Advances in nuclear detection and readout techniques

Abstract

“A Craftsman Must Sharpen His Tools to Do His Job,” said Confucius. Nuclear detection and readout techniques are the foundation of particle physics, nuclear physics, and particle astrophysics to reveal the nature of the universe. Also, they are being increasingly used in other disciplines like nuclear power generation, life sciences, environmental sciences, medical sciences, etc. The article reviews the short history, recent development, and trend of nuclear detection and readout techniques, covering Semiconductor Detector, Gaseous Detector, Scintillation Detector, Cherenkov Detector, Transition Radiation Detector, and Readout Techniques. By explaining the principle and using examples, we hope to help the interested reader underst and this research field and bring exciting information to the community.

1 Introduction

When an energetic particle passes through matter, it induces ionization or excitation. If the particle is charged, its electromagnetic field interacts directly with the orbital electrons of the atoms in the matter. Photon can undergo the Photoelectric effect, the Compton Scattering, or Pair Production, transferring part or full of its energy to the orbital electrons of the atom in the matter, resulting in ionization or excitation. In the case of uncharged neutral particles, such as neutrons, charged particles are produced by nuclear reactions, which then cause ionization or excitation. Elements that utilize the ionizing effect, luminescence phenomenon, and physical or chemical changes caused by nuclear radiation in gases, liquids, or solids for nuclear radiation detection are known as nuclear detectors. The nuclear detectors use an appropriate detection medium as the matter that interacts with the particles, and the ionization or excitation generated by the particles in the detection medium is transformed into various forms of signals. Nuclear electronics reads and processes the signal from the nuclear detectors and extracts the information. This information can then be used to directly or indirectly determine parameters of nuclear radiation, such as the type, energy, intensity, arrival time, or lifetime.

More than 100 types of radiation detectors can give electrical signals. Gas detectors were introduced as early as 1908 [1]. However, it was not until 1931 that the problem of fast counting was solved after the advent of pulse counters [2]. In 1947, scintillation counters appeared, significantly improving the efficiency of detecting particles due to their much greater density than gases [3]. The most notable is the NaI (Tl) scintillator, which has a high energy resolution for $\gamma$ rays [4]. In the early 60 s, the successful development of semiconductor detectors led to a new development of energy spectrum measurement technology. Modern nuclear detectors used in high-energy physics, nuclear physics, and other scientific and technological fields have been rapidly developed over the last few decades. This paper will discuss the principle, short history, development, and recent advances on some representing semiconductor detectors, gaseous detectors, scintillation detectors, Cherenkov detectors, transition radiation detectors, and readout techniques.

2 Semiconductor detector

When the radiation ray or particles incident into the sensitive region of the semiconductor detector, the radiation ray or particles continuously loses energy and generates electron–hole pairs, and is separated from the two ends of the electrode drift under the action of the external electric field to collect, thus forming an output pulse signal. According to the structure classification, the structure of semiconductor detector has crystal conductivity type, p-n junction type, p-i-n junction type, Schottky junction type and so on.

The number of electron holes created is related to the energy of absorbed particles or rays and the energy of electron-hole pair formation, shown in the following formula:

$$\begin{aligned} N=\frac{E}{\varepsilon _{i}} \end{aligned}$$

(1)

where E is the absorbed energy, $\varepsilon _{i}$ is the electron–hole creation energy. For silicon, the electron hole pair creation energy is 3.6 eV, while silicon carbide is 8.9 eV. This section will discuss the silicon detectors and the wide bandgap semiconductor detectors.

2.1 Silicon detector

Silicon detectors are very well suited to detecting and measuring ionizing radiation and light caused by interacting with charged particles and photons (soft X-rays). A great feature of silicon detectors is that they can operate with low noise at room temperature due to the band gap of 1.12 eV. In addition, silicon has a high density of 2.329 g/cm$^3$, a small average ionization energy of 3.62 eV, good mechanical stability, and is easy to produce on a large scale. These advantages make silicon the perfect option for many physics experiments and equipment.

1960 Bromley showed a proposal for a 3D array of silicon diodes that would function as a solid-state “cloud chamber” [5]. The Charge-Coupled Device (CCD), introduced in 1969, with good spatial resolution and low noise in photon detection, received the Nobel Prize in 2009. Since the first half of the 1980s, Silicon Strip Detectors (SSD) have become dominant in particle tracking [6]. In the 1980s and 1990s, an evolution started from strip to pixel detectors, mainly consisting of monolithic and hybrid types. The Low Gain Avalanche Diode (LGAD) recently provided fast detection of Minimum Ionizing Particles (MIPs) with a timing resolution of several picoseconds. Recent decades have witnessed substantial growth in silicon detectors, expanding from a few thousand channels to billion channels with dramatically increased granularity facilitated by rapid advancements in semiconductor technology [7].

