PICOSEC: Charged particle timing at sub-25 picosecond precision with a Micromegas based detector

The prospect of pileup induced backgrounds at the High Luminosity LHC (HL-LHC) has stimulated intense interest in developing technologies for charged particle detection with accurate timing at high rates. The required accuracy follows directly from the nominal interaction distribution within a bunch crossing ($\sigma_z\sim5$ cm, $\sigma_t\sim170$ ps). A time resolution of the order of 20-30 ps would lead to significant reduction of these backgrounds. With this goal, we present a new detection concept called PICOSEC, which is based on a"two-stage"Micromegas detector coupled to a Cherenkov radiator and equipped with a photocathode. First results obtained with this new detector yield a time resolution of 24 ps for 150 GeV muons, and 76 ps for single photoelectrons.


Introduction
The prospect of pileup induced backgrounds at the High Luminosity LHC (HL-LHC) has stimulated interest in developing technology for charged particle timing at high rates [1]. Since the hermetic timing approach (where a large fraction of tracks are used to time interaction vertices) requires a large area coverage, it is natural to investigate both MicroPattern Gas and Silicon structures as candidate detector technologies to address this approach. However, since the necessary time resolution for pileup mitigation is of the order of 20-30 picoseconds (ps), both technologies require significant modification to reach the desired performance.
Photodetectors and charged particle detectors with time resolutions in the sub-nanosecond regime continue to have an impact in both High Energy physics and medical imaging. In High Energy physics the most widespread application is for particle identification, wherein the mass of particles of known momentum is measured with the time-of-flight (TOF) particle identification technique. The current state-of-the-art technology has recently been reviewed in Ref. [2]. Existing collider experiments (e.g. ALICE) now employ large scale TOF systems with performance at the sub-100 ps level but several promising new technologies have demonstrated ∼ 10 ps performance or better (for example the Microchannel PMT we use as a Cherenkov detector during the test beam measurements discussed below).
An early incentive for the development of MicroPattern Detectors (see e.g. [3]) was the promise of higher response speed and timing precision -a consequence of the more rapid signal collection and lower sensor capacitance. Except for early work at CERN (e.g. 1970-80s in the case of [3]), however, the emphasis in MicroPattern Silicon detectors rapidly moved to spatial resolution rather than temporal precision. Similarly, there has been little emphasis, in the 20 years since the GEM [4] and Micromegas [5] MicroPattern Gas Detectors (MPGD) were introduced, on exploiting their potential for fast timing. Nevertheless, in one of the original Micromegas papers [6], it was shown that sub-nanosecond time jitter could be obtained for single electrons photo-produced at the cathode surface. This is the approach that will be followed in the current paper, i.e. the timing attributes of Micromegas are used in a photodetector.
In 2015, our collaboration proposed a structure detecting extreme ultraviolet (UV) Cherenkov light produced in a MgF 2 crystal coupled to semitransparent CsI photocathode and a two stage Micromegas amplifying structure with electron amplification in both stages. In Ref. [7], we reported encouraging results of single photoelectron timing resolution using fast laser pulses, obtained with a chamber operated in sealed mode.
Subsequently, we improved the chamber integrity and the detector grounding in order to guarantee stable operation. For the results presented here we concentrate on a single pixel PICOSEC chamber (1 cm diameter), and use a bulk Micromegas amplification structure with a woven stainless steel mesh [8]. Beam tests using 150 GeV muons at CERN were carried out using several Micromegas detectors with various photocathode materials, gases, different discharge protection schemes, and read-out elements.
In this paper we present a summary of the results obtained, demonstrating the capability of our detector to reach time resolution of tens of ps, an improvement by two orders of magnitude compared to the standard MPGD detector performance. Detailed analysis methods and simulations were developed to better understand single electron detector response and time resolution.

