\section{The Muon Spectrometer}
%
The muon spectrometer~\cite{muon_tdr, ATLAS_tech_paper} of the ATLAS experiment 
is equipped with three layers of muon detectors in a toroidal
magnetic field of $3-6\,$Tm bending power generated by a superconducting
air-core magnet system. 
The spectrometer is designed to provide muon momentum resolution of better
than $10\%$ for transverse momenta up to $1\,$TeV/c over a pseudo-rapidity
range of $|\eta|\leqslant 2.7$. This requires a very accurate track
sagitta measurement with three layers of muon detectors which have to be aligned
relative to each other with an accuracy of up to $30\,$\micron\ in the bending direction
in the magnetic field. Drift chambers with very high
spatial resolution of $40\,$\micron, the Monitored Drift Tube (MDT) chambers,
have been developed to cover the active area of the spectrometer of $5500\,$m$^2$
with only $5\%$ gaps mainly in the region of the detector feet.

\begin{figure*}
\figimage{1}{ATLAS_MDT_barrel_installation}
\labelcaption{fig:ATLAS_MDT_barrel_installation}{The barrel part of the ATLAS muon spectrometer
viewed from the LHC tunnel after completion of the muon
chamber installation in November 2006. The MDT chambers built in Munich are mounted 
on rails on the outside of the eight superconducting magnet coils.}
\end{figure*}

% \begin{figure*}
% \figimage{1}{ATLAS_MDT_ECT_installed}
% \labelcaption{fig:ATLAS_MDT_ECT_installed}{View of one endcap region of the  muon spectrometer
% with the endcap toroid magnet installed in a single cryostat in the inner bore of the barrel magnet
% system (left) and with the muon detector wheel of the middle endcap layer (right) in February 2008.}
% \end{figure*}

The cylindrical central part of the spectrometer (barrel)
contains eight race-track shaped magnet coils of $25\,$m length and $5\,$m radial width.
The layout of the muon chambers follows the eightfold symmetry of the magnet
around the proton beam axis in eight small and eight large azimuthal sectors
(see Fig.~\ref{fig:ATLAS_MDT_barrel_installation}). The barrel part of the spectrometer
is complemented by two endcaps each consisting of eight superconducting coils housed
in a common cryostat fitting into the inner bore of the barrel toroid magnet and three
wheel-shaped layers of muon detectors.% (see Fig.~\ref{fig:ATLAS_MDT_ECT_installed}).

The MDT chambers built in Munich consist of two triple layers of $30\,$mm
diameter aluminium drift tubes of $3.8\,$m length equipped with a central gold-plated tungsten-rhenium
sense wire which are separated by an aluminum space frame.
The drift tubes are operated with Ar:CO$_2$ (93:7) gas mixture at a
pressure of $3\,$bar and a gas amplification of 20,000 (corresponding to a operating voltage between tube wall and wire of $3080\,$V)
and provide a position resolution of about $80\,$\micron\ . The sense wires are
positioned within a chamber with an accuracy of better than $20\,$\micron\
in order to achieve the required spatial resolution of the chambers~\cite{mdt_constr1}.

In the years 2001 to 2006, 88 MDT chambers were constructed at the MPI~\cite{mdt_constr2}
containing about 36000 drift tubes of $3.8\,$m length.
They cover about $15\%$ of the active area of the spectrometer. The installation of these
chambers in the outermost layer of the barrel part of the spectrometer took place in 2005 and 2006.
The commissioning of the chambers in the ATLAS detector was completed in summer 2008, just before the start of LHC data taking \cite{mdt_install1, mdt_commissioning1, mdt_commissioning2}. The one year long interruption of the LHC operation caused by severe beam magnet failures in September 2008 was used to calibrate and align the muon spectrometer and to commission the muon identification with muons from cosmic rays.

