\subsection{Muon Spectrometer}
\label{chapter:muons}

\subsubsection{Thin-Drift Tube Chambers}

At high counting rates, the drift tubes of the ATLAS MDT chambers are known to suffer
from a degradation of the spatial resolution due to space-charge effects~\cite{Aleksa,Deile}
and of the muon detection efficiency due to the increased drift-tube occupancy~\cite{Horvat}.
Both effects can be supressed by reducing the tube diameter while leaving the other operating
parameters of the drift tubes, in particular gas mixture, pressure and gas gain, unchanged.

Decreasing the drift-tube diameter from 30~mm to 15~mm and the operating voltage from 3080 to 2730~V
leads to a reduction of the maximum drift time by a factor of 3.5 from about 700~ns to 200~ns~\cite{Bittner}.
In addition, the background counting rate, dominated by the conversion of the neutron and gamma radiation 
in the tube walls, decreases proportional to the tube circumference, i.e.\ by a factor of two per unit tube length.
Both effects together lead to a reduction of the occupancy by a factor of 7.

At a luminosity of $10\cdot 10^{34}$, using a safety factor of 5 on the current background estimates
and assuming an increase of the background flux proportional to the luminosity,
the occupancy of 15~mm diameter drift tubes stays below $25\%$ up to the highest counting
rate of 1150 kHz reached in 1.5~m long tubes in the Small Wheel inner MDT chamber region.
In the CSC chamber region, the maximum counting rate and occupancy increase to 1750 kHz/tube and $35\%$, respectively.
At the same time, at least twice the number of drift-tube layers can be accommodated in the same
detector volume, for example 16 instead of 8 layers in the Small Wheel. Requiring at least 8 hits per track, this
keeps the reconstruction efficiency of correct track segments in a chamber above $99\%$~\cite{Dubbert}.
The expected increase in detection efficiency of 15~mm diameter drift tubes
has been verified by measurements at the CERN Gamma Irradiation Facility (GIF)
with counting rates up to 300 kHz per tube~\cite{Dubbert}.

The space-charge generated by the ion clouds drifting towards the tube wall modifies the
electric field distribution and, therefore, both the drift velocity and the gas gain. 
By lowering the effective potential near the anode wire, high counting rates and space charge
lead to reduced gas gain. The resulting loss in signal height and, therefore, spatial resolution 
grows with the inner tube radius $R_2$
proportional to $R_2^3\cdot \ln (R_2/R_1)$~\cite{Riegler}, with the wire radius $R_1=25~\mu$m,
and therefore is 10 times smaller in 15 mm compared to 30 mm diameter tubes.
Fluctuations of the space charge and, consequently, of the electric field lead to variations of the drift velocity
causing a deterioration of the spatial resolution in non-linear drift gases like Ar:CO$_2$ (93:7)  
where the drift velocity depends on the electric field. The latter effect increases strongly with the 
drift distance above a value of about 7.5~mm while the gain drop effect
dominates at distances close to the sense wire~\cite{Aleksa,Deile}. In addition, 
the space-to-drift time relationship of the Ar:CO$_2$ (93:7) gas mixture becomes more linear at drift radii 
below 7.5~mm leading to reduced sensitivity to environmental parameters such as gas composition 
and density, magnetic field and, in particular, irradiation rate.

Since the drift-tube spatial resolution improves with the drift distance, the average single-tube
resolution at low rates deteriorates from $100~\mu$m for 30~mm diameter tubes~\cite{Deile,Horvat} to about $110\pm 10~\mu$m
for 15~mm diameter tubes~\cite{GIF2009}. For 30~mm diameter drift-tubes, the
resolution has been measured to deteriorate linearly with the counting rate to about $120~\mu$m at 
500~Hz/cm$^2$~\cite{Deile,Horvat}. For 15~mm diameter tubes, the rate dependence of the resolution, 
dominated by the gain drop effect, is predicted to be more than 10 times smaller causing a degradation of the 
resolution by only $20~\mu$m at the maximum counting rate of 5~kHz/cm$^2$ expected at S-LHC.