2.1.1 Charge-coupled device

CCD comprises a series of coupled Metal-Oxide-Semiconductor (MOS) capacitors as its fundamental structure. Electrons are produced when photons hit MOS capacitors because of the photoelectric effect, and will be collected as signal charge packets by potential wells of each MOS capacitor, which are formed by applying positive voltages to gate electrodes. Subsequently, the packets stored in each MOS capacitor are transferred from one pixel to its neighbor through sequential adjusting gate voltages of each MOS capacitor. The last capacitor dumps its charge into a charge amplifier, which converts the charge into a voltage, and then readout. MOS capacitors share readout circuit, so the transferring process will be repeated continuously until all the signal charge packets are read out.

CCD-based detectors can be implemented in several different architectures. The most common are full-frame, frame-transfer, and interline. In a full-frame device, all of the imaging area is active. While in frame-transfer CCDs, half of the silicon area is covered by an opaque mask, typically aluminum. It is necessary to quickly transfer input signals from the image area to the opaque or storage area to minimize smear in this design. Unlike frame-transfer, the interline architecture involves only a pixel shift from the imaging area to the storage area, enabling shutter times of less than ${1}\,{\upmu \text{s}}$ and virtually eliminating smear.

The advantages of CCD are apparent. It has excellent spatial resolution because its pixel size can be very small. Pixels as small as ${1.56}\,{\upmu \text{m}} \times {1.56}\,{\upmu \text{m}}$ have appeared as early as 2006. Also, the CCD has low noise because its readout process does not produce noise, making it well-suited for small signal detection. In addition, shared readout provides good pixel-to-pixel consistency. What’s more, it’s worth noting that modern CCD technology allows for manufacturing large wafer-level devices, simplifying the mechanical design of detectors, which is crucial for experiments requiring a large sensitive area [8].

The primary utilization of CCD is in astronomical observation. For instance, the Skipper-CCD, designed for the Oscura experiment [9] and employed in low-energy neutrino studies and dark matter searches, is crafted from high-resistance (HR) n-type silicon wafers. The sensor has a thickness of 675 $\upmu$m, an effective area of 1.9 cm $\times$ 1.6 cm, and charge can be read through amplifiers at the four corners. Meeting the Oscura’s stringent requirements, including a readout time of less than 2 h and a radioactive background rate of 0.01 event/kg/day/keV, the sensor exhibits a dark current of approximately 10$^{-6}$ e$^-$/pix/day. Test results conducted at Fermilab (as depicted in Fig. 1) reveal that 71% of the sensors exhibit sub-electron noise, with a surface dark current of about 0.031 e$^-$/pix/day [9].

Fig. 1

(Color online) Left: Skipper-CCD in Cu module. Center and right: Setups at FNAL for testing packaged sensors. Reproduced from [9]

The “Mozi” Wide Field Survey Telescope (WFST) is a new generation survey telescope that is being built in China. It is equipped with a mosaic CCD camera with 0.73 gigapixels on the primary focal plane for high quality image capture over a 6.5-square-degree field of view [10]. Comprising nine E2V CCD290-99 chips, each with a resolution of 9 K $\times$ 9 K and a pixel size of 10 $\upmu$m, the camera supports full-frame or split full-frame readout modes. The 3D model of the CCD detector system is illustrated in Fig. 2. The readout can occur through 8 or 16 output channels, with a typical readout noise of 4 e$^-$@0.5MHz. To meet the scientific objective of rapid sky surveying, the maximum readout speed reaches 3 MHz, and the readout noise is maintained below 15 e$^-$@1MHz [11]. Nowadays, CCD also finds applications in fields such as spectral analysis and heavy ion Computed Tomography (CT) [12].