% \subsection{Detector Installation and Commissioning}
% %
% The capability to trigger on muon tracks above a certain momentum threshold 
% is one of the principal requirements for the muon spectrometer. The MDT
% chambers with their long maximum drift time of about $700\,$ns, which spans about 30 beam
% crossings, are not suited for this task and, therefore, are complemented
% by additional fast trigger chambers. In the barrel region of the muon
% detector, the Resistive Plate Chamber (RPC) technology was selected for
% this purpose. This detector type uses perpendicular pick-up strips to
% sense the avalanches created by traversing particles in the chamber gas delivering
% coordinate information about $20\,$ns after the passage of the particle.
% RPCs are positioned at three radial positions of the barrel region. One RPC 
% per MDT chamber in the outermost detector layer and two RPCs in the middle
% layer below and above each MDT chamber. In this way, three fast coordinate
% measurements are obtained along the track which allow for a coarse
% momentum determination using coincidences between the strip signals in the three
% RPC layers.
% 
% Each of our MDT chambers had to be combined with the complementary
% RPC using a rigid yet light-weight mechanical structure, the common support. 
% The 88 common support frames were designed and manufactured 
% at the MPI. The integration with the RPCs was done at CERN between July
% 2005 and May 2006 (see Fig.~\ref{fig:ATLAS_MDT_mdt_rotator}).
% 
% After arrival at CERN, both chamber types, RPC and MDT, were again
% tested for gas tightness, functioning of
% electronics, noise rate etc. The low failure rate, only three
% additional broken wires, demonstrated that no significant damage had
% occured during transport to CERN~\cite{mdt_install1,mdt_install2,mdt_calib1}. The overall
% drift tube failure rate after all tests was only $0.1\%$.
% 
% \begin{figure} 
% \figimage{1}{ATLAS_MDT_mdt_rotator}
% \labelcaption{fig:ATLAS_MDT_mdt_rotator}{Integration of MDT chambers with RPC
% trigger chambers at CERN. Two assembled MDT/RPC packages can be seen in
% the foreground.  To the right, in a blue support, an assembled package
% is rotated into its nominal angular position for final adjustment
% of the relative position and of the gravitational sag of the chambers.
% In the far background the test setup can be seen in which
% chamber packages are tested with cosmic rays before delivery to the
% ATLAS hall.}
% \end{figure}
% 
% \begin{figure}
% \figimage{1}{ATLAS_MDT_mdt_lowering}
% \labelcaption{fig:ATLAS_MDT_mdt_lowering}{Lowering of a MDT/RPC chamber package by crane
% into the underground ATLAS cavern.}
% \end{figure}
% 
% \begin{figure}
% \figimage{1}{ATLAS_MDT_bos_installation_1}
% \labelcaption{fig:ATLAS_MDT_bos_installation_1}{Installation of a MDT chamber produced at
% MPI in the top region of the ATLAS detector. The chamber will reach
% its final longitudinal position inside the detector by sliding on rails. 
% In order to achieve the correct alignment during installation, a special
% installation frame was constructed which can be manipulated by two
% independent cranes.} 
% \end{figure}
% 
% \begin{figure}
% \figimage{1}{ATLAS_MDT_bos_installation_2}
% \labelcaption{fig:ATLAS_MDT_bos_installation_2}{Installation of a MDT chamber produced at MPI.
% The chamber has been pulled from the installation frame onto the rails mounted
% on the magnet coils on which it can be moved to its final position.}
% \end{figure}
% 
% Each MDT chamber was adjusted such that the gravitational sag of the
% signal wires is matched by the bending of the tube layers in the final
% angular position of the chamber in the ATLAS detector. For this purpose, 
% the integrated RPC and MDT chamber packages had to be rotated
% into their nominal installation angle with a specially designed tool
% (see Fig.~\ref{fig:ATLAS_MDT_mdt_rotator}). Finally, the chambers were tested with cosmic
% rays before being transported to the ATLAS experimental hall.
% 
% After lowering into the experimental cavern (see
% Fig.~\ref{fig:ATLAS_MDT_mdt_lowering}) the chamber support frames were slid onto
% rails on the magnet coils with the help of a special installation frame
% (see Fig.~\ref{fig:ATLAS_MDT_bos_installation_1}) and pulled to their final position
% in ATLAS (see Fig.~\ref{fig:ATLAS_MDT_bos_installation_2})~\cite{mdt_calib1}. The
% exact position of the chambers in the ATLAS detector coordinate frame was
% adjusted with an accuracy of $\pm 1\,$mm.
% The main installation period of the MPI chambers was the first half of 2006.
% Immediately after the installation, all chambers
% have been successfully tested for gas tightness, high-voltage stability and correct
% sag adjustment. The connections
% to the central gas distribution system have been completed end of 2007.
% 
% In parallel to the barrel spectrometer commissioning, the endcap muon chamber wheels
% and the cryostats of the associated superconducting endcap toroid magnets have been 
% installed in the ATLAS cavern in 2007 and early 2008 completing the ATLAS muon spectrometer
% (see Fig.~\ref{fig:ATLAS_MDT_ECT_installed}).
% 
% \begin{figure}
% \figimage{1}{ATLAS_MDT_Cosmics_atlas_07}
% \labelcaption{fig:ATLAS_MDT_Cosmics_atlas_07}{Reconstructed trajectories of muons from cosmic rays
% triggered and reconstructed in the barrel part of the ATLAS muon spectrometer. The majority
% of the muons reaches the underground cavern through the big access shaft directly above the
% detector while the other low energetic muons are absorbed in the soil.}
% \end{figure}
% 
% \begin{figure}
% \figimage{1}{ATLAS_MDT_cosmic_muon_atlas}
% \labelcaption{fig:ATLAS_MDT_cosmic_muon_atlas}{Example of a cosmic muon trajectory reconstructed in the
% upper sectors of the barrel part of the muon spectrometer shown in the projections perpendicular (top)
% and parallel (bottom) to the beam axis, respectively.}
% \end{figure}
%          
% After the installation of the chambers, commissioning of the barrel muon spectrometer
% with data of cosmic ray muons started in the fall of 2006. The first data were taken with
% only the bottom sector of the spectrometer being operational. The reconstructed trajectories
% of triggered cosmic muon tracks are shown in Fig.~\ref{fig:ATLAS_MDT_Cosmics_atlas_07}.
% Since the ATLAS detector hall is at a depth of about $100\,$m, mainly muons passing through
% the vertical access shaft directly above the detector have been registered while only few
% highly energetic muons reach the underground cavern through the soil.
% An example of a cosmic muon track reconstructed in the upper part of the muon
% spectrometer is shown in Fig.~\ref{fig:ATLAS_MDT_cosmic_muon_atlas}.
% 
% During the year 2007, the azimuthal sectors of the barrel muon spectrometer
% have been made operational and connected to the ATLAS data acquisiition 
% system sequentially from the top to the bottom of the detector. By the end of 2007,
% about $25\%$ of the barrel chamber were in operation and $20\,$million cosmic muons
% have been recorded. The data have been used for in-situ studies of the calibration
% of the space drift-time relationship of the drift tubes of the MDT chambers
% and of the relative alignment of the chambers with reconstructed muon tracks
% with and without magnetic field turned on~\cite{mdt_commissioning1,mdt_commissioning2}
% (see next section). Studies of calibration
% and alignment in the nominal magnetic field were performed during a test of the
% barrel toroid magnet in November 2006.

\subsection{Muon Detector Software}
%
The MPI group is contributing to all aspects of the software development for the
analysis of the ATLAS muon detector data, including the calibration of the
space drift-time relationsship of the MDT chambers~\cite{mdt_calib1,
mdt_calib2, mdt_resol, mdt_testbeam1, mdt_testbeam2, mdt_highrates, mdt_calib3, mdt_calib4},
the alignment of the muon spectrometer with muon tracks~\cite{mdt_align1, mdt_align2, mdt_align3, mdt_align4, mdt_align5},
the evaluation and monitoring of the data quality of the 
muon detector~\cite{mdt_muondqa1, mdt_muondqa2},
optimization of the muon reconstruction
for the high background rates expected at the LHC~\cite{mdt_align3, mdt_identification},
and the Monte Carlo simulation programs for the muon spectrometer~\cite{mdt_simulation1, mdt_simulation2}.
The first two projects which are of central importance
for the operation and performance of the ATLAS muon spectrometer and in which the MPI group
plays a leading role are discussed in more detail in the following.

