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Every fibre has an intrinsic attenuation whose specific curve as a function of the wave- length is generally displayed in the fibre datasheet. In fig. 5.11 the attenuation of the fibre BHF48-200 (whose properties are listed in Table 2.1) is shown.

Figure 5.11: Attenuation of the fibre BHF48-200 (Table 2.1) as a function of the wave- length. For about 400 nm the trasmission/m is 99%.

This fibre is a pure silica fibre and it has an attenuation of about 90 dB/km at 400 nm (typical for the Cherenkov effect). In principle, this attenuation can be used for evaluating and localizing losses by comparing the difference of the output signals.

In the configuration shown in Fig. 5.1a., two parallel fibres of about 2 meters in length run parallel to each other. When the Cherenkov photons, created by a beam

loss passing through the fibres, travel a certain distance L (which is the distance the point at which the losses occurred and the end of the fibre where the signal is detected by the SiPMs) the attenuation of the beam will depend on the attenuation curve of the fibre that depends on the fibre material.

To optimize the difference between the two signals, the so called reference fibre is chosen to have the minimum attenuation in the UV regime where the Cherenkov production is maximized (i.e. the beam have a transmission coefficient of about 99%/m, in other words the beam can be considered not attenuated because of the short length of the fibres used for the sensor), whilst the second fibre is chosen to have an attenuation such as to produce a difference in the signal and therefore with a minimum value of the attenuation in the IR (infrared) regime.

Despite the wide commercial availability of fibres with a very low attenuation in the infrared, an important issue has to be taken into account when selecting the right fibre. As explained in chapter 3 the only fibres suitable for being used in harsh environments due to their high radiation hardness and, therefore, with a much longer lifetime are:

• pure silica core and cladding fibre with high OH− content;

• pure silica high OH− content core fibre with fluorine doped silica coating.

This is an important limitation to the choice of the suitable fibres.

Because of the material of these fibres the attenuation curves of the models tested in this thesis do not differ appreciably from the curve shown in Fig. 5.11.

The respective transmission factors at about 400 nm are expressed in Table 5.2. Since the goal of the sensor is to measure the beam losses in 2 meters of fibre with a resolution of about 10-12 cm, the resolution of this fibre configuration has been calculated for all the values of the transmission coefficients shown in Table 5.2.

The attenuation of a beam inside a fibre depends on the traveling distance L,

therefore the output signalS1 can be expressed as:

S1 = S0·βL⇒L = ln S1 S0

1

lnβ (5.7)

where β is the transmission coefficient, S0 is the signal without attenuation, L is the

Table 5.2: Transmission coefficients of the fibre tested in this thesis for a wavelength of about 400 nm. The pure silica (Si) fibre have a similar transmission coefficient than the Fluorine doped fibres.

# Item β, transmission coefficient/m (%) core/cladding material

1 AFS105/125Y 96 Pure silica Si

2 HCG-M0200T 98 Pure Si

3 OptranWF 99 Si/Fluorine doped Si

4 HCP-H0200T 98 Si/Hard polymer

5 BHF48-200 98 Si/Fluorine doped Si

6 BFH48-400 98 Si/Fluorine doped Si

7 PJR-FB500 90 Plastic

the sensor resolution (i.e. the variation ofLwith respect to the measured signal strength is given by: dL dS1 = 1 S1lnβ = 1 S0βLlnβ (5.8)

If the signal strength S1 is measured in the number of cells fired in the SiPM de-

tector, then the minimum possible variation in the number of cells is ∆S = 1. The

corresponding variation in length is:

∆L = 1

S0βLlnβ

(5.9) The quantity ∆Lrepresents the spatial resolution of the detector. Inspection of equa- tion 5.9 shows that the resolution can be improved (i.e. minimized) either by increasing the initial signalS0, by decreasing the transmission ratioβ or by operating at a greater

distance d.

However, the signalS0 which can be achieved is limited by the saturation effects in

SiPM to about 100 cells, and the operating distance to suit all applications should be as small as 2 m. Within these constraints, it is possible to plot the resolution of the detector as obtained from equation 5.8.

Fig. 5.12 shows the resolution as a function of the signal S0 expressed as number

of SiPMs cells fired for the fibres listed in Table 5.2.

The horizontal straight line indicates the target resolution of about 10 cm and the vertical dashed line shows the maximum number of cells that can be fired to avoid SiPM saturation.

Figure 5.12: Attenuation of the output signal in terms of the traveling distance d as a function of the input signalS0expressed as number of SiPMs cells fired for the fibres listed

in Table 5.2. Notice that for low attenuation, i.e. short fibres, S0 =S1. The horizontal

straight line indicates the sensitivity we would like to reach of about 10 cm and the vertical dashed line shows the average number of cells that can be fired to avoid SiPM saturation.

Only fibre 7 is able to reach a resolution of about 8 cm for a maximum signal of 100 cells. Unfortunately this fibre is a plastic fibre and even if it has been used for prototype testing it cannot be used for real applications due to the low radiation hardness of the plastic.

None of the silica fibres are able to reach a resolution of 10-12 cm using a total length of 2 meters, even for high signals of 100 cells (close to the detector saturation). For lower signals the resolution is even worse. Due to these reasons this configuration can only be used when a worse resolution is required, always taking in account the saturation of SiPM: it does not fulfill the requirements of the beam loss monitor design previously described. Finally, as the number of cells before saturation increases with the total number of cells in the device, a possible way to improve the resoluation could be to use large active area devices with a higher number of total cells to increase the resolution.