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We present the results of studies devoted to the development and optimization of the optical part of a high precision time-of-flight (TOF) detector for the Large Hadron Collider (LHC). This work was motivated by a proposal to use such a detector in conjunction with a silicon detector to tag and measure protons from interactions of the type p + p → p + X + p, where the two outgoing protons are scattered in the very forward directions. The fast timing detector uses fused silica (quartz) bars that emit Cherenkov radiation as a relativistic particle passes through and the emitted Cherenkov photons are detected by, for instance, a micro-channel plate multi-anode Photomultiplier Tube (MCP-PMT). Several possible designs are implemented in Geant4 and studied for timing optimization as a function of the arrival time, and the number of Cherenkov photons reaching the photo-sensor.
© 2014 Optical Society of America
1. Introduction
Precision timing is useful for many applications, ranging from Positron Electron Tomography (PET) scans to particle physics (for example TORCH at LHCb [1]). For PET scans, information about the time of the arriving photon pair helps improve the position resolution by determining the locus of the electron-positron pair annihilation, while for high energy physics, it has typically been used in conjunction with a momentum measurement to determine the mass of the particle, which in turn defines the particle’s identity.
Timing detectors can be used as a part of the proton tagging detectors to decrease the background to central exclusive production (CEP) events p + p → p + X + p where X stands for the centrally produced system, which could consist of a pair of jets, a pair of intermediate vector bosons (W + W-), or even a Higgs boson H [2, 3 ]. For the rare processes above, high luminosity is required, which implies that multiple interactions take place in every proton bunch crossing (pile-up). By using timing detectors on both sides of the interaction point, the background is rejected from protons that do not originate from the same vertex as the central system X. The time difference measurement to reduce pile-up was first proposed as an upgrade of the CDF experiment at Fermilab [4, 5 ], but was not implemented. This idea was then adopted by the joint ATLAS-CMS FP420 R&D collaboration for the LHC [6].
At high luminosity, the LHC environment places stringent demands on the timing detectors: unprecedented resolution (~10 ps, equivalent to 2.1 mm interaction vertex resolution), high rate capability (5 to 10 MHz), radiation hardness (integrated charge of 10 C/cm2/yr), and multi-proton detection capabilities (~1 background proton/detector is expected per bunch crossing at standard luminosity).
The first detector to achieve 10 ps resolution was developed by Nagoya, and consisted of a short quartz bar connected to a microchannel plate photomultiplier (MCP-PMT); the charged particle travels the length of the bar with the entire Cherenkov cone captured by the PMT [7]. Building on this concept, Albrow proposed the QUARTIC detector, a matrix of straight quartz bars oriented at the Cherenkov angle (~48 degrees for fused silica). This design has the advantage that the PMT is out of the direct beam and it effectively compensates for time differences between photons emitted at different points along the proton’s path [8].
The QUARTIC design has been studied extensively by FP420 [6, 8 ] and AFP (ATLAS Forward Proton programme) [9], and with some modifications to the MCP-PMT to improve its lifetime [10] the system meets all requirements for operation at the LHC. Because of concerns about the PMT lifetime, CMS investigated a promising alternative, using Silicon photomultipliers (SiPMTs) to read out the fused silica bars. Since the resolution of the SiPMTs are inferior to the MCP-PMT, Albrow proposed a new “L” shape (L-bar) which combines the virtues of having the Cherenkov radiator bar parallel to the beam to maximize the light, with a perpendicular light guide bar to allow the photodetector to be positioned away from the beam [8].
Recently the planned interface to the accelerator was changed from a movable section of beam pipe (Hamburg pipe) to a more traditional Roman pot approach [11, 12 ], which does not have space for QUARTIC, but could house an L(Q)Bar detector. The primary aim of this paper is to study the LQBar performance, as well as several new designs devised to both fit in a 140 mm diameter Roman Pot and to satisfy the resolution goals. This goal is accomplished by simulating and analyzing the propagation of the Cherenkov photons through the different detector geometries to the photo-sensor, studying the resulting hit distributions, and comparing the results to benchmark straight bar detector.