\subsubsection*{Drift Tube Calibration}
%
The pressurized drift-tube technology has been chosen for the ATLAS muon tracking chambers
because of the high spatial resolution of better than $80\,$\micron\ which can be
achieved for individual drift tubes by measuring the drift time of the 
ionization electrons to the sense wires. In order to reach the required
spatial resolution of the chambers of $40\,$\micron\, not only the
the sense wires have to be positioned in a chamber with an accuracy of $20\,$\micron\
but also the space drift-time relationship of the approximately 400,000 drift tubes
in ATLAS has to be known with the same precision. The drift properties of the
electrons depend on the temperature and pressure of the drift gas as well as on the
magnetic field and the rate of background hits from neutrons and photons which can
be very high at the Large Hadron Collider (LHC). For the regular calibration of the
space drift-time relationship, correlations between the positions measurements 
of the drift tubes hit by a traversing muon can be used.

We have developed fast and efficient algorithms for the determination of the
space drift-time relationship~\cite{mdt_calib1, mdt_calib2}
and of the spatial resolution~\cite{mdt_resol} of the MDT
chambers which are now part of the ATLAS data reconstruction software.
The algorithms have been extensively tested with simulated data, cosmic ray 
commissioning data~\cite{mdt_calib1, mdt_commissioning1, mdt_commissioning2}, in a muon beam at CERN~\cite{mdt_testbeam1, mdt_testbeam2} and
under LHC operating conditions, in magnetic fields and at high background rates,
using test beam data taken by our group at the Gamma Irradiation Facility
at CERN~\cite{mdt_highrates}. A model for magnetic field corrections to the
space drift-time relationship has been derived from the measurements~\cite{mdt_calib3}.

\begin{figure*}
%\figimage{1}{ATLAS_MDT_calib_atlas_06}
\includegraphics[width=0.499\linewidth]{accuracy_mc.eps}%
\includegraphics[width=0.499\linewidth]{accuracy_cosmic.eps}
\labelcaption{fig:ATLAS_MDT_mdt_autocalibration}{Accuracy of the calibration of the
space drift-time relationship of the drift tubes of the ATLAS MDT chambers
as a function of the number of cosmic muon tracks used per chamber. Left: Simulated data. Right: Cosmic ray data confirming the predicted $r$-$t$ accuracies.}
\end{figure*}

The large sample of cosmic ray muons recorded by the ATLAS detector in 2008 and 2009 allowed detailed studies of the robustness of the calibration algorithms. The $r$-$t$ calibration algorithm showed robust operation for all the chambers apart from the chambers with muons at 30$^\circ$ incidence angles where all drift radii are equal. The $r$-$t$ calibration method originally applied to straight track segments in triplelayers of the muon chambers had to be extended to curved track segments in the muon chambers to achieve the same level of robustness for all muon chambers \cite{JVL_doc_thesis}. Figure~\ref{fig:ATLAS_MDT_mdt_autocalibration} shows the accuracy of the space drift-time relationship provided by the improved calibration algorithm as a function of the number of collected muon track segments in a chamber for simulation and cosmic ray data. The required accuracy of 20~$\mu$m is realibly achieved with 3000 muons per chamber for all chambers of the muon spectrometer. The predicted accuracy is confirmed by the studies with muons from cosmic rays.

The dependence of the drift time on the magnetic field strength measured with
cosmic rays in the ATLAS detector %\cite{mdt_commissioning1}\cite{mdt_commissioning2}
agrees well with the model based on the test beam measurements
(see Fig.~\ref{fig:ATLAS_MDT_mdt_bfield}).

\begin{figure*}
\centerline{\includegraphics[width=0.9\linewidth]{delta_t.eps}}
\labelcaption{fig:ATLAS_MDT_mdt_bfield}{Magnetic field corrections to the drift time $t$ in different regions of magnetic-field strength (0.47~T on the left, 0.54~T on the right) in MDT chambers
in the middle layer of the large sectors of the barrel muon spectrometer as a function of the
drift distance $r$. The measured difference in the drift times with and without magnetic field $B$ agrees well with the model expectation in red derived from test beam measurements. The error bars of data points correspond to the estimated $r$-$t$ accuracy of 20~$mu$m. The drift time correction increases with
the distance to the wire because of the deflection of the drifting electrons in the magnetic field
oriented in the direction of the tube axis.}
\end{figure*}

The MPI group is operating one of the three computing centres
dedicated to the calibration and the alignment of the ATLAS muon spectrometer~\cite{mdt_calib4}
using a special data stream of muon tracks reconstructed by the ATLAS second level trigger algorithms.
The commitment of the MPI group to calibrate roughly one third of the
MDT chambers and to align the muon detectors
with muon trajectories includes the development of fully automated calibration
and alignment procedures and monitoring tools~\cite{mdt_calib5}.

\subsubsection*{Muon Chamber Alignment with Tracks}
%
To achieve the required momentum resolution of the ATLAS muon spectrometer up to
the highest muon energies, the relative positions of the chambers
have to be continuously monitored and misalignment corrections have to
be applied to the measured track sagitta with an accuracy of $30\,$\micron.
The MPI group contributed significantly to the development and test of the
high-precision optical alignment monitoring system for the muon 
spectrometer~\cite{muon_tdr}. The group also developed algorithms for the alignment of the ATLAS muon spectrometer with muon tracks \cite{mdt_align1, mdt_align2, mdt_align3, mdt_align4, mdt_align5}.

