, where 
. In order to assess the working point and the main features of this detector, extensive tests were performed at the CERN CMS test beam facility. We present here results and relevant studies on the efficiency, drift velocity, linearity and spatial resolution.
The prototypes were operated with an Ar (85%) CO2 (15%) gas mixture and at different Vwire, Vstrip and Vcathode voltages. Since we always kept Vstrip = -Vcathode the working point will be identified by the two voltages:
The gain of the prototype cells has been measured using both cosmic rays and a radioactive source (Am241). Since the electric field close to the wire surface, which the gain of the drift cell depends exponentially on, is proportional to a linear combination (Veff ) of the three voltages applied to the cell, the gas gain can be parametrized in the following way:
1) , where .
Several sets of measurements were done, varying each of the voltages while keeping the remaining two fixed. Fits to the data give the following values for the constants in the expression above:
2) 
Fig 3.2.6 a) is a summary of all the measurements as a function of the effective voltage Veff ; for further details see Ref [2].
Fig. 3.2.6 : Gas gain as a function of Veff; dots are measurements performed with an Am241 radioactive source while the triangles are obtained with cosmic rays; the fit is described in the text.
The efficiency was measured for each half-cell using data taken with orthogonally incident tracks. In Fig. 3.2.7 the average cell efficiency, neglecting dead areas caused by the cathodes, obtained at different voltage settings is given as a function of the effective voltage Veff , computed by eq. 1) using the fitted b, c values given in 2).
Efficiency measurements made at different voltage settings lie on the same curve, confirming that the gas amplification is the significant parameter affecting the value of the efficiency.
Fig. 3.2.7 : Cell efficiency as a function of the effective voltage Veff , proportional to the electric field on the wire (a) ; expanded scale (b).
The data show that the efficiency plateau is reached above Veff = 2100 V, corresponding to a gas gain G= 105. The inefficiency is very low, 0.2%, when the chamber is operated at the reference voltages : Vampl= 1800 V and Vdrift= 3600 V.
The dependence of the efficiency on the threshold applied to the signal was studied using the ASD8 electronics [3]. No significant drop of the efficiency was observed when varying the threshold from 1 to 6 fC.
Data were also collected with another chamber prototype using different front-end electronics with a wider range of discriminator thresholds and with Vdrift = 3000 V. The results indicate that no significant efficiency loss occurs for thresholds smaller than 9 fC.
The onset of the efficiency in proximity of the plastic end plugs was measured in a test beam with a scintillator hodoscope with a resolution of ± 2 mm..
Fig. 3.2.8 : Efficiency as a function of the coordinate along the wire; x = 0 is where the wire emerges from the plastic end-plug, whereas the I-beam cathodes start at x = +5 mm; as it can be seen the efficiency rapidly reaches full value. The errors on the x coordinate correspond to the indetermination of the impinging beam that was defined by a set of scintillators.
As can be seen in Fig. 3.2.8 where the efficiency is plotted against the coordinate along the wire, the cell already reaches full efficiency at 5-8 mm after the point where the wire emerges from the plastic endplug.
In order to study the drift velocity we make use of the presence of staggered planes in our chambers. For orthogonally incident tracks the sum of the drift-time of two consecutive layers (for a linear space-time relation) is a constant called tmax; in case of inclined tracks the same quantity can be obtained from the drift-time of three consecutive layers by :
The drift velocity averaged along the total drift length is obtained from the relation vdrift= d/tmax where d is the wire pitch minus the wire diameter. Fig. 3.2.9 shows the results from data taken at various voltages and threshold settings.
Fig. 3.2.9 : (a) (left) Average drift velocity at different voltage settings vs Veff at 2 fC threshold; (b) (right) same as (a) but 4 fC threshold.
For a given threshold value the average drift velocities measured for different settings of Vdrift lie on the same curve, when plotted as a function of the effective voltage, Veff proportional to the electric field close to the wire. The decrease of tmax as Veff, i.e. the gain, increases indicates that fewer and fewer electrons are needed to trigger the detector. The independence of tmax on Vdrift at constant gain indicates that Vdrift is saturated in a wide interval of drift field values.
