On the space resolution of the μ -RWELL
G. Bencivenni, G. Cibinetto, R. de Oliveira, R. Farinelli, G. Felici, M. Gatta, M. Giovannetti, L. Lavezzi, G. Morello, A. Ochi, M. Poli Lener, E. Tskhadadze
aa r X i v : . [ phy s i c s . i n s - d e t ] J u l Prepared for submission to JINST
On the space resolution of the µ -RWELL G. Bencivenni, a G. Cibinetto, b R. de Oliveira, c R. Farinelli, b G. Felici, a M. Gatta, a M. Giovannetti, a , d L.Lavezzi, b G. Morello, a , A. Ochi, e M. Poli Lener, a E. Tskhadadze a , fa Laboratori Nazionali di Frascati dell‘INFN,Frascati, Italy b INFN Ferrara,Ferrara, Italy c CERN,Meyrin, Switzerland d University of Rome “Tor Vergata”,Rome, Italy e Kobe University,Kobe, Japan f Technological Institute of Georgia,Tbilisi, Georgia
Abstract:
In MPGD detectors evaluation of the space resolution with the charge centroid (CC) methodprovides large uncertainty when the impinging particle is not perpendicular to the readout plane. Animprovement of the position reconstruction, and thus of the space resolution, is represented by the µ TPCalgorithm. In this work we report the application of this algorithm to the µ -Resistive WELL detector.Moreover a combination of the CC method with the µ TPC algorithm is proposed, showing an almost uniformresolution over a wide angular range.
Keywords:
Gaseous detectors; Micro-Pattern Gaseous Detectors; Gas Electron Multiplier; Resistive detec-tors; micro-Resistive WELL; Diamond-Like-Carbon; µ TPC mode. Corresponding author. ontents µ uTPC algorithm 14 Results 25 Conclusions 6A Consideration upon the double gaussian fit 6 Space resolution in MPGD can be affected by several factors: primary statistics, electrons diffusion in gas,readout geometry, Front-End Electronics (digital or analog FEE) and impinging angle θ of the crossingparticle with respect to the normal to the readout electrode (fig. 1). Indeed the larger is the angle the worseis the resolution σ x usually evaluated with the charge centroid method. For an experiment this means anot uniform resolution in the solid angle covered by the apparatus and results that can be consequentlycharacterized by large systematic errors. The first four factors are usually optimized with a dedicated R&Don detector geometry, gas mixture and FEE while for the last factor a new reconstruction algorithm [2] hasbeen proposed to improve the resolution whatever the angle θ . This work describes the implementation ofthe algorithm to the µ -RWELL [1]. For a detector equipped with a strip-segmented readout and instrumented with analog FEE, when a set ofstrips is fired the position of the track can be computed as X CC = Í x k q k Í q k (2.1)where x k is the coordinate of the k -th strip and q k is its integrated charge. The uncertainty associated to thisposition is strongly dependent on the impinging angle ( θ ) of the track (fig. 1). To overcome this issue a newalgorithm has been recently proposed. µ uTPC algorithm The idea developed for the ATLAS MicroMegas of the New Small Wheels [2, 3], and also implemented onthe BESIII cylindrical GEM [11, 12], is to reconstruct a track segment inside the detector conversion gaprather than a single hit. The procedure is inspired to the Time Projection Chamber (TPC) concept [4, 5]exploiting the analog readout of the signals. The electrons created by the ionizing particle drift towards theamplification region. By the measurement of electrons arrival time and knowing their drift velocity in thegas mixture, the position of the ionization clusters can be localized in the chamber. A fit to these clusters– 1 – igure 1 . A simplified sketch showing how the non orthogonal tracks affect the number of fired strips. provide the 3D trajectory of the ionizing particle. In our case the readout is segmented in 1D strips, so only areconstruction in what we define the x − z plane (fig. 1) is available. The fired strips represent the projectionof the track on the readout and each center is the x coordinate of the corresponding ionization. These hits arerecorded at different times t k , depending on the distance of the ionization electrons from the readout plane.Applying the simple formula z k = v drif t · ( t k − t ) (3.1)the z position of the k -th cluster can be computed. The formula 3.1 exploits the good uniformity of thedrift field in MPDG detectors, so that the velocity of the electrons can be considered constant. The driftvelocity v drif t of the electrons as a function of the drift field in several gas mixtures can be found in literature.Anyway a fast tool to catch these measurements is the MAGBOLTZ [6] routine called by the GARFIELDgas detector simulation program [7]. The t is the common trigger time. It