2. Designs for a Roman-pot-based Quartz Cherenkov detector
2.1. Dimension constraints in Roman pot
Despite the excellent resolution of QUARTIC, measured by ATLAS to be better than 15 ps [10], it is not a viable option for a Roman pot (hosting movable device) due to space constraints (the PMT is in-line with the sensors at the Cherenkov angle). In the LBar design, the radiator bar is parallel to the beam and collects more light than QUARTIC because the condition for total reflection is fulfilled along the whole pathway. However, the LBar design lacks time compensation and the amount of material it presents to particles is relatively large.
In this work, we propose a shape which combines the best features of the QUARTIC and LBar designs while satisfying the dimensional constraints imposed by a Roman pot, Fig. 1(a) . The basic component of the new detector is the LQBar, which is a modified LBar with the radiator oriented at the Cherenkov angle as in the QUARTIC design, see Fig. 1(b). This design suggests one train of bars with the radiator arm of the cross-section 2x6 mm (due to higher exposure to the beam), the second one with the radiator cross-section 3x6 mm, and the remaining trains with the radiator cross-section 5x6 mm.
Fig. 1 (a) Typical Roman pot dimensions, (b) proposed design of new TOF with matrix of LQBars with various cross-section profiles of radiator arm.
In contrast to the LBar where the condition for total reflection is fulfilled along the whole pathway to the photodetector, the LQBar requires a mirrored 45 degree elbow (0.79 rad) to get the light up the light guide bar to the PMT. The critical angle of fused silica varies between 40.2 degrees to 43.2 degrees (0.70 rad – 0.75 rad) within the wavelength range 200-600 nm, thus the condition of the total reflection is still fulfilled on side walls of the LQBar (except the elbow). To minimize the effects of color dispersion, one could replace parts of the quartz or fused silica with an air light guide, for example an (internally polished) aluminum tube. Below we present simulation results evaluating different options.
2.2. Radiator and Light Guide design
Studies to optimize the design were performed using Geant4 [13]. The Geant4 simulation focuses on optimizing the details of the LQBar implementation, since neither the LBar nor the straight bar (QBar) fit in the available space. A straight bar of the same total length as the LQBar is simulated, however, since it is the performance standard, and it can be used to connect the simulation to real data [10].
Figure 2 shows the basic size and shape of the LQBar, which is geometrically divided into a radiator arm (vertical arm) traversed by the proton and a light-guide arm (horizontal one) channeling the light to the photo-sensor (the red element at the end of the light guide).
The average Cherenkov angle θc for fused silica is 48 degrees (0.84 rad) for relativistic protons with β ( = v/c) close to one. The angle is a function of wavelength. The value 48 degrees was calculated for the UV region (200-400 nm). The bottom face of the radiator bar is generally made absorbing since this light is directed away from the photo-sensor. However, by making a cut parallel to the beam at α = θc (Fig. 2(c)), these downward emitted photons are redirected back up through the bar and recovered for particles passing close to the bottom end of the radiator bar. Another feature of the LQbar is the “elbow” between the two bars, which is cut at 45 degrees and aluminized to maximize the light transmission. The following detector geometries were studied, see also Fig. 3 (blue colour stands for a fused silica part, yellow colour stands for an air light guide):
- A straight QBar of fused silica, see Fig. 3(a), where the pink circle is the position of the proton track; note that the radiator bar has a square-cut bottom side because this geometry was studied experimentally [10, 14 ] and serves as a benchmark, parameters in analysis: 150 mm long, arm square profile 6 × 6 mm2,
- A regular all fused silica LQBar with a metalized elbow, Fig. 3(b); denoted as Q-Q, parameters in analysis: aluminized elbow (90% reflectivity), radiator arm: length 60 mm and cross section 2 × 6 mm2, and light-guide arm: length 90 mm, cross profile 6 × 6 mm2,
- An LQBar with the radiator arm of fused silica, and the light-guide arm divided into part fused silica and part air-filled light guide, see Fig. 3(c), denoted as Q-QA, parameters in analysis: 90% reflectivity of air light–guide walls, radiator arm: length 60 mm, cross profile 2x6 mm, and light-guide arm: length 90 mm of which 30 mm made of fused silica, cross profile 6x6 mm,
- An LQBar with the radiator of fused silica and the light guide filled with air denoted as QA-A, Fig. 3(d), parameters in analysis: 90% reflectivity of air light-guide walls, radiator arm: length 60 mm of which 30 mm made of fused silica, cross profile 2x6 mm, and light-guide arm: air guide, length 90 mm, cross profile 6x6 mm.
