 mm & 30 mm\\
\hline
Gas mixture & Ar:CO$_2$ (93:7)& Ar:CO$_2$ (93:7)\\
Gas pressure & 3 bar & 3 bar \\
Wire & 50 $\mu$m W-Re & 50 $\mu$m W-Re \\
Tube wall & 400 $\mu$m Al & 400 $\mu$m Al \\
Operating voltage & 2730 V & 3080 V \\
Max. drift time & 200 ns & 700 ns \\
Gas gain & 20000 & 20000 \\
\hline
\end{tabular}
%\vspace{-0.5cm}
\end{table}

\section{Cosmic-ray test in a high radiation environment}

A detector prototype with 15~mm diameter drift tubes has been tested in a high radiation environment at the Gamma Irradiation Facility (GIF) at Cern in April 
2008. The GIF is equipped with a 590~GBq $^{137}$Cs source emitting 662~keV photons. Lead filters of
various thickness are available to partially shield the source \cite{gif}.

The experimental setup at the GIF consisted in two reference chambers used for tracking, 6 15~mm diameter 
drift tubes of 1~m length placed between the reference chambers, and 2 layers of scintillator counters 
(6 counters of 1.15~m length per layer) used to trigger on muons from cosmic rays (see Fig. \ref{fig_gifsetup}). 
The setup was placed at a distance of about 1.50~m from the source.
The counters were shielded from the photon radiation by a 15~cm thick lead wall, who was also partly shielding the lower reference
chamber. The reference chambers were made 
of 2 triple layers of 30~mm diameter drift tubes of 50~cm length (8 drift tubes per layer). The distance between the
upper and lower layers of each reference chamber was 31.5~cm, in order to have a good angular resolution for the
tracking. To minimize multiple scattering between the test drift tubes and the reference chambers, two 
spacers made of hollow 30~mm diameter tubes were used to hold the 6 prototype drift tubes in place
between the two reference chambers. The length of the 30~mm diameter tubes has been chosen to have the same
counting rate per tube as in the 15~mm diameter tubes. This partly compensates the efficiency loss 
in the reference chambers at high counting rates due to the large occupancy.

The readout of both test drift tubes and reference chambers was made with standard ATLAS electronics, which
allows for the measurement of the electron drift time and the collected charge from the signal pulse height
and length. The deadtime of the electronics for the readout of the 15 mm~diameter drift tubes was set to 200
ns, whereas for 30~mm diameter drift tubes the standard ATLAS value of 790~ns was used.
 
\begin{figure}[h]
%\centering
\includegraphics[width=3.4in]{gif-setup.eps}
%\vspace{-1cm}
\caption{Schematic drawing of the experimental setup at the GIF.}
\label{fig_gifsetup}
\end{figure}

\begin{figure}[h]
%\centering
\includegraphics[width=3.4in]{gif-picture.eps}
%\vspace{-1cm}
\caption{The experimental setup at the GIF. The lead wall had not been yet built at the time the picture was
taken.}
\label{fig_gifpicture}
\end{figure}

\section{Measured counting rates}

The highest average counting rate, obtained by averaging the counting rates measured in each 15 mm diameter drift tube,  was
1500~cm$^{-2}$s$^{-1}$. By placing appropriate filters in front of the source, measurements were also made at average counting 
rates of 850 and 1200~cm$^{-2}$s$^{-1}$. About 1 million triggers were collected at each of the four 
average counting rate values, including low rate runs where the source was completely shielded (counting rate less than 
50~cm$^{-2}$s$^{-1}$). 

Due to the different distances from the Cs source, the counting rate measured in the drift tube closest to
the source was about 30\% larger than the average counting rate, and 30\% smaller in the farthest away tube. The maximum measured counting rate in a single 15~mm diameter tube was 
2000~cm$^{-2}$s$^{-1}$, which corresponds to a particle flux 20 times higher than expected in the hottest region of the ATLAS muon spectrometer at LHC
design luminosity (without safety factor). In the single 15~mm diameter tube the counting rate varied from 600 to
2000~cm$^{-2}$s$^{-1}$, in steps of $\sim$100~cm$^{-2}$s$^{-1}$.