In the barrel part of the spectrometer, only the large chamber sectors mounted in between the
magnet coils can be fully aligned with optical sensor measurements.
The small chamber sectors mounted on the coils (see Fig.~\ref{fig:ATLAS_MDT_barrel_installation})
have to be aligned with respect to the large sectors with muon tracks passing through the
overlap regions between the the small and large sectors. The MPI group is 
providing these alignment corrections using the muon calibration data at the Munich
calibration and alignment computing centre~\cite{mdt_calib4, mdt_align1}.

\begin{figure}
    \centerline{\includegraphics[width=0.9\linewidth]{fig_27.eps}}
    \labelcaption{fig:ATLAS_MDT_sagitta_acc}{Mean values of the apparent sagittas of straight muon tracks after the initial alignment with straight muon track in ATLAS cosmic ray data. The station $\eta$-index labels the chamber position from the inside to the outside of the barrel of the muon spectrometer. The results are shown for large barrel chambers; similar results are obtained for the small barrel chambers.}
\end{figure}

\begin{figure}
    \centerline{\includegraphics[width=\linewidth]{fig_28.eps}}
    \labelcaption{fig:ATLAS_MDT_sagitta_res}{Resolution of the sagitta measurement as a function of the muon momentum as measured in ATLAS cosmic ray data. The red line illustrated the fitted resulation which is the quadratic sum of a term proportional to the inverse momentum taking into account multiple scattering and a constant term (of 100~$\mu$m) reflecting the limitation of the resolution by the spatial resolution and the alignment of the muon chambers.}
\end{figure}

Straight muon tracks measured while the toroid magnets
are turned off are needed for the precise determination the initial chamber positions
after installation as a starting point for the monitoring of further chamber movements 
by the optical sensors mounted on the chambers. An efficient algorithm has been developed
and successfully applied to cosmic ray commissioning data \cite{mdt_align2}.
Figure \ref{fig:ATLAS_MDT_sagitta_acc} shows the mean value of the apparent
sagitta of straight cosmic muon tracks after the initial alignment with straight
cosmic muon tracks. The accuracy of the initial alignment is of the order of
50~$\mu$m or better and close to the desired ultimate accuracy of 30~$\mu$m.
Improvements of the alignment accuracy are expected when chamber deformations
will be taken into account in the track reconstruction. The measurement of the
sagitta resolution of straight tracks in the muon spectrometer as a function of
the muon momentum measured by the inner detector is presented in Figure
\ref{fig:ATLAS_MDT_sagitta_res}. It improves with increasing momentum as
multiple scattering decreases with increasing momentum ans reaches a plateau
value of about 100~$\mu$m at high momenta reflecting the limited spatial
resolution and the residual misalignment of the muon chambers. The achieved
resolution is about a factor 2 larger than the target value of 50~$\mu$m because
the chambers are only aligned with 50~$\mu$m instead of 30~$\mu$m precision.

The method is being extended to the alignment of the muon chambers with
curved muon tracks in the magnetic field during normal operation of the experiment
in order to verify the optical alignment corrections. This requires an
independent measurement of the muon momentum which is insensitive to
misalignment of the MDT chambers along the muon track. 
The MDT chambers with their two triple or quadruple layers of precisely positioned drift tubes
measure not only track coordinates with high accuracy but also the local
track direction. This feature can be utilized for independent momentum determination from
measurement of the track deflection angles between the inner and the outer chamber layer
and between the two multilayers of the chambers in the middle layer located inside the magnetic field.
Studies with simulated data showed that the required alignment accuracy
can be achieved within two days of data taking at the nominal LHC luminosity 
of $10^{33}\,$cm$^{-2}$s$^{-1}$~\cite{mdt_align3, mdt_align5}.

\subsection{Measurement of the Performance of the Muon Identification in ATLAS}
The huge sample of cosmic ray muons made it possible to study the performance of the muon identification in great detail up to muon momenta of 300~GeV/c \cite{OK_HCP_2009, MuonCommPaper}. Figure \ref{fig:ATLAS_MDT_cosmics_eff} shows the track reconstruction efficiency in the ATLAS muon spectrometer for cosmic ray muons reconstructed in the inner detector. The efficiency is close to 100\% in the instrumented regions of the muon spectrometer. The drop of the efficiency at $|\eta|=0$ is caused by the acceptance gap of the muon spectrometer which is needed for the services of the inner detector and the calorimeters.

\begin{figure}
    \includegraphics[width=\linewidth]{fig_31.eps}
    \labelcaption{fig:ATLAS_MDT_cosmics_eff}{Track reconstruction efficiency in the muon spectrometer as a function of the pseudorapidity of the cosmic ray muon reconstructed by the inner detector. The muon momentum in the inner detector was requested to be greater than 5~GeV for the top part and greater than 9~GeV for the bottom part. The loss of efficiency in the region near $|\eta|=0$ is due to acceptance holes of the muon spectrometer needed for services of the inner detector and the calorimeters.}
\end{figure}

\begin{figure}
    \includegraphics[width=\linewidth]{fig_35.eps}
    \labelcaption{fig:ATLAS_MDT_cosmics_res}{Transverse momentum resolution of the muon spectrometer evaluated by comparing the momentum of cosmic ray muons measured in the top part of the spectrometer with the momentum in the bottom part of the spectrometer in the barrel region of the muon spectrometer. The results of two complementary track reconstruction algorithms show similar performance.}
\end{figure}

The momentum of cosmic ray muons traversing the entire ATLAS detector are measured twice, first in the top part of the muon spectrometer, then in the bottom part of the muon spectrometer. The comparison of the two momentum measurements allowed us to measure the fractional momentum resolution of the muon spectrometer up to muon with $p_T=300$~GeV/c (see Figure \ref{fig:ATLAS_MDT_cosmics_res}). The measured momentum resolution is in agreement with the expected momentum resolution for $p_T\lesssim100$~GeV/c, but is a factor 2-3 worse than expected above 300~GeV/c due to the residual misalignment of the muon spectrometer.