The Q-A configuration is omitted because it gives very poor results as much of the light gets trapped in the radiator bar. For completeness we also implemented the LBar option.
2.3. Material properties
The properties of the materials implemented in the simulation are those of suprasil (fused silica) with an index of refraction and absorption length as plotted in Fig. 4(a) . The air-filled light guide is implemented as a vacuum. The photosensor is represented by its entrance window with index of refraction 1.474. The choice of the material is not important, however, due to a usual scheme of a sensor handling in the Geant4 by means of the concept of so-called sensitive volumes. When a photon hits the sensor, its state information is stored and then it is killed and not propagated anymore. A spectral sensitivity of the sensor is implemented through its photodetection efficiency discussed below.
2.4. Photoelectron generation
The photoelectron statistics for an event is the number of generated photons that are converted to photoelectrons and measured by the photosensor. The number of photoelectrons is given by
The number of generated photons is linearly dependent on L, the path length of proton in the radiator, and scales with the inverse square of the index of refraction (n) and the wavelength of the radiated photons λ. The photosensor type determines the acceptance of the wavelength range (λ1 and λ2). In Eq. (1), α denotes the fine structure constant, and ε the photodetection efficiency. The accepted wavelength range for the Planacon MCP-PMT is 185 nm to 650 nm [14]. The path length of the proton through the radiator is L = ZDim/sin(θc), where ZDim is the thickness of the QBar; in our case ZDim = 6 mm, and L = 8.1 mm.
When the optical photon reaches the sensor (which is actually the sensitive volume in Geant4), two efficiencies are applied that govern the conversion to photoelectrons: the photodetection efficiency (PDE) and the collection efficiency. If the photoelectron survives, a ‘hit’ is registered (as photoelectron) for analysis. We adopted photocathode quantum efficiency data of the Planacon MCP-PMT published in [14], see Fig. 4(b), and the collection efficiency is set to 0.6. In the case of a full fused silica bar (Q-Q) of 150 mm in the length, losses caused by absorption in the medium (a fused silica radiator and/or a waveguide) and by multiple reflections on the medium boundaries are approximately 30% of the signal, giving a maximum number of accepted photoelectrons N~50 from Eq. (1). Losses in the Q-QA and the QA-A are significantly higher due to the presence of the extra optical boundary between fused silica and air. This in particular affects photons propagated via multiple total reflections on sides of the bar (noted as side wings in this paper, see below).
3. Simulation studies and results
The LQBar geometry studies are divided into two parts. First, we compare the various types of LQBars to the QBar (straight bar) for which there is test beam data [10]. The light guide is always given as a square 6 × 6 mm2 cross section to match the pixel size of the Planacon MCP-PMT, and ends flush against the PMT entrance window (in simulation there is a slight overlap between the light guide volume and the window to ensure a good connection; in practice a good contact must be mechanically ensured, unless an index-matching radiation-tolerant high- transmission gel is obtained).
In the second part of the study, we introduce various geometrical modifications of the basic designs in order to further improve the hit statistics at the sensor.