is crucial to define the best valuefor t k . In our case, using the FEE APV25 [8], the integrated charge is sampled every 25 ns (fig. 2). Theleading edge of this plot is fitted with a Fermi-Dirac function and its flex point is taken as the t k for the eq.3.1. In fig. 3 it is shown the track segment reconstruction of an event using this algorithm. The error bars onthe x axis basically account for the strip pitch and for the fraction of the total charge collected on the strip(errors are increased for small charges possibly associated to charge induction); the error bars on the z axisare propagated from the time measurement uncertainty. Another possible choice for the reconstructed pointerrors is stated in [3].The x coordinate of the event is interpolated from the linear fit, taking the coordinate of the track at themiddle plane of the drift space, following the approach of [3] and [11]. Measurements of the space resolution of the µ -RWELL where only the charge centroid method has beenapplied are reported in [9]. According to those results for the following tests DLC foils with resistivity rangingbetween 60 and 200 M Ω / (cid:3) have been selected for the realization of the detectors. The µ TPC algorithm hasbeen used with µ -RWELLs during a test beam at H8-SPS CERN with a 150 GeV/c muon beam. Two GEMdetectors (fig. 4) have been used to select fully reconstructed tracks in order to clean. Two µ -RWELLs havebeen installed on rotating plates so that the beam could form different angles with respect to the normal to theelectrodes. The µ -RWELLs used in the test (fig. 6) are derivation of the DRL layout [10]: two metallic vias– 2 – Time (a.u.) C ha r ge ( a . u . ) Figure 2 . Integrated charge as a function of the samplingtime, with the fitting Fermi-Dirac function. − − − − − − − − X Coordinate (mm) − Z C oo r d i na t e ( mm ) Figure 3 . Example of a ◦ track segment reconstructionusing the µ TPC algorithm. The line is the linear fit.
Figure 4 . Experimental setup.
Figure 5 . Sketch of the setup with the coordinate system.
Figure 6 . Sketch of the Double Resistive Layer µ -RWELL with embedded resistors. matrices connect two resistive stages to the readout plane for the grounding. The vias density is typically ≤ − . The first stage is a DLC layer, while the second is made of ∼ mm long resistors screen-printedon a substrate. The detectors are equipped with a strip-segmented readout (400 µ m pitch), operated at a gainof 5000 with readout APV25 front-end electronics and flushed with Ar:CO :CF − − − − − − − Residuals (mm) en t r i e s m µ = 145.7 T σ m µ = 82.4 σ m µ = 112.1 σ
95% events in fit
Figure 7 . Residuals distribution before any correction. − − − − − − − − − X Coordinate (mm) − − − − − − − R e s i dua l s ( mm ) Figure 8 . Residuals as a function of the x coordinate. The space resolution can be extracted from the distribution width of the residuals ( σ res ), that are definedas the difference between the coordinates reconstructed by the two µ -RWELLs. Indeed assuming the samecontribution, the µ -RWELL space resolution is obtained as σ x = σ res /√ . For sake of simplicity in thispaper all the plots showing the residual distribution are scaled by a factor of /√ in order to directly givethe detector space resolution. The residuals are evaluated and studied for both the charge centroid and forthe µ TPC reconstruction.In order to take into account the presence of tails, we fit the data with the sum of two gaussian curves,eq. 4.1. The width of the residuals is defined as its standard deviation, eq. 4.2. This is a slightly differentapproach with respect to the analysis reported for MicroMegas ([3]). A discussion about the two methods isshown in appendix A. f ( x ) = Ae − (cid:16) x − µ σ (cid:17) + Be − (cid:16) x − µ σ (cid:17) (4.1) σ = ( A σ + B σ ) q A σ + B σ + AB σ σ (cid:0) ( µ − µ ) + σ + σ (cid:1) (4.2)It has been necessary to evaluate and to reduce the systematic effects present in the measurements,among which the most important are the dependency on the x coordinate and the beam divergence. Thismust be done for both CC and µ TPC algorithm. In the following the correction of the residuals, reconstructedwith the µ TPC algorithm, as a function of the x coordinate is shown as an example of this procedure. Thedetectors have been operated with a drift field of 1 kV/cm and an impinging angle ( θ ) of ◦ .In fig. 7 is shown the raw residual distribution. Plotting it as a function of the µ TPC-reconstructed x coordinate, fig. 8, it is visible a clear dependence, evaluated through a profile, fig. 9a. Such profile isthen fitted with a suitable polynomial and the residuals are corrected accordingly (figs. 9b,10). The