Autocalibration of high precision drift tubes

We present the results on MDT (monitored drift tubes) autocalibration studies obtained from the analisys of the data collected in Summer 1995 on the H8B Muon Test Beam. In particular we studied the possibility of autocalibration of the MDT using four or three layers of tubes, and we compared the calibration obtained using a precise external tracker with the output of the autocalibration procedure. Results show the feasibility of autocalibration with four and three tubes and the good accuracy of the autocalibration procedure.


Introduction
In the framework of the Atlas muon activities we h a v e performed in the H8B test beam at CERN, measurements using an MDT [1] multilayer of four layers, operated with dierent gas mixtures at three Bar absolute pressure. The main aim of the measurements was to show the feasibility and the accuracy of the autocalibration [2] procedure, and the possibility of autocalibration with only three layers of tubes per multilayer; both problems are of relevance for the design of the Atlas Muon Spectrometer. In the following we present the experimental set up, the autocalibration method, the result of autocalibration obtained using both three and four layers of tubes and the comparison between the MDT Radius-Time (R-T) relation obtained with autocalibration and the one measured with the external tracker.

Experimental set-up
In the H8 beam line at CERN, we h a v e set up a muon test facility equipped with a trigger hodoscope made out of four scintillators (2 2, 44, 1010, 10 10 cm 2 ), two beam chambers and a reference system (external tracker) made out of two matrices of four by four drift tubes, Presented by L.Pontecorvo INFN Roma, c/o Dip. Fisica Univ. Roma "La Sapienza" P.le A. Moro 4 00100 Rome (Italy), fax# +39 6 4957697, e-mail Pontecorvo@vxrm70.roma1.infn.it operated in streamer mode. The muon beam momentum varied between 100 and 180 GeV/c. The data aquisition was based on Spider under the OS9 operating system. We h a v e performed measurements on an MDT made out of four layers containing fteen drift tubes each. The chamber was made of single alluminum tubes 400 m thick, 3.010 cm diameter and 80 cm in lenght. We used 50 m gold plated W-Re wires. We used the following gas mixtures : Ar 94.6 % C 2 H 6 0.4 % CO 2 5% at a pressure of 3 Bar absolute. The tubes were operated in proportional mode at 3.1 KV. The front end electronics was based on the VTX chip [3], the amplication was 1 mV/fC and the peaking time 8 ns. After the preamplication board there wa s a v oltage amplier and discriminator card in wich the signal was amplied by a factor of ten and then discriminated. The discrimination threshold was set quite high (300 mV) due to noise and cross talk problems between channels, corresponding, at a tipical gas gain of 410 4 , to about 100 electrons. Finally the discriminated ECL signals were fed in a LeCroy 2277 TDC with a LSB of 1 ns and a range up to 64 s. Some signals were split before the discriminator and were sent to a LRS 2249W ADC to measure the charge spectra and the streamer fraction.