The muon reconstruction efficiency and the momentum scale and resolution will be measured with $Z\to\mu^+\mu^-$ decays in $pp$ collision data at the LHC \cite{CSCBOOK, HCP2007}. The position of the $Z$~resonance peak is a measure for the momentum scale, its width a measure for the momentum resolution. The muon reconstruction efficiency will be measured by the so-called "tag-and-probe method". In the tag-and-probe method events with an isolated muon and an inner detector track giving an invariant mass compatible with the $Z$ boson mass are selected. The fact that one of the two tracks is identified as muon ensure that the second track is also a muon and one can count how often the second track is reconstructed as a muon. The method has been studied on Monte-Carlo data and is able to reproduce the muon reconstruction efficiency with a systematic uncertainty of 0.2\%.

\begin{figure}
    \includegraphics[width=\linewidth]{fig_08.eps}
    \labelcaption{fig:ATLAS_MDT_rel_eff_collisions}{Comparison of the relative efficiency of the standard muon reconstruction algorithm with respect to reference muons as defined in the text with the Monte-Carlo prediction for $p_T>4$~GeV/c. The star-shaped symbols labelled as MC truth show the standard muon reconstruction efficiency for muons identified as true muons in the simulation.}
\end{figure}

In the early phase of the LHC operation the rate of dimuon decays of $Z$ bosons is too low for the tag-and-probe method and alternative methods have to be used to get a handle on the muon spectrometer reconstruction efficiency. The efficiency of the standard muon reconstruction is measured with respec to an alternative muon identification approach. In the alternative approach an inner detector track which deposits only little energy in the calorimeters and which can be matched with a track segment in the muon spectrometer is identified as muon. The relative efficiency of the standard muon reconstruction with respect to the alternative selection is shown as a function of the transverse muon momentum in Figure \ref{fig:ATLAS_MDT_rel_eff_collisions} \cite{ATLAS-CONF-2010-036}. The relative efficiency agrees with the Monte-Carlo prediction within errors. It is lower than the true efficiency as the alternative muon selection has a lower rejection power against muons from pion and kaon decays in flight than the standard reconstruction.

At transverse momenta below 20~GeV/c the momentum resolution in the momentum resolution is significantly larger than in the inner detector and can be measured by comparing the momentum measured in the muon spectrometer with the momentum measured in the inner detector. The resolution measured this way is in agreement with the Monte-Carlo prediction and the measurement with cosmic ray muons within the measurement uncertainties (see Figure \ref{fig:ATLAS_MDT_res_collisions}) \cite{ATL-COM-PHYS-2010-430}.

\begin{figure}
    \includegraphics[width=\linewidth]{Barrel_scale_res_withMC.eps}
    \labelcaption{fig:ATLAS_MDT_res_collisions}{Comparison of the momentum resolution in the barrel part of the muon spectrometer measured with muons from $pp$ collisions in comparison with the expected resolution from Monte-Carlo data and the analysis of cosmic ray data. The measured resolution agrees with the prediction within the measurement uncertainties.}
\end{figure}

The analysis of cosmic ray data and the first results of the analysis of $pp$ collision data confirm the expected performance of the muon spectrometer.

\subsection{Detector Development for ATLAS Upgrades}
%
For the searches for the Higgs boson and other new phenomena at the LHC,
as high as possible luminosity of the accelerator is desirable. The design 
luminosity of the LHC of $10^34\,$cm$^{-2}$s$^{-1}$ is expected to be reached
after a few years of data taking at lower luminosity. With a series of upgrades
of the CERN accelerator complex a further increase of the
LHC luminosity by an order of magnitude can be envisaged (Super-LHC or SLHC). Then, at the latest,
a major upgrade of the ATLAS detector will be necessary including parts of the muon spectrometer,
in particular in the forward regions with respect to the proton beams where the background 
rates will be the highest. The planning of a possible detector upgrade has started already within the
ATLAS collaboration. In this context, we have developed a research program and submitted proposals 
for the development of improved muon drift tube detectors~\cite{mdt_EoItubes},
of radiation tolerant readout electronics~\cite{mdt_EoIelectronics}
and of methods to reduce the data volume~\cite{mdt_EoIreadout} or increase the bandwidth of the
data acquisition system of the MDT chambers~\cite{mdt_EoIelectronics} for operation of the ATLAS detector
at very high luminosities.

\begin{figure}
\figimage{1}{ATLAS_MDT_drifttime1}
\labelcaption{fig:ATLAS_MDT_mdt_tspectra}{Comparison of the drift-time spectra of $30\,$mm and
$15\,$mm diameter drift tubes with Ar:CO$_2$ (93:7) gas mixture at $3\,$bar and the same gas
amplification of 20,000 which are in good agreement with the simulations with the GARFIELD program.
The $15\,$mm diameter tubes show the same drift time spectrum as the $30\,$mm diameter tubes up to the cut off at
the maximum drift time of $180\,$ns which corresponds to the smaller tube diameter.}
\end{figure}

\begin{figure}
\figimage{1}{ATLAS_MDT_big-small-tubes2}
\labelcaption{fig:ATLAS_MDT_smalltubes}{Front view of bundles of drift tubes with 30~mm (left) and
15~mm (right) diameter.}
\end{figure}

Already at the design luminosity, the MDT chambers have to cope with
unprecedentedly high background count rates from neutrons and photons as
byproducts of the proton-proton collisions. The effects of high count
rates in the MDT chambers of up to $500\,$Hz/cm$^2$ at the design luminosity in the inner layers of the forward
regions have been studied by our group in a muon beam at the Gamma Irradiation Facility
at CERN~\cite{mdt_highrates}. In addition to a degradation of the spatial resolution
of the drift tubes from $80\,$\micron\ without background to about $100\,$\micron\ at the highest rates
caused by fluctuations of the increasing space charge in the tubes,
the muon detection efficiency of the tubes deteriorates quickly from $94\%$ to $70\%$.
New muon chambers with faster response time and high track reconstruction efficiency are required 
for the ten times higher background rates expected at a Super-LHC in the spectrometer endcap regions,
and are desirable for the highest-rate regions already at the LHC design luminosity.

The development of faster muon detectors for Super-LHC at MPI builds on the extensive
experience with the design and operation of the present ATLAS MDT chambers.
First tests~\cite{mdt_slhc} confirmed the expectation that by reducing the drift tube diameter 
by a factor of two while leaving the gas mixture, pressure and gain unchanged, the maximum drift
time is reduced by a factor of 3.5 (see Fig.~\ref{fig:ATLAS_MDT_mdt_tspectra}).
At the same time, the count rates caused by neutron and
photon conversions in the drift tube walls will decrease proportional to the tube circumference
by a factor of two, reducing the drift tube occupancy (the product of
maximum drift time and count rate) and, consequently, the efficiency loss by a factor of 7.
In addition, the number of drift tube layers fitting into the same volume as the present
muon chambers can be increased by up to a factor of two (see Fig.~\ref{fig:ATLAS_MDT_smalltubes})
improving the chamber resolution and track reconstruction efficiency.

