Behaviour of large cylindrical drift chambers in a superconducting solenoid

Nuclear Instruments and Methods 176 (1980) 167-173 © North-ttolland Publishing Company

BEHAVIOUR OF LARGE CYLINDRICAL DRIFT CHAMBERS IN A SUPERCONDUCTING SOLENOID W. de BOER, W. FUES, G. GRINDHAMMER, R. KOTTHAUS, H. L I E R L and L. MOSS Max-Planck-Institut fftr Physik und Astrophysik, Fdhringer Ring 6, D-8000 Mfinchen 40, FRG

We describe the construction and behaviour of a set of cylindrical drift chambers operating inside a superconducting solenoid with a central magnetic field of 1.3 T. The chambers are part of the 4rr detector CELLO at the e+e- storage ring PETRA in Hamburg. The chambers were designed without field shaping to keep them as simple as possible. In order to parametrize accurately the nonlinear space-time relation, we used a computer simulation of the drift process in inhomogenous electric and magnetic fields. With such a parametrization we achieved a resolution of 210 gin, averaged over the whole drift cell and angles of incidence up to 30° .

netic field the drift velocity is reduced b y a factor which depends strongly on the electric field. Both effects lead to substantial nonlinearities in the s p a c e time relationship. Even without magnetic fields, nonlinearities are usually present for tracks which are not normal to the chamber cylinder. In order to parametrize these nonlinearities we use a computer simulation o f the drift process which directly calculates the coefficients o f third-order spline functions describing the s p a c e - t i m e relationship. In section 2 we describe the chamber construction and the electronics. In sections 3 and 4 we describe the analysis o f cosmic ray data for B = 0 and B = 1.3 T, respectively. Section 5 summarizes the results.

1. Introduction We have constructed a set o f cylindrical drift chambers for use in CELLO, which is one o f the large 4rr magnetic detectors installed at the e+e- storage ring PETRA. The central tracking detector is mounted inside a thin superconducting solenoid (4 m long, 1.4 m diameter, 0.5 radiation lengths in thickness), which is surrounded b y a 4rr liquid argon calorimeter, a 47r iron hadron absorber and muon chambers. The design criteria for the central tracking detector were that it should [1]: (a) operate in a high magnetic field; (b) provide accurate position determination in b o t h the axial and azimuthal direction; (c) be able to resolve multiparticle jets expected from high energy e*e - collisions; (d) provide a trigger if one or more charged particles are passing through the chambers. Cylindrical proportional chambers interleaved with drift chambers were chosen to fulfill these criteria. The proportional chambers, which were built at ORSAY [11, are equipped with analog readout of 90 ° and 30 ° cathode strips to provide an accurate determination o f the position along the axial anode wires. The drift chambers have axial sense wires and measure the azimuth o f charged particles with high precision. A high transverse magnetic field affects the drift process in two ways. First, the electrons drift in the direction o f the Lorentz force which makes an angle as large as 5 0 0 - 6 0 ° with the electric field lines for E = 1 kV/cm and B = 1.3 T. Second, in a high mag-

2. Chamber construction and electronics The drift chamber system is composed o f three cylindrical modules, inserted in between proportional chamber modules, as shown in fig. 1. Each separately constructed module has its own gas volume, which is filled with a 90/10 argon/methane mixture for the drift chambers. Thick bars between the end flanges o f the drift chambers made them self-supporting during the construction. The end flanges were fixed on spokes, to transmit the wire tension to an outer 4 mm thick aluminum cylinder (see fig. 2). Finally, the bars were removed through special holes in the end flanges, thus reducing the total thickness o f the 22 readout planes o f the tracking detector to about 1% of a radiation length. The drift cells consist o f 2.2 m long anode wires at 167

III. CYLINDRICAL CtfAMBERS, VERTEX DETECTORS

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distances of 15 mm separated by groups of three grounded wires (see fig. 3a). The small cell size has two main advantages compared with arrangements in which the drift angle is compensated by a tilted electric field [2]: no field-shaping cathodes are needed, which makes the construction of low mass cylindrical chambers considerably easier, and simple "single hit" electronics can be used, since the probability that two or more tracks pass through the same cell is sufficiently small, even for multiparticle jets. The anode wires are gold plated tungsten with 2% rhenium. They

Fig. 2. End cap view of the detector. The amplifiers/discriminators are mounted between the spokes, which transmit the wire tensions to the outer aluminum cylinder, which has a wall thickness of 4 mm.

