\documentclass[a4paper,12pt]{article}
\usepackage{a4}
%\usepackage{ieee_tns}
\usepackage{epsfig}

\def\dj{d\hskip-.4em\hbox{\char'26}\hskip-.1em}
\def\Dj{D\hskip-.8em\lower.4ex\hbox{\char'26}\hskip.3em}

\oddsidemargin 0.1cm
\evensidemargin 0.1cm
\setlength{\textwidth}{17.0cm}
\setlength{\textheight}{25.0cm}
\setlength{\topmargin}{-0.5cm}

\begin{document}

\begin{center}

{\bf \large Operation of the ATLAS Muon Drift-Tube Chambers at
High Background Rates and in Magnetic Fields}\\
\vspace{4mm}

S. Horvat, O. Kortner, H. Kroha, S. Mohrdieck-Moeck,
R. Richter, W. Stiller, Ch. Valderanis
\vspace{2mm}

{\small Max-Planck-Institut f\"ur Physik, F\"ohringer Ring 6, D-80805 Munich, Germany} \\
\vspace{4mm}

J. Dubbert, F. Rauscher, A. Staude
\vspace{2mm}

{\small Ludwig-Maximilians-Universit\"at M\"unchen, Am Coulombwall 1, D-85748 Garching, Germany}

\end{center}
\vspace{4mm}

For the muon spectrometer of the ATLAS detector at the Large Hadron Collider 
(LHC), large drift tube chambers, the Monitored Drift Tube (MDT) chambers,
are used for precision tracking in the toroidal 
field of superconducting air core magnets. The MDT chambers consist of two
triple- or quadruple-layers of aluminum drift tubes with 30~mm diameter and
0.4~mm wall thickness mounted on either side of an aluminum space frame
containing optical deformation monitoring systems.
In order to achieve a momentum resolution of better than $10\%$ up to muon momenta 
of 1~TeV, the chambers have to provide a spatial resolution of $40~\mu$m.
With a positioning accuracy of $20~\mu$m of the sense wires within a chamber,
the spatial resolution of a drift tube has to be better than $100~\mu$m
using an Ar:CO$_2$~(93:7) gas mixture at 3 bar and a gas gain of $2\cdot 10^4$.
%
\begin{figure}[h]
\begin{center}
\mbox{\epsfig{figure=/home/iwsatlas1/kroha/pictures/x5_setup_2004.eps,
width=1.00\linewidth}}
\end{center}
\caption{The experimental setup at the Gamma Irradiation Facility at CERN with
a 740~GBq~$^{137}$Cs $\gamma$ source and with
a MDT chamber and a silicon strip detector telescope in the 100~GeV muon beam.
The magnetic field of up to 1~T is oriented parallel to the drift tubes.
\label{setup}
}
\end{figure}
%
%
\begin{figure}[h]
\begin{tabular}{cc}
\begin{minipage}{0.48\textwidth}
\mbox{\epsfig{figure=/home/iwsatlas1/kroha/pictures/x5_res_r.eps,
width=0.98\linewidth}}
\end{minipage} &
\begin{minipage}{0.48\textwidth}
\mbox{\epsfig{figure=/home/iwsatlas1/kroha/pictures/x5_resolution.eps,
width=0.98\linewidth}}
\end{minipage} \\
\end{tabular}
\caption{Left: Spatial resolution of the driftc tubes as a function of the 
impact radius $r$ of the muon track for different photon irradiation rates. 
Right: Average drift tube resolution as a function of the irradiation
rate with and without time slewing corrections.
\label{resol}
}
\end{figure}
%

In the ATLAS experiment, the muon chambers will experience unprecedentedly 
high neutron and photon background count rates which have a significant impact on
their performance. At the LHC design luminosity of
$10^{34}$~cm$^{-2}$s$^{-1}$, count rates of up to 500~Hz/cm$^2$ have to be expected
in the inner forward layers of the muon spectrometer. Variations of the magnetic
field strength across chambers close to the toroid coils can be up to 0.4 T.
The space-to-drift time relationship of the drift tubes varies not only with 
temperature and magnetic field strength, but also with the background count rate.
It has to be recalibrated in short time intervals with the required accuracy of better
than $20~\mu$m using muon tracks (autocalibration).

The resolution and efficiency of the MDT chambers with the final readout electronics,
using bipolar shaping and a fixed deadtime of 800~ns,
has been studied in a 100~GeV muon beam at the Gamma Irradiation Facility at CERN for
varying magnetic fields and photon irradiation rates of up to 990~Hz/cm$^2$ (see Figure~\ref{setup}).
A silicon strip detector telescope at a distance of 60~cm from the chamber was used as 
external reference in the beam.
Efficient autocalibration algorithms have been developed
and tested under the high background conditions.

The drift tube resolution as a function of the impact radius of the muon extrapolated
from the silicon detector telescope is shown in Figure~\ref{resol} (left) for increasing
photon irradiation rates. The photon irradiation induces a space charge in the drift tubes 
which alters the electric field and the drift velocity in the Ar:CO$_2$ gas. Fluctuations
of the space charge cause a deterioration of the spatial resolution which is most pronounced 
at large impact radii. 

Without photon irradiation, an average drift tube resolution of $80~\mu$m is
achieved by employing time-slewing corrections based on the pulse height measurement
provided by the readout electronics (see Figure~\ref{resol}, right).
The spatial resolution of the drift tubes is found to deteriorate linearly with
increasing background count rate. At the maximum expected rate in ATLAS of 500~Hz/cm$^2$,
the resolution is degraded by not more than $25~\mu$m which is compatible with the design goals.
The probability of a drift tube to detect a muon hit decreases linearly with increasing
count rate as expected from the fixed deadtime. At the maximum rate, 
the efficiency loss amounts to $25\%$.

The results are reproduced by detailed simulations of the drift tube response.
The consequences and possible improvements for the operation of the chambers 
at even higher LHC luminosities and background rates have been investigated.
\end{document}
