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{\itshape\bf Performance of Drift Tube Detectors at Very High Counting Rates at High-Luminosity LHC}

\vspace{4mm}
B.~Bittner, J.~Dubbert, O.~Kortner, H.~Kroha, A.~Manfredini, S.~Nowak, S.~Ott, R.~Richter, Ph.~Schwegler, D.~Zanzi 

\vspace{1mm}
{\itshape Max-Planck-Institut f\"ur Physik, Munich, Germany}

\vspace{1mm}
O.~Biebel, R.~Hertenberger, A.~Ruschke, A.~Zibell

\vspace{1mm}
{\itshape Ludwig-Maximilians-Universit\"at M\"unchen, Garching, Germany}

\end{center}

\vspace{4mm}
\noindent
The muon detectors of the LHC experiments require high precision tracking
detectors covering large areas. Drift tube detectors provide a robust and
efficient solution even at the high background rates of neutrons and $\gamma$ rays 
experienced in the forward regions of the muon spectrometer of the ATLAS experiment
which is equipped with muon drift-tube (MDT) chambers with 30~mm tube diameter.
For the high-luminosity upgrades of the LHC, the background flux is expected to
increase by almost an order of magnitude compared to the design lumnosity to
about 14~kHz/cm$^2$.

Muon detectors with 15~mm diameter aluminium drift tubes 
filled with an Ar:CO$_2$(93:7) gas mixture at 3 bar
absolute pressure and operated at 2760~V leading to a maximum drift time of
185~ns have been developed.
A complete prototype chamber with 8 layers of 1~m long tubes has been constructed 
with an anode wire positioning accuracy of 16~$\mu$m  
as measured with cosmic rays using precise reference chambers
%~\cite{prototype}. 
Several such sMDT chambers are under construction for the upgrade of the ATLAS
muon spectrometer in the 2013/14 LHC shutdown period. One chamber is already
in operation in the high-background forward region of the muon spectrometer
since the start of the 2012 LHC run.

The high-rate performance of the drift tube chambers has been studied with cosmic rays 
in the Gamma Irradiation Facility (GIF) at CERN in 2011 at background rates up to 1400~kHz/tube
and 8.5~kHz/cm$^2$ and in a high-intensity 20~MeV
proton beam at the Munich Van-der-Graaf Tandem accelerator in 2011 and 2012 up to irradiation rates 
of 2800~kHz/tube and 1330~kHz/cm$^2$, far beyond the background rates expected in the ATLAS
muon spectrometer at high-luminosity LHC upgrades.
With the 3.8 times shorter maximum drift time of 185~ns
the drift-tube occupancy per unit length is reduced by a factor of 7.6. The degradation rate
of the drift-tube spatial resolution due to space charge effects is reduced by more than 
an order of magnitude (see Fig.~\ref{results}, left). The effect of space charge fluctuations
deteriorating the resolution of the 30~mm diameter drift-tube detectors in the ATLAS experiment 

The shorter maximum drift time allows also for a reduction of the
adjustable deadtime of the readout electronics from 790~ns to the minimum of 175~ns
reducing by a factor of 4 the rate of degradation with the background counting rate of the 
$3\sigma$ efficiency (see Fig.~\ref{results}, right), the probability 
for detecting the correct muon hit in a tube within 3 times the drift-tube resolution which is 
the relevant quantity for evaluation of the tracking efficiency.
With signal shaping optimised for 175~ns deadtime with faster baseline restoration than in the present ATLAS MDT chamber
readout electronics used for the tests, an improvement by a factor of 6.5 is expected from 
the simulation (see Fig.~\ref{results}, right).

With not more than 2 times 6 tube layers, a chamber spatial resolution   
of better than $40~\mu$m and a tracking efficiency of better than $99\%$ is achieved 
up to background rates far beyond the rates expected at high-luminosity LHC. At the
latter rates, there is negligible degradation compared to the performance without irradiation. 

\begin{figure}[hbt]
\begin{center}
    \includegraphics[width=0.48\linewidth]{resolution_GIF-Tandem_max.pdf}
    \includegraphics[width=0.48\linewidth]{efficiency_GIF-Tandem_max.pdf}
    {\small\caption{\label{results}Comparison of the single-tube resolution (left) and of the 
     $3\sigma$ efficiency of 0.5~m long drift tubes (right)
     for 15~mm and 30~mm tube diameter. The expected improvement of the efficiency 
     for signal shaping optimised for 175~ns deadtime is also shown. The maximum background rate expected 
     at LHC luminosity upgrades is indicated.}}
\end{center}
\end{figure}



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