Fig. 3. Drift-cell geometry (fig. 3a) and electric field distribution inside a drift cell (fig. 3b).

have diameters of 20 /lm and are strung with a tension of 39 g. The copper-beryllium cathode and potential wires have diameters of 50 and 100/am and are strung with tensions of I00 and 400 g, respectively. The electric field distribution is shown in fig. 3b. The m i n i m u m field along the center line is 700 V/cm, if a 1950 V potential is applied to the anode wire. The gas volumes are enclosed by mylar foils at distances of 16 m m from the anode wires. The foils are electrically grounded by means of a thin layer of conducting paint * to prevent the collection of electric charge. The wires are soldered and glued in electrically isolated brass tubes mounted in the end flanges. The position of each wire is determined by a laserdrilled, conically shaped hole in a thin brass disc in front of the brass tube. The hole diameter is about 10 /am bigger than the wire diameter. Each feedthrough was inspected under a microscope. Each sense wire is equipped with an amplifier/discriminator mounted directly on the chamber and connected via a 2 4 m long twisted pair cable to a CAMAC TDC. Each TDC has a capacitor, which is discharged between start and common stop signals, a sample-and-hold amplifier, and one inexpensive 8-bit ADC **. The total range of the TDC is 810 ns. The nonlinearity is less than 3 ns and the stability, tested over several months, has been measured to be better than 1%.

* Latex base, Eccocoat SEC, Emerson and Cuming. ** MM5357, National Semiconductor.

W. de Boer et al. / Cylindrical drift chambers in a superconducting solenoid

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nonlinear space-time relations in the corners of the drift cell. We parametrize these nonlinearities in an iterative fashion. Electron drift trajectories are computed by integrating an initial estimate o f the drift velocity. A third order spline function is fitted through the space-time points corresponding to a given angle of incidence (see fig. 5) and the residuals of fitted tracks are computed. The shape and magnitude of the drift velocity as a function of electric field are then varied, and the whole process is repeated until the residuals are minimized.

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We have tested and calibrated our chambers with cosmic rays triggered by scintillators arranged in pairs outside the hadron absorber, thus selecting muons o f at least 1 GeV/c at the position of the chambers. As shown in fig. 4 we triggered on tracks with angles of incidence up to 30 ° in the r~ projection. The drift velocity in argon/methane depends on the electric field f o r E < 1 kV/cm [3]. From the electric field distribution, as shown in fig. 3b, we except

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1.06 ns). III. CYLINDRICAL CHAMBERS, VERTEX DETECTORS

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W. de Boer et al. / Cylindrical drif~ chambers in a superconducting solenoid 0.2

4. Data analysis and results in a 1.3 T magnetic field

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Pure experimental s p a c e - t i m e curves in a 1.3 T magnetic field for the three layers o f the middle drift chamber module are shown in fig. 8 for angles o f incidence smaller than I0 °. These curves are obtained by reconstructing tracks in the p r o p o r t i o n a l chambers and plotting the drift t i m e versus the track distance from the anode wire. The s p a c e - t i m e relation is symmetric around the origin for the middle layer. However, for the layers adjacent to the grounded gas foils a strong left-right asymmetry is seen which changes sign depending on the side on which the foils are located.

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171

IV. de Boer et al. / Cylindrical drift chambers in a superconducting solenoid

In order to study the influence o f these foils more carefully, we calculate again the drift trajectories b y integrating the measured drift velocity. The drift velocity in crossed E and B fields has been studied extensively, b o t h theoretically [ 4 - 7 ] and experimentally [ 2 , 8 - 1 0 ] , but it cannot be calculated in most cases since such a calculation requires knowledge o f the velocity distribution o f the electrons. To circumvent this difficulty we have developed a simple phenomenological model, which requires as input only the drift velocity without magnetic field plus two additional gas-dependent parameters k and l. A detailed description o f this model will be given elsewhere [11]. Here we summarize only the main assumptions. The drift velocity parallel to the electric field is given b y WII(B,E ) = W(B = 0, E)/(1 + co2r 2) .