The PICOSEC detection concept and the experimental setup
The detection concept presented here consists of a "two-stage" Micromegas detector coupled to a front window that acts as Cherenkov radiator coated with a photocathode, as shown in Fig. 1. A MgF 2 crystal is a typical radiator with light transmission down to a wavelength of 115 nm, a typical photocathode is CsI [9] with high quantum efficiency for photons below 200 nm. This configuration provides a large bandwidth for Cherenkov light production-detection in the extreme UV. The drift region is very thin (100-300 µm), which minimizes diffusion effects on the signal timing (of several ns in a MPGD-based drift region).
Due to the high electric field, photoelectrons also undergo pre-amplification in the drift region.
The readout is a bulk Micromegas [8], which consists of a woven mesh (18 µmdiameter wires) and an anode plane, separated by a gap of 128 µm, mechanically defined by pillars. This type of readout, operated in neon-or CF 4 -based gas mixtures, can reach gains of 10 5 − 10 6 , high enough to detect single photoelectrons [10].
In normal operation, a relativistic charged particle traversing the radiator produces UV photons, which are simultaneously (RMS less than 10 ps) converted into primary (photo) electrons at the photocathode. These primary electrons are preamplified in the drift region due to the high electrical field (∼20 kV/cm); then, they partially traverse the mesh, and are finally amplified in the amplification gap, where a high electric field (∼40 kV/cm) is applied.
The arrival of the amplified electrons at the anode produces a fast signal (with a risetime of ∼0.5 ns) referred to as "electron peak", while the movement of the ions produced in the amplification gap generates a slower component -"ion tail" (∼100 ns). A typical waveform is shown in Fig. 2.
It should be noted that due to preamplification in the thin drift gap the relative contribution to the overall signal of direct ionization by the traversing particle is negligible. In "COMPASS gas" (80%Ne+10%C 2 H 6 +10%CF 4 ) and for the conditions described in Sec. 2.3, relativistic muons create ∼ 21 ion clus- ters/cm with few ionization electrons per cluster. The probability to produce enough ionization charge that undergoes the same amplification (i.e. in the first ∼30 µm) as the typically 10 photoelectrons from the Cherenkov signal is only a few percent.

Prototype description
A sketch of the first PICOSEC prototype is presented in Fig. 3. The readout is a bulk Micromegas detector with a single anode of 1 cm diameter and an amplification gap of 128 µm, i.e. the distance between the anode and the mesh wires. The mesh used for the prototype is formed of 18 µm-diameter wires and has a 51% optical transparency. The amplification gap (between the mesh and the anode in was deposited serving as photocathode 1 . During beam tests, an additional 18 nm-thick CsI layer was deposited over the Chromium substrate in order to increase the number of photoelectrons produced by charged particles. In both configurations, a 10 nm-thick metallic ring is placed on the crystal to establish the potential of the photocathode. The whole detector is installed inside a stainless steel chamber, which is then filled with "COMPASS gas" at 1 bar absolute pressure. Other gases, like 80%CF 4 +20%C 2 H 6 at 0.5 bar absolute pressure, have also been used but this article will focus on the results obtained with the "COMPASS gas". The vessel has a transparent (quartz) entrance window to allow the passage of either UV light or laser pulse; it has two gas valves for gas circulation, as well as a large vacuum port for evacuating the vessel.  The schematic diagram of the detector is shown in Fig. 3. The cathode, anode, and mesh elements are electrically connected by SMA or SHV feedthroughs, as indicated. The cathode is connected to one CAEN High Voltage Supply (HVS) channel, the anode to a CIVIDEC preamplifier 2 (2 GHz, 40 dB), biased by a separate channel of the HVS, and the mesh is connected to ground by a 50 m long BNC cable, terminated with a 50 Ohm resistor in order to avoid signal reflections. Special attention was paid to proper grounding throughout the electronics design, and referred to the ground layer of the Micromegas readout.
Each of the high voltage lines has a dedicated low-pass filter to suppress ripples from the HVS.