In all studies, protons with 7 TeV were used to generate Cherenkov light while passing bars without smearing of their direction and position. The simulation was set up so that the beam direction was along the z-axis in the simulation scene.
3.1 Comparison among types of LQBars
First, we compared the QBar and the three types of LQBars: Q-Q, Q-QA and QA-A as listed in section 2.2 a visualized in Fig. 3. All four designs have the same total geometrical path length of 150 mm and the light guides all have a cross section of 6 × 6 mm2.
Simulated time profiles are plotted in Fig. 5(a) for a 1 ns wide time window and a 3.0 mm vertical offset of the beam (see Fig. 2(c)). More than 90% of all hits fall inside this time window, except for the straight QBar, which has a significant tail at longer arrival times. Because of the different optical path lengths, the first hits generally occur sooner in the case of LQBars with air light guides (Q-QA and QA-A). For instance, the first hit on the sensor occurs at 541 ps measured from the time the proton enters the trigger volume, compared to 730 ps in a straight bar (see t 0 in legend). The optical path length for the Q-Q LQBar is the same as for the straight QBar, thus their first hit arrival times are the same. In the case of the Q-Q LQBar, the total signal is split between a first and a second (late) peak. The late peak is linked to the presence of the so-called side wings of the photon trajectories, see Fig. 7 and text below.
Cutting the radiator bar at the bottom parallel to the beam significantly increases the total hit count, and results in a strong dependence of the total hit count on the vertical beam offset. This behavior is illustrated in Fig. 5(b) and occurs for vertical offsets in the range from 0 mm to 4 mm (this depends on the cross section of the radiator). For larger offsets, most of the downward Cherenkov photons leave the bar.
For a very small offset, for instance 0.1 mm, the light yield is significantly higher than for a large offset. In the case of the Q-QA design the yield factor is almost 2, and for the Q-Q design the factor is 1.3, which brings it to the level of the straight bar. One can design the detector to take advantage of this behavior when the beam position has a small spread in height.
Note that this effect is negligible for the QA-A LQBar as it corresponds to the strong angular selection of photon directions in that design. In general, the hit count is independent of the vertical offset if the radiator bar is square cut, as is the case of the reference straight QBar. Both effects are further discussed below in the context of the photon acceptance as a function of the origin. Unless noted otherwise a parallel cut of 3mm will be used as the default.
Figure 6(a) summarizes hit statistics per event for all these time windows. Only the Q-Q LQBar design approaches the reference bar in hit count. As for total hit count, the Q-QA and QA-A designs suffer from reflections at the extra optical boundary between the fused silica and air light guide because of intrinsic reflection (4%), and additional total internal reflection of photons incident on the interface at large angle. As for the Q-Q design, there is a jump of the hit count between 0.3 and 0.4 ns due to arrival of the second peak, see Fig. 5(a).
In Fig. 6(b), the percentage of hits in an arrival time window of the total is plotted as function of the time window size for several LQBar designs. In the case of the hybrid Q-QA design, almost all photons reach the sensor in the first 200 ps (97%), while for the QA-A case, all photons arrive even within the first 50 ps. This is explained by the fact that photons move faster and with less velocity dispersion within a hybrid design because of the shorter optical path. However, the total hit count is low compared to all fused silica designs because of reflections on the extra Q-A boundary. Therefore Q-Q and Straight Bar designs perform better for time windows greater than 400 ps. The total hit count is 360 per passing proton in the reference QBar design. Referring to Fig. 5, the hit count for the Q-Q LQBar design is similar for a vertical beam offsets close to zero.
The distribution of azimuth emission angle φ (the angle in the plane perpendicular to the beam direction) of the generated Cherenkov photons is plotted in Fig. 7(a) . Except for the reference straight bar QBar design, the φ distributions feature empty intervals caused by the geometry which strongly influences the acceptance of the photons. As seen in Fig. 7(b), the φ distribution has wings in the φ vs. arrival time distribution.
