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Streamlined Calibration of the ATLAS MuonSpectrometer Precision Chambers

Daniel S. Levinfor the ATLAS Muon Collaboration

Randall Laboratory, University of Michigan

Abstract—The ATLAS Muon Spectrometer is comprised ofnearly 1200 optically Monitored Drifttube Chambers (MDTs)containing 354,000 aluminum drift tubes. The chambers areconfigured in barrel and endcap regions. The momentum res-olution required for the LHC physics reach (dp/p = 3% at10% at 100 GeV and 1 TeV) demands rigorous MDT drifttube calibration with frequent updates. These calibrations (RTfunctions) convert the measured drift times to drift radii and area critical component to the spectrometer performance. They aresensitive to the MDT gas composition: Ar 93%, CO2 7% at 3 bar,flowing through the detector at a rate of 100,000 l hr−1. We reporton the generation and application of Universal RT calibrationsderived from an inline gas system monitor chamber. Resultsfrom ATLAS cosmic ray commissioning data are included. TheseUniversal RTs are intended for muon track reconstruction inLHC startup phase.

I. INTRODUCTION

THis paper reports on the production of drift-time todrift-radius RT functions derived from the ATLAS muon

spectrometer Gas Monitoring Chamber (GMC), their use inthe spectrometer cosmic ray commissioning runs and theanticipated application in muon track reconstruction duringthe initial phase of LHC beam collisions. The ATLAS muonspectrometer[1] is a cylindrical detector 45 m long and 22m diameter and comprises nearly 1200 Monitored Drift Tube(MDT) chambers in a toroidal, air-core, 0.6 T magnetic field.Calibration of these chambers is an ambitious undertakinginvolving the combined efforts of three Tier-2 calibrationcenters[2] which have been established to process data from adedicated calibration data stream. During normal LHC runningthese centers are expected to produce sets of calibrationconstants with a 24 hour latency. However this calibrationprocessing is resource intensive and requires adequate hitstatistics (several thousand tracks per chamber) for optimalperformance. An alternative, streamlined calibration source isoffered by the GMC. This choice is especially appropriateduring the initial low luminosity LHC phase when muon eventrates are expected to be low.

The GMC performs two tasks: First, it continuously ana-lyzes the MDT gas drift spectra and provides hourly updatesof gas quality[3]; Secondly, it generates twelve times daily aUniversal RT (URT) calibration function corresponding to astandard temperature and pressure of 20 C0 and 3000 mbar.This URT function represents a calibration anchor for theMDT gas at any time[4]. With appropriate compensation for

Randall Lab, University of Michigan

the local spectrometer chamber temperature and pressure, andwhere appropriate, for the magnetic field, the compensatedURT can serve as an effective calibration and used directly forthe track reconstruction. As these URT functions are producedas a byproduct of the normal gas monitoring task, they conveya convenient calibration source whose production requiresminimal computational resources.

II. DRIFT TIME

The spectrometer’s precision coordinate is transverse to thechamber plane and is determined by the radial distance tothe anode wire of a charged particle track passing througha drift tube. Ionization electrons accelerate towards the wire,initiating an avalanche and yielding a signal. The drift timeis defined as the time of arrival at the wire of the first driftelectrons along a trajectory corresponding to the distance ofclosest approach to the passing ionizing particle. This drifttime is the primary measured physical quantity in the MDTsystem. Part of deposited charge is also read out, but notconsidered further here. Technically the readout time is thediscriminator threshold crossing time of the anode signal col-lected by chamber mounted front-end readout electronics[5].The drift time is this threshold crossing relative to that of azero impact parameter track, one passing at the wire. The drifttime of track passing a the wire is called a T0 and representsa timing offset. Generally each tube or electronics channelis characterized by a specific T0, which is a function of theaggregate cable delays and particle times of flight.

A. Drift time calibration

The drift radius is computed from the drift time by meansof a time-to-space function, commonly referred to as an RTfunction. The RT function is expressed as a lookup tablespecifying the drift radii corresponding to drift times. Toachieve optimal resolution over the entire spectrometer theRT functions must be tuned to local chamber conditions:gas composition, temperature, pressure, magnetic field andhigh voltage. Ideally the RT function is determined for aregion over which conditions are homogeneous. The varia-tion of drift times due to changes in these parameters areestimated from Garfield simulations[6] and are validated bymeasurement[7][8]. In ATLAS, the local chamber environmen-tal conditions are measured from embedded sensors. Thereforechanges in the drift spectra, after accounting for perturbationsin temperature and pressure are attributable to variations in

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the gas composition. Other factors such as the magnetic fieldstrength and applied high voltage are tightly constrained anddo not exhibit significant temporal variations.