Laser test: single photoelectron measurements
The time response of the PICOSEC detector for single photoelectrons was measured at the Saclay Laser-matter Interaction Center (IRAMIS/SLIC, CEA).
The experimental setup (Fig. 4) includes a femtosecond laser with a pulse rate ranging from 9 kHz to 4.7 MHz at a 267-288 nm wavelength and a focal length of  The PICOSEC detector was operated with the "COMPASS gas" at 1 bar absolute pressure. The anode voltage (HV2 in Fig. 1 Table 1. In general, the lowest voltage used corresponds to a detector gain high enough to distinguish the signal from the noise level (gain ∼ 10 5 ), while the highest voltage is the maximum value for which the detector operates in stable conditions (up to gains of ∼ 10 6 ). For each voltage configuration, more than 10 4 events were recorded with the oscilloscope, and subsequently analyzed offline.
During a fraction of the data-taking, the photocathode efficiency was less than 0.5%, which led us to include the PICOSEC signal in the trigger chain, in the interest of data collection efficiency. The trigger threshold varied between 10 and 90 mV, as shown in Table 1, leading to a bias of the recorded PICOSEC pulse height spectrum. In a later data-taking campaign, the photocathode was replaced to increase the signal efficiency up to ∼5% thus allowing us to remove the PICOSEC signal from the trigger chain. The detector was operated in the same voltage conditions as the data set with a trigger bias on the PICOSEC amplitude so they could be used to confirm that the charge distribution follows a Polya function [11], as discussed in Sec. 3.

Beam tests with 150 GeV muons
The time response of the detector to 150 GeV muons was measured dur- This information is later analyzed to estimate the mean number of photoelectrons produced by muons during beam tests.

Waveform analysis
In this section, we briefly describe the analysis performed on both laser and beam test data. For each PICOSEC signal, the baseline offset and noise level are determined using the 75 ns precursor of the pulse. Then, the "electron peak" amplitude (V max ) is defined as the difference between the highest point of the waveform and the baseline. For the timing measurement, a Constant Fraction (CF) method based on a sigmoid function is used to minimize the contribution of the noise. Other algorithms to determine the CF have been used with similar results. In this approach, a sigmoid function is fit to the leading edge of the electron peak. This function is defined as where P 0 and P 3 are respectively the maximum and the minimum values, P 1 is the inflection time (i.e. where the slope changes derivative), and P 2 quantifies the speed of the sigmoid change (i.e. is correlated to the signal risetime). The 20% CF is calculated as follows: For the photodetectors used as the time reference (i.e. MCP, or PD0 in the case of laser tests) a simpler approach is applied as signals are almost immune to any source of noise: after the calculation of the pulse baseline and amplitude, a cubic interpolation between four points around CF=20% is used to extract with better precision the temporal position of the signal. The "Signal Arrival Time" (SAT) is then defined as the difference between the PICOSEC CF time and that of the reference detector, as shown in Fig. 2.
The "electron peak charge" is defined as the integral of the waveform between the start and the end points, defined as those situated before and after the maximum and whose amplitude is less than one standard deviation away from the baseline. For those pulses with no clear separation between the electron peak and the ion tail, the end point has been alternatively defined as the time when the pulse derivative changes sign. The resulting value is then transformed to Coulombs, using the input impedance of 50 Ohm.