residualdistribution after all the corrections is shown in fig. 11. The distributions are fitted with function 4.1 over95% of the events in the histogram.The space resolution has been evaluated at different θ using both CC and µ TPC methods. As expectedfor orthogonal tracks the CC provides better results while increasing the angle they quickly worsen, fig. 12a.Viceversa the µ TPC algorithm shows a better behavior for large angles than for small ones (fig. 12b) for wichthe longer projected track segment on the readout plane corresponds to a larger number of points to be fitted.Since the µ TPC method depends on the drift velocity of the ionization electrons in the gas mixture, andconsequently on the drift field, a study at different drift fields has been performed (fig. 12b). For our gasmixture the electron drift velocity increases with the drift fields, in the range 0.5 ÷ − − − − − − − − − X Coordinate (mm) − − − − − R e s i dua l s ( mm ) (a) Profile before the correction. − − − − − − − − − X Coordinate (mm) − − − − R e s i dua l s ( mm ) (b) Profile after the correction. Figure 9 . Dependencies of the residuals distribution on the x coordinate. − − − − Residuals (mm) en t r i e s m µ = 80.0 T σ m µ = 50.3 σ m µ = 93.3 σ
95% events in fit
Figure 10 . Residuals distribution after the x coordinatecorrection. − − − − Residuals (mm) en t r i e s m µ = 69.6 T σ m µ = 46.8 σ m µ = 97.5 σ
95% events in fit65% events in core
Figure 11 . Residuals distribution after all the systematiccorrections. drift velocity allows the reconstruction of the z coordinate with a smaller uncertainty, improving the µ TPCfit. It is worth noticing that in an experiment it is not possible to determine which algorithm is the best sincethe track inclination is known just a posteriori . Just to estimate the effect of this combination on the globalspace resolution we consider the following trivial relation: σ comb = σ CC + σ µ T PC (4.3)In fig. 13a the resolutions for both CC and the µ TPC are compared and displayed along the combinedresolution from eq. 4.3.To complete our study we report in fig. 13b the combined space resolution at different drift fields. Thecombination of the two algorithms results in space resolutions below 100 microns over a large set of angles θ ., for fields up to 2 kV/cm.For orthogonal tracks the CC resolution prevails in the combination and it does not depend on the driftfield in this range. – 5 –
10 20 30 40 50 ) ° Angle ( m ) µ S pa c e R e s o l u t i on ( cm / kV = 3.0 D E cm / kV = 2.0 D E cm / kV = 1.0 D E cm / kV = 0.5 D E (a) CC spatial resolution. ) ° Angle ( m ) µ S pa c e R e s o l u t i on ( ns / m µ =95 D , v cm / kV =3.0 D E ns / m µ =74 D , v cm / kV =2.0 D E ns / m µ =40 D , v cm / kV =1.0 D E ns / m µ =20 D , v cm / kV =0.5 D E (b) µ TPC spatial resolution.
Figure 12 . The results of the two reconstruction algorithm, over a large angle, for various drift field values (E D ). ) ° Angle ( m ) µ S pa c e R e s o l u t i on ( CC-TPC µ Combined (a) Comparison of the two reconstruction algorithms at a drift fieldE D =1 kV/cm. ) ° Angle ( m ) µ S pa c e R e s o l u t i on ( cm / kV = 3.0 D E cm / kV = 2.0 D E cm / kV = 1.0 D E cm / kV = 0.5 D E (b) Combined space resolution at different drift fields (E D ) withcorresponding drift velocity. Figure 13 . Results from the CC and µ TPC methods.
The µ TPC method has been succesfully implemented for the tracks reconstruction on the µ -RWELL. Bycombining the µ TPC algorithm with the charge centroid, an almost uniform space resolution over a widerange of track incidence angles is reached. At low drift field the measured space resolution is improvedreaching values below 80 µ m, reaching a minimum of 60 µ m. A Consideration upon the double gaussian fit
As previously stated, equations 4.1 and 4.2 were used to estimate the spatial resolution of the µ -RWELLdetectors. There is not an univocal approach to this task, for example in [3] the width of the residualdistribution, fitted with the same function 4.1, was defined as σ = V σ + V σ V + V , (A.1)in which V , are the integrals of the two gaussian functions: V = √ π A σ and V = √ π B σ [14]. Theequation 4.2 reduces to A.1 only if the two gaussian curves have the same mean, µ = µ , namely for a– 6 –ymmetric residual distribution. The proof follows straightforward: σ = A σ + B σ + AB σ σ (cid:0) σ + σ (cid:1) ± AB σ σ ( A σ + B σ ) (A.2) = ( A σ + B σ ) + AB σ σ ( σ − σ ) ( A σ + B σ ) = ( V σ + V σ ) + V V ( σ − σ ) ( V + V ) (A.3) = ( V + V V ) σ + ( V + V V ) σ ( V + V ) = V ✘✘✘✘ ( V + V ) σ + V ✘✘✘✘ ( V + V ) σ ( V + V ) ✄ (A.4) References [1] G. Bencivenni et al.,
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