A concept for the drift tube and chamber design has been developed
with the aim to construct and test a prototype chamber in 2008. 
The development of new radiation hard readout 
electronics for the MDT chambers has also started.

%%%%%%%%%%%%%%%%
% References
%%%%%%%%%%%%%%%%

\begin{Biblio}

\bibitem{muon_tdr}
ATLAS Collaboration,
{\itshape Technical Design Report for the ATLAS Muon Spectrometer},
CERN/LHCC/97-22, May 1997.

\bibitem{ATLAS_tech_paper}
The ATLAS collaboration, {\sl The ATLAS Experiment at the CERN Large Hadron Collider}, JINST-3, 2008.

\bibitem{mdt_constr1}
J.~Dubbert, S.~Horvat, O.~Kortner, S.~Kotov, H.~Kroha, S.~Mohrdieck-M\"ock, R.Richter,
{\itshape Final Evaluation of the Mechanical Precision of the ATLAS Muon Drift Tube Chambers},
proceedings of the 2006 IEEE Nuclear Science Symposium, San Diego, USA, 29 October--4 November 2006,
MPI report, MPP-2006-167, November 2006.

\bibitem{mdt_constr2}
F.~Bauer et al.,
{\itshape Construction and Test of MDT Chambers for the ATLAS Muon 
Spectrometer},
Nucl.\ Instr.\ and Methods \textbf{A461} (2001) 17; \\
{\itshape Construction and Test of the Precision Drift Chambers for the
ATLAS Muon Spectrometer},
IEEE Trans.\ Nucl.\ Sci., Vol.~48 (2001) 302;\\
{\itshape The First Precision Drift Tube Chambers for the ATLAS Muon 
Spectrometer},
Nucl.~Instr.\ and Methods \textbf{A478} (2002) 153;\\
{\itshape Large-Scale Production of Monitored Drift Tube Chambers for the
ATLAS Muon Spectrometer},
Nucl.\ Instr.\ and Methods \textbf{A518} (2004) 69.

\bibitem{mdt_install1}
J.~Dubbert et al.,
{\itshape Integration, Commissioning and Installation of Monitored Drift Tube Chambers
for the ATLAS Barrel Muon Spectrometer},
proceedings of the $10^{\mathrm th}$ Pisa Meeting on Advanced Detectors, Isola d'Elba, Italy,
21.--27.5.2006,
Nucl.~Instr.\ and Methods \textbf{A572} (2007) 53;\\
{\itshape \sl Integration, Commissioning and Installation of Large Drift-Tube Chambers
for the ATLAS Barrel Muon Spectrometer},
proceedings of the 2006 IEEE Nuclear Science Symposium, San Diego, USA, 29 October--4 November 2006,
Nuclear Science Symposium Conference Record 2006, IEEE, Volume 3, pp 1368-1372, 2006,
MPI report, MPP-2006-164, November 2006.

% \bibitem{mdt_install2}
% M.~Groh,
% {\itshape Test von Driftrohrkammern f\"ur das Myonspektrometer des ATLAS-Detektors
% am Large Hadron Collider},
% Diploma Thesis, \TUM, 
% MPI report, MPP-2006-004, January 2006.

\bibitem{mdt_commissioning1}
J.~Dubbert (for the ATLAS collaboration),
{\itshape First Experience with the ATLAS Muon Spectrometer},
proceedings of the $11^{\mathrm th}$ Vienna Conference on Instrumentation, Vienna, Austria,
19.--24.2.2007,
Nucl.~Instr.\ and Methods \textbf{A581} (2007) 507.

\bibitem{mdt_commissioning2}
J.~von Loeben (for the ATLAS collaboration),
{\itshape First Cosmic Ray Results of the ATLAS Muon Spectrometer with Magnetic Field},
proceedings of the 2007 IEEE Nuclear Science Symposium, Honolulu, Hawaii, USA, 28 October--2 November 2007,
MPI report, MPP-2007-175, November 2007.

\bibitem{mdt_calib1}
J.~von Loeben, M.~Deile, N.~Hessey, O.~Kortner, H.~Kroha, A.~Staude,
{\itshape An Efficient Method to Determine the Space-to-Drift Time Relationship of the ATLAS Monitored
Drift Tube Chambers},
proceedings of the 2007 IEEE Nuclear Science Symposium, Honolulu, Hawaii, USA, 28 October--2 November 2007,
MPI report, MPP-2007-176, November 2007.

\bibitem{mdt_calib2}
J.~von Loeben, 
{\itshape Test und Kalibrierung der Pr\"a\-zi\-si\-ons\-drift\-rohr\-kam\-mern des
ATLAS-Myon\-spek\-tro\-me\-ters},
Diploma Thesis, \TUM, 
MPI report, MPP-2006-241, December 2006.

\bibitem{mdt_resol}
%%%%%%%% -> MPP server
S.~Horvat, O.~Kortner, H.~Kroha,
{\itshape Determination of the Spatial Drift-Tube Resolution Using Muon Tracks},
ATLAS Note, ATL-MUON-PUB-2006-008, July 2006.

\bibitem{mdt_testbeam1}
%%%%%%%% -> MPP server
C.~Adorisio et al.,
{\itshape System Test of the ATLAS Muon Spectrometer at the H8 Beam at the CERN SPS},
Nucl.~Instr.\ and Meth.~{\bf A593} (2008) 232-254;

\bibitem{mdt_testbeam2}
%%%%%%%% -> MPP server
C.~Adorisio et al.,
{\itshape Study of the ATLAS MDT Spectrometer Using High Energy CERN Combined Test Beam Data},
Nucl.~Instr.\ and Meth.~{\bf A598} (2009) 400-415.