Laser test results
Two aspects of the PICOSEC time response in the laser measurements are discussed below. Firstly, we discuss the dependence of the time response on signal amplitude as this dependence (particularly concerning the role of the drift field and fluctuations in the preamplification at a given field) elucidates the physical origin of the PICOSEC time resolution. Secondly, we convolute this amplitude dependence with the actual amplitude distribution corresponding to a single photoelectron. Using this convolution, i.e. the full "single photoelectron time response", we can then calculate the PICOSEC response to the case of many photoelectrons produced in the Cherenkov signal from 150 GeV muons discussed in the next section.
Since the experimental data on the SAT resolution approximately follow a Gaussian time distribution, we could simply report the standard deviation as the time resolution of the PICOSEC detector. However, there is a small tail at high SAT values, due to small charge (or amplitude) signals with late arrival time, which accounts for a small fraction of the total events. This results in a correlation between the SAT and the electron peak charge (or amplitude). This correlation is quantified for each voltage setting by dividing the charge distribution in narrow bins and fitting a Gaussian distribution to the corresponding SAT values. A typical dependence of the resulting mean and standard deviation values on the electron peak charge is shown in Fig. 6. For both variables, there is a decrease with the charge, which can be described by the following parametric function: where y is either the mean or standard deviation of the SAT, x is the electron The same conclusion is derived from the dependence of the time resolution as a function of the electron peak charge on the anode voltage, which is shown in Fig. 7. Indeed, signals with the same electron peak charge and lower anode voltage (i.e. higher drift voltage) show a better time resolution, i.e. pulses with a higher preamplification gain have better timing properties than those with a higher amplification gain.
The CF algorithm discussed above is used to eliminate the expected correlation between signal amplitude and SAT observed for signals with similar shapes but different amplitudes (known as "time walk correction" [13]) normally observed when timing is derived from a fixed threshold. Nevertheless, there are also well known examples where both amplitude and signal risetime can vary from pulse to pulse, requiring "amplitude and risetime correction". We also considered this hypothesis since the time resolution varies by several hundreds of picoseconds, for different signal amplitudes-even with the CF method. However, as shown in Fig. 8, the average electron peak shape remains essentially identical. There is a real correlation between electron peak charge and the signal arrival time. This must be a consequence of the physical mechanism generating the PICOSEC signal (rather than an artifact of the timing algorithm).

Derivation of the overall "single photoelectron time distribution function"
As described in Sec. 2.2, data are collected with an electronic trigger generated by the PICOSEC detector for part of the dataset. The threshold level was in some cases high in comparison to the Root Mean Square (RMS) baseline noise (typically ∼2.5 mV), as detailed in Table 1. Supposing that the derived dependence of the mean and standard deviation of the SAT with the electron peak charge are also valid for pulse amplitudes lower than the threshold, the where µ i and σ i are the mean and standard deviation of the SAT in an interval i (i = 1, N ) of the electron peak charge (Q i ), and a i is the probability density function (PDF) for a given charge Q i , i.e. a i = A(Q i ) × ∆T , and N i=1 a i = 1. For all cases, the minimum electron peak charge Q 1 threshold is set to 0.033 pC (i.e. 10 mV in amplitude), equivalent to four times the typical RMS baseline noise. Meanwhile, the A(Q) PDFs are obtained by fitting each electron peak charge distribution by a Polya function [11] which is expressed as: where Q e is the single photoelectron charge, N is the number of photoelectrons (N = 1 in this case), and θ is the Polya parameter. This function describes well the single electron peak charge response of the PICOSEC detector, as shown in Fig. 9, including also the dataset without a PICOSEC threshold bias (Fig. 9, right). In each fit bin sizes and fitting regions were varied in order to estimate the systematic errors, which were then combined with the statistical errors.

Beam tests results with 150 GeV muons
The same analysis as in Sec. 3 is applied to the SAT distributions of 150 GeV muons, as a correlation with the electron-peak charge is expected. However, as shown in Fig. 11 (left), the mean of the SAT distribution is almost constant for each setting; this is explainable by the high drift fields (and preamplification gains) at which the PICOSEC detector is operated. Meanwhile, the time resolution decreases as the electron peak charge increases (Fig. 11, right).

Conclusions
In this paper, we present a new detector concept, called PICOSEC, composed of a "two-stage" Micromegas detector and a Cherenkov radiator equipped with a photocathode. The good timing resolution performance for single photoelectrons (σ t ∼ 76 ps) and for 150 GeV muons (σ t ∼ 24 ps) is promising and motivates further development towards practical applications. Among the significant issues to be addressed to ensure suitability for a large area detector to be used in high rate experiment are: 1) the development of efficient and robust photocathodes (or secondary emitters), and 2) scalability, including the development of the corresponding readout electronics.