The calibration of the drift tubes is done with autocalibrationalgorithms which operate, as noted above, on groups ofchambers for which the environmental conditions are homo-geneous. In practice these regions generally correspond to asingle chamber or chamber multilayer. The frequency at whichcalibrations should be updated can be guided by the outputfrom gas monitoring. In this way determination of the overallhealth of the MDT gas mixture is a central component to thiscalibration program.

III. THE MONITOR CHAMBER

The GMC[9] utilizes the same type of 3.0 cm outer diameterdrift tubes employed in the spectrometer. 96 tubes are gluedinto a pair of three-layer multilayer arrays with overall dimen-sions 50 cm wide × 70 cm length × 21 cm deep. While muchsmaller than ATLAS muon spectrometer chambers, the cham-ber construction mirrors that of conventional chambers. Thedrift tubes were manufactured and assembled into a chamberat the University of Michigan using the same tooling used toproduce the ATLAS Endcap tubes[10] and chambers[11] ofthe MDT system.

The GMC is thermally insulated with temperatures varying1◦C. Multiple temperature sensors provide precise thermalmonitoring with 0.1◦ C precision, used to correct the measureddrift times to those of a 20◦C equivalent gas. Similarly,pressure sensors placed at the output and input gas ports enablegas pressure measurements with a relative precision of 1 mbar.With thermal and pressure variations removed, any change inthe measured drift spectra or RT functions are characteristicof the drift gas composition.

Spectrometer gas monitoring is achieved by strategic place-ment of the GMC in the ATLAS gas facility, a surface buildinglocated 100 m above and 50 m displaced from the detectorcavern. The GMC samples gas from the MDT supply andreturn gas trunk lines at the beginning and end of a 300m round trip to the subterranean gas manifolds feeding thespectrometer. The MDT gas system supplies and exhaustsall chambers in parallel,therefore the gas in the two monitorpartitions is representative of the gas in all chambers in thespectrometer. The GMC supply and return lines are connectedthrough flow controllers to two independent gas partitions. TheGMC acquires cosmic ray muon data from a scintillator triggerat 15 Hz. Every hour ∼ 50000 tracks are collected duringwhich time the gas volume has been mostly flushed.

The analysis of the drift spectra are expressed as a setof fit parameters characterized by the gas conditions underwell-controlled conditions of temperature and pressure. Inparticular, the maximum drift time, Tmax(spectrum) is a sin-gle parameter representing the average electron drift velocityacross the tube radius. After the effects of temperature andpressure are compensated, Tmax(spectrum) is very sensitiveto the gas composition. An addition of 100 ppm of water vapor,for example, increases the Tmax by ∼ 7 ns. An observedvariation in Tmax signals a change in composition and issues

an alarm for recalibration. The GMC runs independentlyand acquires data asynchronously from ATLAS and producesoutput rapidly and continuously: Drift time measurements aregenerated hourly and RT functions are computed bi-hourly.

IV. MEASUREMENT OF MAXIMUM DRIFT TIME

The Tmax(spectrum) is determined by fitting the risingand trailing edges of the drift spectra (Figure 1). These fitsuse modified Fermi-Dirac functions of the form: f(t) =

A+D×t(1+e(B−t)/C)

The 50% point of the rise/fall is B, C is therise/fall time and D allows for a small slope before thetail of the distribution. For fits to the rising edge D isset to zero. Operationally, the difference of the parameterscorresponding to the 50% rise/fall defines Tmax(spectrum):Tmax(spectrum) = Btrailing − Brising When all 48 tubesfrom one chamber partition are combined into a singlespectrum, about 150,000 histogram entries per partition areaccumulated per hour. The resultant statistical error on a singleTmax(spectrum) measurement is 0.6 ns.

Fig. 1. Drift time spectrum showing the fit to rising edge and tail,corresponding to tracks passing at the wire and tube wall respectively.

A. Drift time monitoring results for 2009

The GMC has been in nearly continuous operation withnegligible downtime since September, 2007. Over more thana two years, a reliable image of the MDT gas system perfor-mance has been established. Figure 2 reports the gas systemperformance for a 4 month period. Several features are evident.The Tmax(spectrum) is observed to vary on any time scalefrom one day to over a month. The variations are due primarilyto the change in water vapor in the gas mixture. The sourceof the water is from ambient humidity and intentional waterinjection to nominal level of 1000 ppm. Variation can be 1 to2 ns on daily scale to tens of ns over a week or more.