Autocalibration method
The aim of autocalibration is to obtain the R-T relation, the position of the wires and the zero time (T0s) from the data of the tubes themselves without the help of external detectors. To obtain this we used an iterative procedure in which w e rst get the 0-approximation of the R-T relation using the well known technique of the integration of the time spectrum, assuming a uniform illumination of the tubes [4]; then using it we t the tracks in the detector and we measure the systematic error of the current R-T relation from the value of the residuals vs the drift time in the tubes. The 1-approximation of the R-T relation is then obtained correcting the 0-approximation with the value of the systematic error measured at each drift time. This procedure is iterated until the dierence between the n-approximation and the n-1 approximation of the R-T relation is negligible. The T0s of each wires is set at the beginning of the procedure to the value of the rise of the time spectrum, known with an accuracy of few ns. The rst approximation position of the wires is given by their nominal geometrical position; a better determination of the T0s and of the wire positions is obtained during the iterative procedure studing the residuals of the track t separately for tracks crossing the tubes on the upper and the lower side of the wires. An error on the T0 is reected in a separation of the up and down residuals by the quantity: T0 = ( Res up Res down ) where V drift is the average drift velocity in the tube. After this correction the accuracy on the T0s is about 300 ps. The same technique is used to determine the error on the position of the wires with an accuracy of about 10 micron (assuming no systematic error introduced by the tting procedure): One of the problem in the autocalibration procedure is the setting of the absolute scale of distances. Usually this is done using the end point o f the time spectrum and assuming that this correspond to the physical dimension of the detector. This approach is not very precise because of several reasons: 1) it is always quite dicult to precisely determine the end point of the time spectrum; 2) the tube geometrical dimensions could be dierent from the dimension where the tube is really ecient and 3) the time spectrum could be distorted close to the end wall of the detector by the presence of electrons. To o v ercame this difculties we h a v e used a dierent approach. From our geometry and from the fact that the tracks are almost perpendicular to the detector it is easy to see that tracks crossing the rst tube at R/2, where R is the geometrical tube radius, will cross all the other tubes almost in the same position. In this condition it is possible to select all the tracks passing at the center of the tubes asking that the drift time of the tubes being nearly equal ( 5 ns). In this way w e obtain a gaussian distribution of drift time correspondig to a drift distance equal to R/2 Fig (1), which sets the absolute scale with high precision. Another common problem of the autocalibration method is due to the least square tting procedure in presence of systematic errors coming from the R-T relation. It is possible to demonstrate that the reconstruction of a track, obtained using four measured points all aected by systematic errors of the same magnitude, results in a wrong reconstructed direction of the track while the intercept of the track in the mid plane of the detector is not aected. To correct for this we h a v e used dierent w eights in the t for the dierent measured points, namelly the two outer layers' weight is set to 1 while the internal layers' weight is set to 3. In the case of three tube autocalibration the situation is dierent, in fact the direction of the reconstructed track is not affected by the systematic errors on the measured point while the intercept at the central plane of the detector is wrong. In this case the weights used are 1 for the external layers and 2 for the internal one. This weighting technique is used only in the autocalibration procedure and not during the track tting after calibration.

Result on external trackers
The external tracker is made of two identical detectors each of which consist in a matrix of 4 4, 500 m thick alluminum drift tubes, 3.030 cm diameter, 30 cm long, wired with a 100 m alluminum wire. The gas mixture used was 60% I-Butane and 40% Argon at normal pressure, the high voltage was set to 5200 V, the detector was operated in streamer mode. The readout chain for each c hannel consisted simply in a discriminator whose threshold was set to 30 mV, and a LRS 2277 TDC. We h a v e autocalibrated the two trackers using the procedure previously explained on groups of four aligned tubes (quadruplet). Using the 0-iteration R-T relation we measure the residuals Fig (2) with respect to the tted tracks for each tube dened as: (3) From this gure we see that the systematic error on the 0-iteration R-T relation is as high as 500 m, and is rapidly varing with the drift time; at the distance of R/2, the error is zero by denition because that point w as used to set the space absolute scale. In Fig (3) we present the situation of the residuals of the four tubes after the rst iteration. The residual distribution vs the drift (4) where Y n meas indicates the measured distance in tube n, and R, in our geometrical situation should be equal for each e v ent, to the distance between the wires of two staggered planes. We see that the mean value of this distribution 1.514 cm is in very good agreement with what expected from the tracker mechanical construction, proving the good accuracy of the absolute distance scale. We have repeated the procedure for other two iterations and the measured R-T relation shows no relevant dierence with the previous ones, indicating the very fast convergence of the autocalibration procedure. We h a v e applied the autocalibration procedure to dierent quadruplets in the rst and the second tracker obtaining always consistent results, so that we can use a single R-T relation for each detector (there is a small systematic dierence between the R-T relation of the two trackers). We h a v e also studied the variations with time of the R-T relation nding it very stable. After the calibration procedure we h a v e t tracks in the two detectors separately, using an average single point resolution of 65 m, the resulting distribution of the 2 probability Fig (4) is at showing the good space accuracy of the single tubes. After aligning the two detectors we have t tracks using both trackers. The two detectors were set at a distance of about 9 metres on the beam line to assure a good determination of the direction of the beam tracks. Unfortunatelly, due to the presence on the beam line of material (radioactive source shielding) introducing a large multiple scattering, the precision of the interpolation of the tracks on the MDT in between the two trackers is not very accurate (' 300 m) because of the big distance between the two trackers.