The dependence of the maximum drift-time tmax on the threshold values and on Veff, and thus on the gas amplification, indicates that the first drifting electron is not sufficient for signal detection. This effect must vanish at high amplification values. However, a plateau is not to be expected because in the region of high electric field close to the wire the drift velocity is not saturated.
Fig. 3.2.10 : Effective drift velocities for different orthogonal incident angles.
The variation of the effective drift velocity as a function of the angle of incidence of the tracks was studied by taking data with the chamber rotated around an axis parallel to the electric field (longitudinal angle) and an axis parallel to the wires (transverse angle). The results, shown in Fig. 3.2.10, confirm the expectation that the average drift velocity should be independent of the longitudinal angle and should increase with the transverse angle. In the CMS set-up, the incidence angle of high energy tracks will always be smaller than 200 in the bending plane, and in this angular region no large effects are observed. Only low momentum muons could enter the chambers with a larger angle, but in this case even a worse resolution is sufficient for the pt measurement.
The dependence of the apparent drift velocity on the incidence angle can be corrected at the track measurement stage, but this can generate systematic effects on the trigger efficiency, since the trigger algorithm expects the correct alignment of the hits to occur after the fixed delay tmax from the bunch-crossing. A preliminary study of this subject has been reported in [4].
A linear space-time relationship along the full drift space is essential for the Mean Timer method at the trigger level, as we shall see later.
The linearity of the space-time relation was verified with the following formula:
,
where t is the drift-time, r(t) is the density function of the incoming tracks, which can be extracted from the beam profile ( Fig. 3.2.11 a) ) and dN/dt is the drift-time distribution in a cell ( Fig. 3.2.11 b) ).
Fig. 3.2.11 : (a) Beam profile distribution; (b) Typical drift-time distribution of a cell.
The integral of the drift-time distribution, weighted by the density function r(t), was calculated for each half cell. The resulting integral distribution x(t) was then fitted to a straight line and the deviation from linearity at a given value of t, converted to a length assuming a constant drift velocity, was plotted as a function of the corresponding distance from the wire along the half cell axis. Figure 3.2.12 shows this deviation averaged among the half cells illuminated by the beam. The non-linearity is within 0.1 mm everywhere, well below the intrinsic cell resolution. The drift time distribution of all cells will be continuously monitored during the data taking to check for possible local variations. The method allows to check the drift velocity along a single wire coupling data from Z and F SL.
The cell spatial resolution after corrections for non-linearities, measured at several amplification voltages and discriminator threshold settings, is shown in Fig. 3.2.13. The values at the plateau are well within the specifications required for the single-cell resolution and give some safety margin for the overall track resolution.
Fig. 3.2.12 : deviation from a linear space-time relationship.
Fig. 3.2.13 : Single cell spatial resolution evaluated at different voltage and threshold settings for orthogonally incident tracks.
The dependence of the resolution, measured along the middle plane of the drift cell, on the track incidence angle and position in the cell is shown in Fig. 3.2.14. The values are uniform and within the specifications along the full drift space for a wide range of transverse incidence angles, while a substantial deterioration can be observed for very large angles. However, their influence on the track position error is also reduced by the cosine of the angle, i.e. by 66% at the largest angle.
Fig. 3.2.14 : Single-point resolution calculated from the residuals of a track fit at different positions along the cell and for different incident angles.
In order to study the impact of the central electrodes on the cell performance, a prototype was constructed where 50% of the drift cells were not equipped with strip electrodes. The comparison of the resolution obtained for the two types of drift cells as a function of discriminator thresholds and for orthogonally incident tracks is shown in Fig. 3.2.15. In all cases, the resolution is considerably better for cells with the central electrodes.
Fig. 3.2.15 : Single cell resolution as a function of the threshold applied to the front end electronics; as it can be seen the addition of the central strip electrodes results in a uniform improvement at all threshold values.
Tests were performed also with the 3 m long chamber prototype in a muon beam at CERN. Measurements at points close to the wire ends and at the center of the chamber evidenced a uniform performance along the drift cells.