\bibitem{mdt_highrates}
M.~Deile et al., 
{\itshape Performance of the ATLAS Precision Muon Chambers under LHC Operating Conditions},
proceedings of the $9^{\mathrm th}$ Pisa Meeting on Advanced Detectors, Isola d'Elba, Italy,
25--31 May 2003,
Nucl.~Instr.\ and Methods \textbf{A518} (2004) 65; \\
{\itshape Resolution and Efficiency of the ATLAS Muon Drift-Tube Chambers at High Background Rates},
proceedings of the $10^{\mathrm th}$ Vienna Conference on Instrumentation, Vienna, Austria,
16--21 February 2004,
Nucl.~Instr.\ and Methods \textbf{A535} (2004) 212; \\
S.~Horvat et al.,
{\itshape Operation of the ATLAS Muon Drift-Tube Chambers at High Background
Rates and in Magnetic Fields},
IEEE Transactions on Nuclear Science, Vol.~53, No.~2 (2006) 562.

\bibitem{mdt_calib3}
J.~Dubbert et al.,
{\itshape Modelling of the Space-to-Drift-Time Relationship of the
ATLAS Monitored Drift-Tube Chambers in the Presence of Magnetic Fields},
Nucl.~Instr.\ and Methods \textbf{A572} (2007) 50.

\bibitem{mdt_calib4}
P.~Bagnaia, O.~Biebel, C.~Guyot, H.~Kroha, D.~Orestano, B.~Zhou,
{\itshape A Proposal for the Calibration and Alignment of the ATLAS Muon Spectrometer},
ATLAS Note, ATL-MUON-INT-2006-006, October 2005; \\
P.~Bagnaia et al.,
{\itshape Calibration Model for the MDT Chambers of the ATLAS Muon Spectrometer},
ATLAS Note, ATL-COM-MUON-2008-006, February 2008.

\bibitem{mdt_calib5}
M.~Cirilli et al.,
{\itshape Conditions Database and Calibration Software Framework for ATLAS Monitored Drift Tube Chambers},
Nucl.~Instr.\ and Methods \textbf{A572} (2007) 38.

\bibitem{mdt_align1}
Ch.~Amelung et al.,
{\itshape The ATLAS Muon Alignment System},
proceedings of the First LHC Alignment Workshop, CERN, Geneva, Switzerland, 4--6 September 2006,
CERN report, CERN-2007-004, 2007; \\
J.C.~Barriere et al.,
{\itshape The Alignment System of the Barrel Part of the ATLAS Muon Spectrometer},
ATLAS Note, ATL-MUON-PUB-2008-007, April 2008.

\bibitem{mdt_align2}
I.~Potrap, O.~Kortner, S.~Kotov, H.~Kroha,
{\itshape Alignment of the ATLAS Muon Spectrometer with Straight Tracks Using MILLEPEDE Method},
ATLAS Note, ATL-COM-MUON-2007-017, December 2007.

\bibitem{mdt_align3}
 O.~Kortner, S.~Kotov, H.~Kroha, J.~Schmaler, Ch.~Valderanis,
{\itshape Alignment of the ATLAS Muon Spectrometer with Tracks and
Muon Identification at High Background Rates},
Nucl.~Instr.\ and Methods \textbf{A581} (2007) 545-548.

\bibitem{mdt_align4}
O.~Kortner, S.~Kotov, H.~Kroha, I.~Potrap, J.~Schmaler,
{\itshape New Methods for the Alignment of the ATLAS Muon Spectrometer with Tracks},
proceedings of the 2007 IEEE Nuclear Science Symposium, Honolulu, Hawaii, USA, 28 October--2 November 2007,
MPI report, MPP-2007-177, November 2007.

\bibitem{mdt_align5}
J.~Schmaler,
{\itshape Test and Alignment of the ATLAS Precision Muon Chambers},
Diploma Thesis, \TUM, MPI report, MPP-2007-30, March 2007;
B.~Bittner,
{\itshape Alignment of the ATLAS Muon Spectrometer Using Muon Tracks},
Diploma Thesis, \TUM, MPI Report, MPP-2008-270, November 2008;
St.~Kaiser,
{\itshape Search for the Higgs Boson in the Process $pp\to Hqq$, $H\to WW$ with the ATLAS Detector},
PhD Thesis, \TUM, MPI Report, MPP-2010-38,
CERN-THESIS-2010-043, January 2010.

\bibitem{mdt_muondqa1}
M.~Schott, N.~Benekos, L.~Chevalier, J.-F.~Laporte,
{\itshape Impacts of Misalignment on the Reconstructed Z-Boson Resonance at the ATLAS
Muon Spectrometer},
proceedings of the $10^{\mathrm th}$ Pisa Meeting on Advanced Detectors, Isola d'Elba, Italy,
21--27 May 2006,
%MPI report, MPP-2006-176, June 2006,
Nucl.~Instr.\ and Methods \textbf{A572} (2007) 16;\\
{\itshape Z-Boson Resonance as a Calibration and Alignment Process for the ATLAS Muon Spectrometer},
proceedings of the 2006 IEEE Nuclear Science Symposium, San Diego, 10 October--4 November 2006,
MPI report, MPP-2006-173, November 2006.

\bibitem{mdt_muondqa2}
N.~Benekos, M.~Schott,
{\itshape Study of Z-Boson Measurements at the ATLAS Experiment},
proceedings of the "Physics at LHC" conference, Cracow, Poland, 3--8 July 2006,
MPI report, MPP-2006-174, July 2006.

\bibitem{mdt_identification}
D.~Primor, O.~Kortner, G.~Mikenberg, H.~Messer,
{\itshape A Novel Approach to Track Finding in a Drift Tube Detector},
Journal of INstrumentation, JINST \textbf{2} P01009, January 2007.

\bibitem{mdt_simulation1}
S.~Baranov et al.,
{\itshape Muon Detector Description as built and its Simulation for the ATLAS Experiment},
proceedings of the $10^{\mathrm th}$ Pisa Meeting on Advanced Detectors, Isola 'Elba, Italy,
21--27 May 2006,
Nucl.~Instr.\ and Methods \textbf{A572} (2007) 14;\\
D.~Rebuzzi et al.,
{\itshape Muon Detector Description as built and its Simulation for the ATLAS Experiment},
proceedings of the 2006 IEEE Nuclear Science Symposium, San Diego, 10 October--4 November 2006,
MPI report, MPP-2006-170, November 2006.