\section{Drift properties of 15 mm diameter tubes}

Muon tracks from cosmic rays were reconstructed separately in both reference chambers. A vertical track was 
required in each
chamber, and both tracks were required to have similar slope.  
The position of the muon hit in the 15~mm diameter tube crossed by both tracks was given by the average distance of the two reference tracks (one from each chamber) 
from the tube wire, $(d_{\rm low}+d_{\rm up})/2$.

In Fig. \ref{fig_rtsmall} the measured space-time relationship for 15~mm diameter drift tubes is shown. As
expected, the maximum drift time is about 200~ns, and the drift velocity has a weak dependence on the drift radius.
The hits below the thick band which follows the expected space-time
distribution for the mixture Ar:CO$_2$ (93:7) are due to delta electrons created by muons in the
tube wall.


\begin{figure}[h]
\centering
\includegraphics[width=3.2in]{rt_small_34mV.eps}
%\vspace{-1cm}
\caption{The space-to-time relationship in 15~mm diameter tubes as a function of the counting rate.}
\label{fig_rtsmall}
\end{figure}

The shown space-time distribution at low rate was used to extract the $r(t)$ relationship, which allows for the 
determination of the drift radius $r$ from the measured drift time $t$, as described in \cite{sandra}.
At higher counting rates, however, the number of reconstructed muon tracks decreases by almost a factor 20, due to the
degradation of the tracking in the reference chambers and to spurious triggers coming from insufficient shielding
of the scintillators. Therefore the $r(t)$ relationship measured at low counting
rate was also used to determine the position of muon hits from the measured drift time at high rates. The
differences in the $r(t)$ relationships at various rates are smaller than the experimental uncertainties. 

\section{Performances of 15 mm diameter drift tubes at high rates}


The quality of the measurement of the drift radius of muons crossing the 15~mm diameter drift tubes can be evaluated by 
studying the residual distribution, defined as the difference between the muon hit position determined by the $r(t)$ 
 relationship and the hit position measured by the external tracking reference,
$r-(d_{\rm low}+d_{\rm up})/2$ (see Fig. \ref{fig_residuals}). The residual distribution is significantly non-gaussian for tracks close to the wire 
\cite{deile}. Moreover space charge fluctuations, who cause variations of the electric field over
time, and as a consequence a deviation from the expected $r(t)$ relationship, have larger effect 
at larger radii. The residual distribution is therefore expected to be the superposition of several
gaussian distributions of different widths. These effects were neglected in this analysis due to limited available
statistics, and the residuals were described with a single gaussian (see Fig. \ref{fig_resall}). 

At high rates space charge fluctuations cause a
significant degradation of the tracking performance, the reference chambers being equipped with
30~mm diameter tubes, and the residuals are domined by the uncertainty on the measurement of the track position. 
The measurement of the spatial resolution of the 15~mm diameter drift tubes is therefore not viable with this setup.

\begin{figure}[h]
\centering
%\includegraphics[width=3.2in]{residual_att_inf_36_mV.eps}
\includegraphics[width=3.2in]{residuals.eps}
\caption{Residual distribution at low counting rate as a function of the distance of the muon hit from the wire. }
%\vspace{-1cm}
\label{fig_residuals}
\end{figure}

\begin{figure}[h]
\centering
\includegraphics[width=3.2in]{res_att_inf_36mV.eps}
\caption{Residual distribution at low counting rate. }
%\vspace{-1cm}
\label{fig_resall}
\end{figure}

Non-gaussian tails in the residual distribution may arise due to delta rays and background hits.
The 3$\sigma$ efficiency, defined as the probability that the reconstructed muon radius is
within 3$\sigma$ from the value predicted by the external reference tracking, was used
to characterize the importance of such tails. The $\sigma$ was extracted by a gaussian fit of the residual distribution
in each drift tube, as above described.

