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\title{Alignment of the ATLAS Muon Spectrometer with Tracks}
\author{Igor Potrap, Bernhard Bittner, Steffen Kaiser, Oliver Kortner, Sergey Kotov, Hubert Kroha \\ \\ \\
{\it Max-Planck-Institut f\"ur Physik, Munich} }

{\bf Abstract}

%\begin{abstract}
The muon spectrometer of the ATLAS experiment at the Large Hadron Collider 
is designed to measure momenta
of highly energetic muons up to 1~TeV with a resolution of better than $10\%$
in a toroidal magnetic field of superconducting air-core magnets.
This requires alignment of the precision muon tracking chambers
with an accuracy of better then $30~\mu$m in the track bending plane.
An optical alignment system monitors movements of the muon chambers with
a precision of few microns. In order to determine the chamber positions in the
spectrometer, the initial chamber positions have to be measured with $30~\mu$m
accuracy using straight muon tracks from proton-proton collisions in a dedicated
run of the ATLAS detector with the toroid magnets turned off. A global $\chi^2$ minimization 
algorithm determining the misalignment parameters of each
azimuthal sector of the barrel muon spectrometer has been developed and
tested with straight cosmic muon tracks during the commissioning of the ATLAS experiment.
Simulations show that the required alignment accuracy of a sector is reached with only
$10^5$ muons of $p_T > 10$~GeV from the interaction point. Several
barrel sectors have already been aligned with better than $30~\mu$m accuracy using
the cosmic muons tracks. In addition, a new method based on curved tracks has been
developed as an alignment monitoring tool during normal operation of the experiment.
The method uses a muon momentum determination from the angular deflection of the
muon tracks between the inner and outer chamber layer which is independent of the
standard track sagitta measurement.
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