Fig. 7 (a) Vertex φ distribution of generated vertices, (b) its profile as function of arrival time.
Referring to Fig. 7(a), gaps occur in the distributions for the hybrid Q-QA and QA-A designs for the intervals from −0.73 rad to + 0.73 rad, from + 2.4 rad to + π rad, and from -π rad to −2.4 rad (so-called ‘side regions’). These intervals correspond to those outside of area of total internal reflections in the interface between the fused silica and air light guide. The φ distribution wing lying at around 1.57 rad (90 degrees) corresponds to those photons traveling straight to the sensor (thus called the direct wing in the direct region). The decrease from the central peak at 1.57 rad is due to an increase in optical path length including one or more reflections. Note the additional φ wing at negative φ between −2.4 rad and −0.73 rad which corresponds to similar photons but after reflection off the cut at the bottom end of the radiator bar. The detailed photon content of this negative φ wing depends on the vertical offset of the beam. In our case, a 6 mm wide bar, the photon content diminishes for offsets higher than 4 mm, see Fig. 5(a). Because the reference straight QBar has a square-cut bottom the negative φ photons are all lost.
Peaks in the photon arrival time distribution are seen in the QA-A design; this is caused by a strong φ dependence of the photon survival (‘hits’) and it corresponds to the total internal reflection of all photons emitted away from the vertical direction (φ = ± 1.57 rad) on the Q/A boundary. This applies to the Q-QA case as well, but there is not such a strict φ selection. A scan varying the length of the fused silica part indicates that the radiator length has a minor effect on the total hit count (~5%). Additionally, for square-cut LQbar versions, the φ distribution is almost identical to the parallel-cut counterparts except for the missing negative φ wing.
Referring to Fig. 7(b), one can note that photons in the wings are increasingly delayed going away from the vertical. Notably for the Q-Q LQBar design, the fronts of the wings in the side regions are delayed by 270 ps with respect to the front of the direct wing (which is identical in shape to the direct wing of the straight Qbar). This corresponds to the second peak in the time profile (Fig. 5). The time delay of the negative φ wing with respect to the direct wing depends on the beam offset. For vertical offsets in the range from 0 mm to 4 mm, the time delay increases 7 ps/mm. For higher offsets it grows roughly 200 ps/mm but bigger portion of the negative wing go outside the bar until it diminishes at the offset of 5.5 mm.
It is obvious that only the Q-Q LQBar comes close to the straight bar in terms of photon efficiency. The other bars suffer from the additional optical boundary between the fused silica and air light guide. On the other hand, the Q-Q LQbar signal is divided into a main, early photon bunch represented by direct wing (along with weaker negative φ wing) and two delayed side wings resulting in a spread in photon arrival time. However, much of this time spread can be countered by additional design modifications discussed in the next section.
3.2. Geometry extensions of Q-Q LQBar
In order to catch as many photons as possible in the shortest possible time window in the Q-Q LQBar design, small modifications of the light guide were studied, see Fig. 8 . These consist in a shift of the light guide (dimension exty – extended vertical shift) in the vertical direction and tapering near the 90 degree elbow at a given taper angle. Unsurprisingly, the tapered part together with 45° elbow act as a rough approximation to a semi-parabolic collimating mirror, see Fig. 8(b).
A variety of shifts and taper angles was studied. The taper angle was varied over the interval from 0 degrees to 35 degrees in 5 degree steps (2 degree steps in the vicinity of the optimal taper of 25 degrees), taking a fixed vertical shift value of 2 mm. The vertical shift was varied over the range from 0 mm to 4 mm in 0.5 mm steps with a fixed 22 degree taper angle.