\bibitem{mdt_simulation2}
D.~Rebuzzi et al.,
{\itshape GEANT4 Muon Digitization in the ATHENA Framework},
proceedings of the 2006 Computing in High Energy Physics Conference, Mumbai, India, 13--17 February 2006,
MPI report, MPP-2006-178, February 2006.

\bibitem{JVL_doc_thesis}
J. von Loeben,
{\itshape Calibration of the ATLAS Muon Precision Chambers and Study of the Decay $\tau\to\mu\mu\mu$ at the LHC},
doctoral thesis, Technical University Munich, 2010.

\bibitem{OK_HCP_2009}
O.~Kortner on behalf of the ATLAS collaboration,
{\itshape Commissioning of the Charged Lepton Identification with Cosmic Rays in ATLAS}, PoS (HCP2009) 009.

\bibitem{MuonCommPaper}
The ATLAS collaboration,
{\itshape Commissioning of the ATLAS Muon Spectrometer with Cosmic Rays},
arXiv:1006.4384, submitted to EPJC (18 Jun 2010).

\bibitem{CSCBOOK}
The ATLAS collaboration,
{\itshape Expected Performance of the ATLAS Experiment:
Detector, Trigger and Physics},
arXiv:0901.0512; CERN-OPEN-2008-020, 2008.

\bibitem{HCP2007}
M.~Antonelli et al.,
{\itshape n-situ determination of the performance of the ATLAS muon spectrometer}, Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 177-178} (2008) 326.

\bibitem{ATLAS-CONF-2010-036}
The ATLAS collaboration,
{\itshape Muon Performance in Minimum Bias pp Collision Data at $\sqrt{s}$=7~TeV with ATLAS},
ATLAS conference note ATLAS-CONF-2010-036, 2010.

\bibitem{ATL-COM-PHYS-2010-430}
The ATLAS collaboration,
{\itshape Muon Reconstruction Performance},
ATLAS conference note ATLAS-CONF-2010-036, 2010.

\bibitem{mdt_EoItubes}
O.~Biebel, J.~Dubbert, S.~Horvat, O.~Kortner, H.~Kroha, R.~Richter, D.~Schaile,
{\itshape Expression of Interest: R\&D on Precision Drift Tube Detectors for Very High Background Rates at SLHC},
ATLAS document, ATL-M-MN-0006, March 2007.

\bibitem{mdt_EoIelectronics}
O.~Biebel, J.~Dubbert, S.~Horvat, O.~Kortner, H.~Kroha, R.~Richter, D.~Schaile,
{\itshape Upgrade of the MDT Readout Chain for the SLHC},
ATLAS document, ATL-M-MN-0003, March 2007.

\bibitem{mdt_EoIreadout}
O.~Biebel, J.~Dubbert, S.~Horvat, O.~Kortner, H.~Kroha, R.~Richter, D.~Schaile,
{\itshape Upgrade of the MDT Electronics for the SLHC Using Selective Readout},
ATLAS document, ATL-M-MN-0005, March 2007.

\bibitem{mdt_slhc}
J.~Dubbert, S.~Horvat, O.~Kortner, H.~Kroha, F.~Legger, R.~Richter, F.~Rauscher,
{\itshape Development of Precision Drift Tube Detectors for the Very High Background Rates at the Super-LHC},
proceedings of the 2007 IEEE Nuclear Science Symposium, Honolulu, Hawaii, USA, 28 October--2 November 2007,
MPI report, MPP-2007-172, November 2007.

%%%%%%%%%%%%%%%%%%%%%% Neue Referenzen mit MPP Autoren %%%%%%%%%%%%%%%

\bibitem
J.~Dubbert, O.~Kortner, H.~Kroha, F.~Legger, R.~Richter, A.~Engl, R.~Hertenberger, F.~Rauscher,
{\itshape Precision Drift Tube Chambers for the ATLAS Muon Spectrometer at Super-LHC},
proceedings of the 2008 IEEE Nuclear Science Symposium, Dresden, Germany, 19--25 October 2008,
MPI report, MPP-2008-191, November 2008.

\bibitem
B.~Bittner, S.~Kaiser, O.~Kortner, S.~Kotov, H.~Kroha, I.~Potrap, R.~Harrington, J.~Love, N.~Nation,
{\itshape Alignment of the ATLAS Muon Spectrometer with Muon Tracks},
proceedings of the 2008 IEEE Nuclear Science Symposium, Dresden, Germany, 19--25 October 2008,
MPI report, MPP-2008-192, November 2008.

\bibitem
I.~Potrap, B.~Bittner, S.~Kaiser, O.~Kortner, S.~Kotov, H.~Kroha,
{\itshape Alignment of the ATLAS Muon Spectrometer with Tracks},
proceedings of the $11^{\mathrm th}$ Pisa Meeting on Advanced Detectors, Isola d'Elba, Italy,
24--29 May 2009,
Nucl.~Instr.\ and Meth.~{\bf A617} (2010) 186-187.

\bibitem
B.~Bittner, J.~Dubbert, O.~Kortner, H.~Kroha, F.~Legger, R.~Richter, O.~Biebel, A.~Engl, 
R.~Hertenberger, F.~Rauscher,
{\itshape Development of Muon Drift-Tube Detectors for High-Luminosity Upgrades of the Large Hadron Collider},
proceedings of the $11^{\mathrm th}$ Pisa Meeting on Advanced Detectors, Isola d'Elba, Italy,
24--29 May 2009,
Nucl.~Instr.\ and Methods~\textbf{A617} (2010) 169.
 
\bibitem
%%%%%%%% -> MPP server
B.~Bittner, J.~Dubbert, S.~Horvat, O.~Kortner, H.~Kroha, F.~Legger, R.~Richter, S.~Adomeit, O.~Biebel, A.~Engl,
R.~Hertenberger, F.~Rauscher, A.~Zibell,
{\itshape Development of Fast High-Resolution Muon Drift-Tube Detectors for High Counting Rates},
proceedings of the $12^{\mathrm th}$ Vienna Conference on Instrumentation, Vienna, Austria,
15--20 May 2010, MPI report, MPP-2010-xx, February 2010,
submitted to Nucl.~Instr.\ and Methods.

\end{Biblio}