V. GENERATION OF RT FUNCTIONS

RT functions are the transfer functions relating the driftradius R to the drift time T via the electron drift velocity:vdrift = dR/dT . They are determined from an iterative

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Fig. 2. Trend of maximum drift time over a four month period: May-August2009.

autocalibration algorithm. The algorithm commences with anensemble of about two hours data, yielding 90000 tracks. Theaverage track residuals from this collection are determinedat each of 100 radial bins spanning from the tube wire totube wall. These residuals are then used to correct an initialestimated RT to produce the next generation. This procedureis repeated until no further convergence. Convergence is mea-sured as a change in the Tmax, the drift time at a radius equalto the tube inner diameter.

Autocalibration takes as a starting point an approximationof the desired RT function. This initial function can be an RTdetermined under different gas conditions or can be deriveddirectly from the the integral of the drift spectrum dN/dT ,and assuming a uniform flux, dN/dR=constant: dR/dT =dR/dN × dN/dT . In normal running mode the starter RTis simply the previously computed RT from an earlier dataset.An example of an RT from an MDT chamber is shown inFigure 3. Such functions are output every two hours fromthe gas monitor. A composite daily function is compiled atmidnight each day and is comprised of the average of theprevious 12 RTs generated during the previous 24 hours.

Fig. 3. Example of RT function obtained from the gas monitor for 93% Ar,7% CO2, 3 bar and 20◦ C

1) Self-Test of RT Generation: For each RT function com-puted from gas monitor data, a Tmax(RT ) is defined asthe drift corresponding to the tube radius. This RT derivedmaximum drift time is expected to track the Tmax(spectrum).Figure 4 reports the difference: Tmax(RT )−Tmax(spectrum)over one month. Aside from an offset, the result of differ-ent operational definitions of the maximum drift time, theTmax(RT ) tracks the Tmax(spectrum) quite well.

Fig. 4. Difference of Tmax(RT )−Tmax(spectrum) over 4 month interval.

A. Temperature Corrections

The URT described above represents the nominal calibrationfor standard temperature and pressure. While the actual MDTgas pressure is regulated to be within a few mbar of 3000 mbar,many MDT chambers have temperatures that deviate from 20◦

C. Figure 5 shows the distribution of temperatures within themuon spectrometer. Each measurement is an average of severalon-board sensors. The vertical gradient is nearly 7◦ over 22m. These temperature variations introduce a timing correctionwhich has been calculated using Garfield[6], and is shown inFigure 6. This curve is computed for a 1.2◦C increase. It isscaled by the measured deviation of the chamber temperaturefrom 20◦, then applied bin by bin to the RT function to obtainthe chamber specific RT.

Fig. 5. Distribution of temperatures within the muon Spectrometer. Thevertical gradient is nearly 7◦ over 22 m.

Figure 7 which shows the residual distribution as a functionof drift radius for two RTs: One is the Universal RT, the second

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Fig. 6. Garfield calculation of the change in drift time as a function of driftradius for a 1.2◦ increase from 20◦.

after it has been corrected to the measured MDT chamberaverage temperature of 24◦C. The temperature corrected RTsyield residuals which are quite flat across the tube radius,and whose mean values fall mostly within a 20 micron errortolerance for the MDT calibration error budget.

Fig. 7. Application of a temperature corrected RT to cosmic ray commis-sioning data: This plot shows hit residuals as a function of drift radius for achamber at 24◦C using the universal RT without (black) and with (red) thetemperature compensation to the drift time.

VI. RESULTS: APPLICATION OF URTS TO ATLAS COSMICRAY COMMISSIONING DATA

An effective test gas monitor URTs is established by thequality of track segment reconstruction in a large ensembleof MDT chambers. the preferred metric for this test is theresiduals. This residual is defined as the radial distance ofa given tube hit, normally considered to be part of the track,from the best fit track segment where the tested hit is excludedfrom the fit. The hit residual serves as a conservative proxy ofthe tube resolution. The residual width is the convolution ofthe intrinsic resolution and the fit extrapolation/interpolationerror. The residual distribution is fit with a double Gaussianfunction.

An example of the hit residual distribution for a singleendcap chamber is shown in Figure 8 and in Figure 9. The98 micron width of the narrow Gaussian is comparable toresults obtained with direct autocalibration produced RT usingthe chamber data. Other factors discussed below, specific tothe cosmic ray commissioning data, contribute to resolution

Fig. 8. Hit residual distribution for a single endcap chamber. The narrowgaussian width is 98 microns.

Fig. 9. Hit residual distribution as a function of drift radius for a singleendcap chamber.

smearing. The result in Figure 8 indicates that the chamber iscalibrated to near the design resolution.