\begin{figure*}[h]
\centering
\subfigure{\includegraphics[width=3.2in]{eff.eps}}
\hfil
\subfigure{\includegraphics[width=3.2in]{eff.36mV.eps}}
\caption{3$\sigma$ single tube efficiency for 15 mm  and 30 mm diameter drift tubes as a function of the
counting rate (with different scales in the left and right plots). The green dots in the left plot are measurements from the GIF tests described in this letter,
whereas the remaining curves were measured in 2004 tests of 30~mm diameter tubes at the GIF
\cite{sandra2}. The 3$\sigma$ single tube efficiency for 15 mm diameter drift tubes is not shown in the right plot for clarity.}
\label{fig_eff}
\end{figure*}		

In Fig. \ref{fig_eff} the measured 3$\sigma$ efficiencies for 15~mm  and 30~mm diameter drift tubes 
are shown as a function of the counting rate. The 5\% inefficiency at low counting rate for both
15 and 30~mm diameter drift tubes is due to the creation of delta electrons in the tube wall.
At higher rate the degradation of the performances is due to background hits. 

The measurements for 30~mm diameter drift tubes were
made in a testbeam in 2004 \cite{sandra2}, and correspond to data taken with the standard ATLAS settings for 
the deadtime of the readout electronics, 790 ns, and with a shorter deadtime, 200 ns. If a muon arrives
in the dead-time window after a background hit, the muon hit is not detected. Hence reducing the
electronics deadtime has as a consequence an increased tube efficiency. To improve the efficiency
in data taken with 200 ns deadtime and more than one hit in a sigle drift tube, muon hits were recovered
by using the second hit if the first one had a radius falling outside the required 3$\sigma$
window. 

The measured 3$\sigma$ efficiency for 15~mm diameter drift tubes follows that of
30~mm diameter tubes with 200 ns deadtime and second hit recovery, which allows for the extrapolation of drift tubes 
performances at higher counting rates.
We remind the reader that due to the smaller tube surface, the maximum expected counting rate per tube at the Super-LHC is 1.5~MHz/tube
for 15~mm diameter drift tubes, whereas for 30~mm diameter tubes one expects twice higher counting rates per tube. The extrapolated 
3$\sigma$ efficiency for 15~mm diameter drift tubes at the Super-LHC is therefore $\sim$60\%. At the Super-LHC counting rate of 
3~MHz/tube, the 30~mm diameter tube 3$\sigma$ efficiency is less than 20\%.




\section{Conclusion}

The ATLAS MDT chambers are designed to withstand particle fluxes up to 500~cm$^{-2}$s$^{-1}$.
However counting rates up to 5 kHz/cm$^{2}$ are to be expected at a luminosity of 
10$^{35}$cm$^2$s$^{-1}$ at the Super-LHC, the luminosity upgrade foreseen for the LHC. This corresponds to a counting rate
of 1.5~MHz/tube in 15~mm diameter tubes (2 meter long), and to 3~MHz/tube in the 15~mm diameter drift tubes currently used in
the ATLAS muon spectrometer. We investigated the performances of drift tubes with smaller diameter. A prototype detector equipped with such small tubes
was tested in a high radiation environment, with measured counting rates up to 
2~kHzcm$^{2}$ (corresponding to 350~kHz/tube). At low counting rate
the measured 3$\sigma$ single tube efficiency is 95\% (the 5\% inefficiency is due to delta rays), and the
degradation at higher counting rates was found in agreement with expectations. 
The smaller diameter drift tubes can therefore be considered a promising solution for the 
replacement of MDT chambers in the hottest region of
the ATLAS muon spectrometer at the Super-LHC luminosity. However more conclusive tests are still needed to
demostrate that a chamber equipped with small tubes could meet the design requirements of the
ATLAS MDT chambers, i.e. ensure a chamber spatial resolution of at least 35 $\mu$m. In
particular, multiple scattering effects within a chamber due to the increased amount of material
(in case more drift tubes than in the present design are needed) need to be better understood. We
plan to build a chamber prototype equipped with 15~mm diameter tubes and test it in the GIF during 2009.


\vfill

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\end{thebibliography}




% that's all folks
\end{document}