Results on MDT
A t ypical time spectrum for an MDT tube is shown in Fig (5). We notice that the rise of the spectrum is rather slow because of the high threshold used. It gives problems in the rst determination of the T0s and introduces a dead region close to the wire (' 1 mm). The residuals vs the drift time using the 0-iteration R-T relation are shown in Fig (6), also in this case we see the big systematic errors due to the wrong 0-iteration R-T relation. After few iterations the autocalibration procedure converges and the residuals vs drift time, shown in Fig (8), are at and centered to zero. The distribution of the variable (Y 1 meas +Y 3 meas )/2+Y 2 meas is centered to 1.504 cm showing again the precision of the abso- lute space scale. After the calibration procedure we t tracks in the MDT, the resulting distribution of the 2 probability is at using an average single point resolution of 110 m. The resolution is mainly limited by the high threshold used, infact our resulution gure is in good agreement with the resolution calculated by a detailed simulation of the drift tube response [5] in which the threshold was set to 100 electrons.

Three vs four tubes autocalibration
We h a v e repeated the calibration procedure on both the external tracker and the MDT using only three contiguous tubes instead of four tubes and we h a v e compared the resulting R-T relations bin by bin. The R-T relations obtained with the two procedures give v ery similar results on the whole drift distance (about 10 m dierence) except close to the wire and to the end wall of the tube where we notice a peak structure of about 40 m in the R-T relations dierence. We still have t o i n v estigate the nature of this systematic dierence, but from the practical point of view we think that it is not relevant because it inuences a v ery small part of the tube where anyway the space resolution is quite degraded ( 100 m).

Comparison between autocalibration and external tracker calibration
The easiest way to measure the R-T relation for a drift tube is to use a precise tracking detector to determine, event b y e v ent, the distance of closest approach of a track to the wire of the tube, and to correlate it with the corresponding drift time. We used our external tracker to dene tracks inpinging on the MDT and we measured the R-T relation for the MDT tubes in an independent way with respect to the autocalibration procedure. The distribution of the dierence between the distance of closest approach dened by the external tracker and the one measured using the autocalibration is shown in Fig(8). The width of this distribution ('300 m) is due, as previously stated (cfr 4), to multiple scattering on the source shielding. We see that there is a good agreement between the two R-T relations in the whole tube apart from a region of 1.5 mm from the wire and the corresponding region close to the tube wall. This systematic error is due to the high threshold used for the MDT; this is explained in the following. Consider a track crossing the tube right on the wire, then ideally the measured time and distance from the wire would be zero. Now i f w e set a threshold of N electrons and a crossing muon produces M electrons/cm wich drift toward the wire with a constant v elocity V drift the minimum time detectable will be the time needed by N electrons to reach the wire: the factor 2 being due to the fact that the electrons are produced on both sides of the wire. Correspondigly all the tracks passing very close to the wire will be reconstructed at a minimum distance from the wire given by: In our case, with a threshold of 100 electrons, 300 electrons/cm produced and an average drift velocity V drift of about 30 m/ns the minimum distance from the wire is 1.6 mm and the minimum time to collect the 100 electrons is about 50 ns. Those values gives us respectively the size of the zone interested by the sistematic error in the R-T relation obtained with the autocalibration procedure and the slowness of the rise of the time spectrum for the MDT.

Conclusions
During the summer 1995 we h a v e set up and succesfully operated a muon test facility in the H8B zone, where we made measurements on one MDT prototype. The focus of our studies was centered on the autocalibration procedure used to calibrate both the MDT prototype and a set of drift tubes used as a precision external tracker.
The results on the tracker shows the very good spacial resolution of this device, 65 m each single point , and the fast convergence of the autocalibration procedure. The MDT results shows a resolution of about 110 mm and also in this case the convergence of the calibration procedure is very fast. We demonstrated the possibility of autocalibrating the tubes using three layers of tubes showing that there is a very small dierence between the R-T relations obtained using three or four layers. Eventually we c hecked the autocalibration procedure comparing the R-T relation for the MDT measured using the external tracker with the one obtained by autocalibration. For the whole drift distance, except for a small region close to the wire and the end wall, the two R-T relation are in good agreement, showing the correctness of the autocalibration procedure.