An important test of the URT is its application to all ofthe spectrometer MDT chambers. The performance of a largeensemble of spectrometer chambers is extracted from fitssimilar to Figure 8. A single overnight cosmic ray run fromthe Fall of 2008 was analyzed. Muon events are triggered bythe resistive plate chambers (RPCs)[1] in the barrel region.The acceptance of the RPCs in these cosmic ray runs alsocovers many endcap MDT chambers. Chambers having morethan 2000 segment hits were fit with double gaussians, andthe width and means of the narrow Gaussian were extracted.

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These results are shown in the meta-histograms: Figure 10and in Figure 11. The 4 micron means of the residuals arevery close to zero and within allowable error tolerance. Thepeak of the distribution of residual widths is at 107 micronsand about 90% of chambers have widths under 140 microns.We note that additional sources of uncertainty associated withcosmic ray runs reported below limit the minimum resolutionobtainable.

Fig. 10. Distribution of narrow Gaussian mean values of individual chamberhit residual distributions.

Fig. 11. Distribution of narrow Gaussian widths of individual chamber hitresidual distributions.

A. Contributing factors to residual width broadening

Three factors unrelated to the accuracy of the RT functioncombine to broaden the residual distributions reported here.The first is a 25 ns trigger timing jitter characteristic of allcosmic ray commissioning data. This jitter directly degradesthe T0 drift time pedestal offset. It is partially removed by aT0 tuning algorithm, but the resultant timing jitter is estimatedto be 2 ns. Secondly, cosmic tracks are not constrained to passthrough the beam interaction point and in many chamberscan have different hardware trigger pathways. This distortsthe rising edge of many chamber drift spectra and rendersthe associated T0, which is determined from a rising edgefit, very uncertain. Lack of a well-fit T0 in these cases

significantly degrades the resolution. Thirdly, in all instancespresented here, for lack of a sufficient number of tracks, asingle uniform T0 is obtained for an entire chamber and notseparately for each tube. In summary, uncertainties in the tube-specific T0s are estimated to exist at the 3 ns level or larger.On average this results in ∼ 60 micron resolution smearing.Added in quadrature with the 80 micron intrinsic resolutionyields approximately 100 microns.

VII. CONCLUSION

This report describes a streamlined daily production of RTfunctions which will provide an initial calibration source forthe ATLAS muon spectrometer precision chambers. Thesefunctions are generated daily with temperature correctionsspecific to each chamber. Cosmic ray commissioning datasuggest that nearly all chambers using these RT functionsexhibit residual distributions centered within 4 microns ofzero, with residual widths of 100 microns, consistent with orapproaching design expectations.

REFERENCES

[1] ATLAS Collaboration, ATLAS Muon Spectrometer Technical DesignReport, CERN/LHCC/97-22 31 May, 1997.

[2] F. Petrucci, Calibration Software for the ATLAS Monitored Drift TubeChambers,NSS/MIC 2005 , San Juan, El Conquistador Resort, PuertoRico , 23 - 29 Oct 2005 - pages 153-157 Geneva: CERN, 2004

[3] N. Amram et al Long Term Monitoring of the MDT Gas Performance,IEEE-NSS Dresden, Germany N53-3 October 2008

[4] D.S. Levin for the ATLAS Muon Collaboration Calibration of the ATLASMuon Precision Chambers with a Universal Time-to-Space FunctionIEEE-NSS Dresden, Germany N30-192 October 2008

[5] E. Hazen et al., Production Testing of the ATLAS MDT Front-End Elec-tronics 9th Workshop on Electronics for LHC Experiments, Amsterdam,The Netherlands, 29 Sep - 3 Oct 2003, pp.297-301

[6] R. Veenhof GARFIELD CERN Program Library, W5050; Geneva: CERN[7] M. Cirilli Drift Properties of Monitored Drift Tubes Chambers of the

ATLAS Muon Spectrometer IEEE Transactions on Nuclear Science, Vol51, No. 5, October 2004

[8] F. Cerutti et al Study of the MDT Drift Properties Under Different GasConditions ATL-MUON-PUB-2006-004; Geneva : CERN, 03 Feb 2003

[9] D. S. Levin et al Drift Time Spectrum and Gas Monitoring in the ATLASMuon Spectrometer Precision Chambers, Nuclear Inst. and Methods inPhysics Research A Vol 588/3 pp 347-358

[10] S. Mckee, J.W. Chapman, T. Dai, E. Diehl, C. Ferretti, D.S. Levin,R. Thun, Z. Zhao, B. Zhou Long Precision Drift Tube Production atMichigan, ATL-MUON-2005-011,ATL-COM-MUON-2002-012, CERN-ATL-COM-MUON-2002-012.- Geneva : CERN, 2002

[11] Diehl et al, Michigan ATLAS MDT Chamber Mass Production, ATL-MUON-2002-006; Geneva CERN, 2001