The hit count distributions as function of shift and taper angle are summarized in Fig. 9 for 200 ps, 400 ps, and full photon arrival time windows. The maximum hit count is obtained for shifts between 2.0 and 2.5 mm for all these time windows. The hit count maximum is reached for taper angles between 20 and 25 degrees for the 200 ps and the full time windows. However for the 400 ps window, the optimal taper angle is shifted to 15 degrees. The maximum hit count in the full time window is 408 per proton for the modified Q-Q LQBar design with optimized parameters (those maximizing hit count), i.e. a factor 1.10 higher compared to the reference straight QBar design (hit count 370). This value is obtained for a vertical beam offset of −3 mm from beam axis.
The modified/optimized Q-Q LQBar design, with a vertical shift 2.5 mm and the taper angle of 25 degrees, is compared with the original Q-Q LQBar design and with the reference straight QBar. The resulting distributions are plotted in Fig. 10 . It is obvious that the modifications result in a shift of the side wings by about 200 ps towards shorter arrival times, see Fig. 10(b). The same applies to the negative φ region. This wing shift gives a higher hit count of 408 compared to 290 for the non-modified Q-Q bar design, an increase by a factor 1.4. This results in a beneficial time compression of the arrival time distribution.
Fig. 10 Comparison of the optimized Q-Q LQBar design compared to the non-modified LQBar: (a) distribution of generated photon φ angle, (b) photon arrival time distribution.
The number of accepted photoelectrons (PE) by the photosensor is plotted in Fig. 11(a) for various arrival time windows up to 500 ps. The PE statistics of the optimized Q-Q LQbar design are generally higher than those of the straight QBar design. Distributions of photoelectrons accepted in the sensor in first 400 ps are plotted in Fig. 11(b). This particular size of time window was chosen because it is thought to best approximate the real signal acquisition conditions of the AFP DAQ system. The modified Q-Q LQBar design is better at photoelectron detection than the reference straight QBar (25 vs. 20 photoelectrons) and almost two times better than unmodified Q-Q LQBar.
4. Hit characteristics on sensor surface
The studies discussed above are intended guide design of a modified LQBar geometry optimizing the photon hit statistics and arrival time distribution. In this section, the focus is on the hit count distribution at the surface of the sensor with the optimized Q-Q LQBar design. Note that the following results are based on hits passing the PDE and collection efficiency criteria (see section 2.4 above). These criteria affect the accepted photon wavelength distribution and are therefore somewhat coupled with the time-of-arrival distribution and the resulting PE pulse profile. Due to the dispersion, see Fig. 4(a), photons with higher wavelengths reach the sensor sooner but their contribution is reduced due to lower quantum efficiency of the sensor in the region, Fig. 4(b). This in turn affects a sharpness of the pulse.
Figures 12 and 13 show histograms of the number of photoelectrons as a function of photon wavelength, generated photon φ angle, and the time of arrival at the sensor surface. The distribution of the optical signal at the sensor surface is plotted in Fig. 12(a). It is noted that the signal is not uniform in the z-direction along the sensor surface (which corresponds to the beam direction rotated by the Cherenkov angle in the plane containing the beam and the vertical axis). Figure 12(b) shows the wavelength distribution of photons hitting the sensor as a function of arrival time. One notes that photons of 200 nm – 400 nm wavelengths dominate the first 270 ps of the pulse. Thus an appropriate optical band-pass filter within this range could filter out a portion of an eventual light background. Figure 13 shows the distribution of generated photon φ angle as function of time and photon wavelength. Note the high statistics (red and orange colors) in the direct and negative wings in the first 270 ps of the pulse, see Fig. 13(a). The wavelengths of photons in this part of the pulse are mostly in the 200 nm – 400 nm range, see Fig. 13(b).