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completely defined and we can integrate to obtain the electron trajectories. After optimizing the parameters k and l in the iterative fashion described in section 3, we reproduce the experimental s p a c e - t i m e relations quite well, as shown in fig. 9 for one layer adjacent to a gas foil. The calculated curve for an angle o f incidence o f 0 ° (solid line) follows closely the inside o f the distribution o f experimental points between 0 ° and I0 °. The l e f t - r i g h t asymmetry is due to the change in the drift paths near the foils, as shown in fig. 10 for three layers with foils at the outside (a), inside (c) and with no adjacent foils (b). The numerical values o f the dimensionless parameters k and l are 4.0 -+ 0.2 and 5.0 + 0.2, respectively. The residuals as a function o f the position in the cell are shown in fig. 11. The data still show systematic errors comparable with the total resolution as II1. CYLINDRICAL CHAMBERS, VERTEX DETECTORS

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also indicated b y the non-Gaussian distribution in fig. 12a. The Gaussian curve has a sigma of 210 /am, which is slightly better than the resolution without magnetic field, since the average drift time in a 1.3 T magnetic field is about a factor of three longer than in zero magnetic field. Therefore the contribution of electronic errors is correspondingly reduced. If the resolution is not averaged over the wbole drift cell and all angles, a resolution better than 100 /am is obtained (see fig. 12b), showing that the resolution of the detector is determined by systematic errors at present.

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We can summarize the behaviour of our large cylindrical drift chambers in strong transverse magnetic fields as follows: (1) the simple drift cell design with signal wires at distances of 15 m m separated by a triplet of grounded wires works satisfactorily without further field shaping in magnetic fields up to 1.3 T. (2) The spatial resolution of the system in a 1.3 T magnetic field, averaged over the whole drift cell and angles of incidence up to 30 ° , is 210/am. This resolution is limited by systematic effects. (3) To obtain this result we have developed a simple, phenomenological model of the drift process, which allows us to parametrize accurately the s p a c e time relations for different angles, geometries and higll voltages. (4) Since the nonlinear space-time relations can be parametrized b y third-order spline functions, the computer time needed to determine spatial coordinates is small compared to the total time needed for the complete event reconstruction. We wish to thank W. Erbe and his collaborators for the skillful construction of the chambers, and P. Weissbach and W.D. Cwienk for the careful construction of the electronics.

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Fig. 12. Spatial accuracy. (a) Distribution of residuals averaged 9ver the whole drift cell and all angles of incidence. The smooth curve is a Gaussian distribution with a sigma of 210 urn. (b) The residuals of one chamber at 2 mm from the sense wire. A comparison between (a) and (b) shows that the intrinsic resolution of the chambers is at least a factor of two better than the overall resolution, which is limited by systematic errors.

References [ 1] PETRA proposal 76/13 (1976). [2] A. Breskin, G. Charpak, F. Sauli, M. Atkinson and G. Schultz, Nucl. Instr. and Meth. 124 (1975) 349. [3] B. Jean-Marie, V. Lepeltier and D. L'Hote, Nucl. Instr. and Meth. 159 (1979) 213.

W. de Boer et al. / Cylindrical drift chambers in a superconducting solenoid

[4] V. Palladino and B. Sadoulet, Nucl. Instr. and Meth. 128 (1975) 323 ; and refs. therein. [5] P. Langevin, C.R. Acad. Sci. Paris 146 (1908) 530. [6] J.S. Townsend, Electrons in gases (Hutchman's, London, 1947). [7 ] W.P. Allis, Handbuch der Physik, ed., S. Fliigge, vol. 21 (Springer Verlag, Berlin, 1950) p. 383. [8] B. Sadoulet and A. Litke, Nucl. Instr. and Meth. 124 (1975) 349.

173

[9] G.tI. Sanders, S. Sherman, K.T. McDonald, A.J.S. Smith and J.J. Thaler, Nucl. Instr. and Meth. 156 (1978) 159. [10] W. de Boer, B. Budjarek, W. Fues, G. Grindhammer, R. Kotthaus, H. Lierl and L. Moss, Nucl. Instr. and Meth. 156 (1978) 249. [ 11 ] W. de Boer, to be published.

III. CYLINDRICAL CHAMBERS, VERTEX DETECTORS