The baseline design of new thin-drift tube chambers for the endcap regions of the muon spectrometer replacing the
existing precisison tracking chambers in the Small Wheels and the inner part of the Big Wheels 
(see Figs.~\ref{fig_SWlayout} and \ref{fig_chamber})
comprises two multilayers with eight tube layers each separated by an aluminum space frame which closely follows the design
of the supports structures of the present MDT chambers including the in-plane alignment system and the optical sensor
connections to the alignment reference bars. Using at least 8 hits per track, the spatial resolution of these chambers will be
better than $50~\mu$m up to counting rates of 5~kHz/cm$^2$ with a sense wire positioning accuracy of $20~\mu$m as in the 
current MDT chambers.

Central to the chamber design is the development of the tube endplug (see Fig.~\ref{fig_endplug}) which insulates 
the sense wire against the tube wall, centers the wire in the tubes with respect to an external reference surface 
on the central brass insert of the endplug with an accuracy of few microns
and provides interfaces to the gas distribution system and the readout and high-voltage distribution boards 
(see Fig.~\ref{fig_gasmanifold}). 
The tubes are assembled to a chamber using the precision jig shown in Fig.~\ref{fig_jig}.
The 8 tube layers of a multilayer can be assembled and glued together in a single step requiring only one working day. 
A module of $8\times 12$ one meter long drift tubes has been assembled with this procedure and equipped with readout 
electronics (see Fig.~\ref{fig_module}) for the tests in the H8 muon beam and in GIF in 2009~\cite{GIF2009}.
Standard aluminum tubes with 0.4~mm wall thickness and tolerances of $\pm 0.1$~mm on diameter, roundness
and concentricity and of $\pm 0.5$~mm on straightness have been used successfully. Measurements of the module in a cosmic
ray test stand with two MDT reference chambers confirmed the wire positioning accuracy of $20~\mu$m.

\begin{figure*}[!ht]
\centering
\includegraphics[width=\textwidth]{endplug1} 
\caption{Endplug for 15~mm diameter drift tubes with interfaces to gas distribution system and electronics boards. The first injection}
\label{fig_endplug} 
\end{figure*}

\begin{figure}[!h]
\centering
\includegraphics[width=0.5\textwidth]{gasmanifold}
\caption{Gas distribution system for a multilayer consisting of eight layers of 15~mm diameter drift tubes (see text).}
\label{fig_gasmanifold}
\end{figure} 

\begin{figure}[h]
\centering
\includegraphics[width=0.5\textwidth]{jigging}
\caption{Jigging for the assembly of a eight-layer package of 15~mm diameter aluminum drift tubes.}
\label{fig_jig}
\end{figure}
 
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{package}
\label{fig_jig}
\end{figure}

\begin{thebibliography}{1}

% ---------------------------------------------------------------------------- %
\bibitem{Aleksa}
M. Aleksa~{\it et al.}, \emph{Rate Effects in High-Resolution Drift
Chambers, Nucl}. Instr. and Meth. A 446 (2000) 435-443.
% ---------------------------------------------------------------------------- %
\bibitem{Deile}
M. Deile~{\it et al.}, \emph{Performance of the ATLAS Precision Muon
Chambers under LHC Operating Conditions}, Nucl. Instr. and Meth.
A518 (2004) 65-68.
% ---------------------------------------------------------------------------- %
\bibitem{Horvat}
S. Horvat~{\it et al.}, \emph{Operation of the ATLAS Precision Muon
Drift-Tube Chambers at High Background Rates and in Magnetic Fields},
IEEE trans. on Nucl. Science Instr. Vol. 53, 2 (2006) 562-566.
% ---------------------------------------------------------------------------- %
\bibitem{Bittner}
B. Bittner~{\it et al.}, \emph{Development of Muon Drift-Tube Detectors
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Nucl. Instr. and Meth. A (2009), doi:10.1016/j.nima.2009.06.086.
% ---------------------------------------------------------------------------- %
\bibitem{Dubbert}
J. Dubbert~{\it et al.}, \emph{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, Nuclear Science Symposium Conference Record 2008,
IEEE, 2008, MPI report, MPP-2008-191, November 2008.
% ---------------------------------------------------------------------------- %
\bibitem{Riegler}
W. Riegler, \emph{High Accuracy Wire Chambers}, Nucl. Instr. and Meth. A494 (2002)
173-178.
% ---------------------------------------------------------------------------- %
\bibitem{GIF2009}
B. Bittner~{\it et al.}, \emph{Efficiency and Resolution of 15~mm Diameter
Drift Tubes at High Counting Rates},
MPI report, MPP-2010-xxx, January 2010.
% ---------------------------------------------------------------------------- %

\end{thebibliography}
\end{document}