Timestamps of accepted hits are used for a crude preliminary estimate of the timing resolution of a device consisting of the optimized extended Q-Q LQBar, the PMT and a constant fraction discriminator (CFD). This analysis does not include all aspects of the signal processing which is outside of the scope of this paper. Instead, we use a simplified model of the PMT timing performance by means of its impulse response. The impulse response is a function of a rise time, a fall time, a transit time, a transit time spread, and a gain of the PMT. We use following values: the rise time of 300 ps, the fall time of 1500 ps (the Planacon 85011-501 datasheet), a transit time spread of 35 ps (based on [14]), and a gain of 105. The transit time itself has no effect on the timing performance in this model and it is set to 0 ns. The constant fraction value of the CFD is set 20% of the signal amplitude. First, the timing model is validated on results of the reference straight bar with a measured σ = 19 ps [10]. The model is then applied to the optimized Q-Q LQBar. We obtain σ~15 ps for a single bar. Adding N bars in a train of the QUARTIC detector, the timing resolution improves to σ/sqrt(N). This gives the timing resolution of 8 ps for the QUARTIC of N = 4 bars per train and a beam without position smearing.
5. Conclusion
We have studied several possible designs of an LQBar Cherenkov radiator for a new Time-Of-Flight (TOF) detector suitable for measurements in the vicinity of proton beams at high luminosity. The Roman Pot near-beam interface is well established for such measurements, but presents severe space constraints on the design of suitable TOF detectors. We performed simulation studies of several different LQBar designs, and a variety of possible modifications, compared to a straight QBar design which has well known characteristics from test beam measurements [10].
A hybrid combination of fused silica radiator and an air light guide (QA-A or Q-QA LQBar designs) was studied and was found to be promising because of the narrow hit profile in time. Almost all photons reach the sensor in the first 200 ps (97%) in the case of the Q-QA hybrid variant, compared to 43% for the reference straight QBar, see Fig. 6(b). However, the QA-A hybrid gives a significantly lower hit count and therefore it is not a satisfactory design. The Q-QA hit count is comparable to the regular Q-Q designs for short arrival time windows (less than 300 ps). Thus for timing purposes, the Q-QA is also a promising design in a sense that its light pulse is more compressed than the one for the Q-Q type, see also Fig. 6(a).
Geometric modifications (taper, light guide shift) are proposed to further improve the LQBar design. These modifications are seen to strongly improve the arrival time distribution of the Q-Q LQBar design with an optimal vertical light guide shift of about 2.5 mm and a taper angle around 25 degrees. The Q-QA type, however, shows only a small improvement with design modifications, therefore it is also discarded in favor of the Q-Q design.
The modified and optimized version of the Q-Q LQBar design is thus a promising solution for the AFP TOF detector because of its narrow hit profile and improved hit count in short arrival times. In fact this design gives a higher signal than the reference straight bar by a factor of 1.25 assuming the vertical offset of 3 mm, and the factor is still higher if the beam passes closer to the bottom cut. One can design the detector to take advantage of this behavior when the beam position has a small spread in height. Noting that wavelengths in the range from 200 mm to 400 nm dominate the first 300 ps of the light pulse, adding a band-pass filter could further improve the detector performance.
The final steps to measure the resolution of the detector/MCP-PMT system would be to model how the phototube converts the photon time distribution to an electrical pulse, and then simulate the constant fraction discriminator and TDC operation, a task that is well outside the scope of this paper. Given the straight bar normalization point of 19 ps, however, a reasonable estimate of the resolution/bar can be obtained by scaling this by the square root of the ratio of the amount of photons (LQBar/straight bar) in the relevant time window, implying that an LQBar-based detector could exceed the performance of QUARTIC by 10-40%.
In summary, we can conclude that it is possible to construct the Q-Q based detector with a resolution better than the standard QUARTIC detector.
Acknowledgments
The authors gratefully acknowledge the support by the “Mezinarodni experiment ATLAS-CERN (MSMT INGO II č. LG13009)”, the U.S. National Science Foundation grants PHY1068677 and PHY1119200 and the U.S. Department of Energy grant DE-SC0007054 (Stony Brook University), IGA_PrF_2014005 of the Palacky University, and Texas ARP, Department of Energy (UTA).
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