Sensor quality factor

The sensor sensitivity indicates how much the sensor output signal changes when the bunch charge of the beam passing through the fibre varies. More specifically, it is given by the slope of the characteristic curve ∆S/∆qf ibre where qf ibre indicates the charge

passing through the fibre and S the corresponding signal amplitude. At the optimum

angle of incidence of 49◦ the characteristic curve is shown in Fig. 5.10. The slope should be calculated on the first part of the curve near a bunch charge of 6.3 pC, where saturation does not occur.

However, since the electron beam has a width that is large compared to the diameter of the fibre, for the measurements are required to determine the actual amount of charge (for a given known total bunch charge) passing through the fibre. For measuring the sensitivity the fibre was vertically translated over 11.5 mm by moving the stepper motor connected to the vertical stage where the fibre was mounted. The angle of the fibre was kept fixed, so that the angle of incidence of the beam was 49◦. It was not possible to move the fibre vertically over a larger range due to space constraints around the equipment. With a transmitted intensity of the photoinjector laser of 10%, the signal observed on the oscilloscope was roughly constant at about 295 mV (see Fig. 5.10). Since the fibre core diameter is 0.4 mm, the beam was distributed over a range at least 28.75 times larger than the fibre core, but it is reasonable to assume that the beam spread was much larger, and thus the estimate provided for the sensitivity is a conservative one. Assuming a bunch charge of 6.3 pC, and a beam spread uniformly over 11.5 mm the charge passing through the fibre was about 200 fC. In the following analysis charge homogeneity is assumed, because the height of the signal read during 11.5 mm of vertical translation of the fibre was approximately constant, only showing

some reduction at the end of the range. Although the charge in the bunch clearly extends beyond the range of the scan, it is assumed that the charge falls to zero outside the scan range: this leads to a conservative estimate of the sensitivity. The signal height S read on the oscilloscope is given by:

S = kqf ibre = kρdf ibre (5.1)

whereqf ibre is the charge passing through the fibre,k is the sensor sensitivity,ρ is the

charge density of the ALICE beam and df ibreis the fibre diameter. qf ibreis proportional

to the laser intensity (as shown in Fig. 5.10) that, in turn, is proportional to the bunch charge of the beam in ALICE, Qtot, (as shown in Fig. 5.9). Qtot is the value given by

the Faraday cup and it can be expressed as:

Qtot = ρ∆y⇔ρ = Qtot

∆y (5.2)

where ∆y is the vertical scan of 11.5 mm. Substituting Eq. 5.2 in Eq. 5.1 the signalS

is: S = kQtot ∆ydf ibre⇒k = S∆y Qtotdf ibre (5.3) whereS/Qtot is the slope of the linear part of the curve marked with green squares in

Fig. 5.10 (at the maximum angle of 49◦): this givesk = 1346 mV/pC. The resolution of the sensor R is defined as the smallest change of current that produces a measurable signal variation, for an angle of 49◦. Since the SiPM is an array of cells the smallest signal is the one produced by a single cell (i.e. 15 mV). Using k = 1346 mV/pC, the resolution of the sensor is the ratio of the smallest signal over the sensitivity k, i.e. R = 11 fC. This value varies following the curves in Fig. 5.10 for different angles of incidence.

The sensitivity measured by k includes effects associated with the electronics used to amplify and display the signal from the SiPM. A standard way to characterize the intrinsic sensitivity of a radiation sensor, independent of the detector electronics, is in terms of the quality factor, i.e. the charge generated in the sensor (in our case, the SiPM) per unit radiation dose (in this case, in the fibre, in rads). The quality factor for the detector described here, can be estimated as follows. We assume that the rate of energy loss per electron in the silica fibre is 0.4 keV/m [153]. The fibre has diameter 400µm and the angle of incidence is 49◦; then the distance traveled through the fibre

by an electron with zero impact parameter is approximately 610 µm; so the energy deposited per incident electron is 244 keV. The minimum detectable charge variation of 11 fC, i.e. the detector resolution, is assumed to be distributed along 10 cm of fibre length, corresponding approximately to the typical length of the accelerator section over which the losses are expected to be localized. Thus the radiation dose is:

D = E

m ≈

2.7×10−9J

0.028g ≈10 mrad (5.4)

whereE is the energy deposited by incident electrons, andm is the mass of the fibre. The resolution of 11 fC is based on a signal produced by a single cell, therefore the charge generated in the SiPM from 11 fC of charge passing through the fibre is:

Qc = CcellVop = 120 pC (5.5)

whereCcell = 4 pF is the capacitance per cell, andVop= 30V is the bias voltage across

the SiPM. The quality factor of the detector is then:

Qc

D = 12 nC/rad (5.6)

A comparison of the quality factor in the fibre BLM with other types of detector [1] is shown in Table 5.1. The Cherenkov fibre shows a quality factor of the same order of

Table 5.1: Comparison between the quality factors of different beam loss detectors as given by [1] and the Cherenkov fibre.

Detector Quality factor

SEM detector 100 pC/rad

Ionization chamber 50-500 nC/rad

Cherenkov fibre 12 nC/rad

LAMPF detector 1000µC/rad

magnitude as some of the ionization chambers previously used for beam loss monitoring at ALICE (and widely used on other accelerators). This confirms that the Cherenkov fibre can be useful as a beam loss monitor: however, it should be remembered that the geometry of the fibre is very different from that of a typical ionization chamber. In particular, the volume of the fibre is small compared with an ionization chamber. Further tests have been performed to characterize the performance of the Cherenkov

fibre beam loss monitor second arm during regular ALICE operations and they are described in the next section together with a calculation of the sensor sensitivity of the second arm of the sensor.