Fig. 2

(Color online) 3D model of the CCD detector system on “Mozi”. Reproduced from [11]

2.1.2 Silicon strip detector

The SSD is the first detector device using the lithographic capabilities of microelectronics, mainly used as a vertex and tracking detector. As shown in Fig. 3, the SSD is commonly fabricated through selective etching of microstrips on the surface of N-type silicon wafers. The highly doped P⁺ microstrip forms a PN junction on the surface and extends its depletion layer across the entire N-type substrate with applied bias voltage. After covering aluminum on the top, a microstrip that acts as a charge-collecting electrode is completed. Multiple strips form a single-sided SSD, which provides one-dimensional position detection. When particle hits, electron–hole pairs are generated in the depletion region because ionization caused by deposited energy. Holes, driven by an external electric field, are collected by the strips, converted into electrical signals, and processed by the readout circuit. The double-sided SSD featuring heavily doped P⁺ junction strips that collect the holes and the N⁺ ohmic strips that collect electrons can realize two-dimensional position detection. Since SSDs have low noise, good linearity, a high count rate, and excellent position and energy resolution, they are widely used in high-energy physics, nuclear physics, and space detection facilities [13, 14].

Fig. 3

(Color online) Working principle diagram of AC coupled single-sided SSD. Reproduced from [15]

In high-energy physics, the radiation-hardened Silicon Microstrip Vertex Detector (SVX’) was incorporated into the CDF experiment during the Tevatron ${{\overline{p}}}p$ collider run 1B in 1993. As the first silicon vertex detector in a hadron collider environment, SVX’ modules (also referred to as barrels) consist of four layers of SSDs segmented into twelve ${30}^\circ$ wedges. Three wafers are bonded to form a 25.5 cm long “ladder” with strips aligned for $\gamma \phi$ coordinate measurements. The AC-coupled readout is facilitated by the radiation-resistant SVXH3 chip [16], utilizing a ${1.2}\,{\upmu \text{m}}$ CMOS process with radiation tolerance exceeding 1 Mrad. The chip provides a gain of 21 mV/fC and an equivalent input noise of 1300 e$^-$ at a strip input capacitance of approximately 30 pF [17], supporting data sparse and serial readout modes [18]. When a single strip is hit, the positional resolution can reach ${13}\,{\upmu \text{m}}$ [16]. The SSD has also been widely used in high-energy experiments, such as the Semiconductor Tracker (SCT) in ATLAS for two-dimensional track measurement [19], the Silicon Strip Tracker (SST) in CMS for readout of the $\gamma \phi$ coordinate and measuring three-dimensional information for the separation of particle tracks [20],and the NA11 spectrometer at CERN SPS for flight paths reconstruction [21], and so on.

SSD plays a vital role in nuclear physics experiments. The Institute of Modern Physics (IMP) has constructed a gas-filled recoil separator called Spectrometer for Heavy Atom and Nuclear Structure (SHANS) to study the heavy and superheavy nuclei properties. A silicon semiconductor detector box (Si-box) is installed at the focal plane position of the separator, as illustrated in Fig. 4. The Si-box incorporates three Position Sensitive Silicon Detectors (PSSD) at the back as implantation detectors, with a thickness of ${300}\,{\upmu \text{m}}$ and a collective effective area of 150 mm $\times$ 50 mm, offering 3 mm horizontal position resolution. The PSSD demonstrates a typical energy resolution of 50 keV FWHM for 5–10 MeV $\alpha$ particles. Leveraging this PSSD detector, it can be used to measure $\alpha$ particles of 1–20 MeV, implantation and fission fragments with energies of 5–200 MeV, and detect the esca** radioactive decay events [22]. Similar applications of SSD in nuclear physics can also be found in MUST, TIARA, and HIRFL-RIBLL. The MUST (“MUr $\grave{a}$ Strips”) detector consists of 8 SSD–Si (Li) telescopes used to identify recoiling light charged particles through time of flight, energy loss and energy measurements and to determine precisely their scattering angle through X and Y position measurements [23]. The Transfer and Inelastic All-angle Reaction Array (TIARA) consists of 8 resistive charge division detectors forming an octagonal barrel around the target and a set of double-sided silicon-strip annular detectors positioned at each end of the barrel, designed to study direct reactions induced by radioactive beams in inverse kinematics [24]. The detection system consists of five $\Delta E - E$ telescopes, consisting of one double sided silicon strip detector (DSSD) as the $\Delta E$ detector, and a square silicon detector as the E detector, designed to measure the angular distributions of both elastic scattering and breakup simultaneously, on the Radioactive lon Beam Line in Lanzhou at Heavy lon Research Facility in Lanzhou(HIRFL-RIBLL) [25].

Fig. 4

(Color online) Schematic view of the focal plane detection array. Reproduced from [26]

The SSD has been a “standard” component for space detection [27]. The Dark Matter Particle Explorer (DAMPE), launched in 2015, incorporates silicon-tungsten tracker-converter (STK) to collect the electron-positron pairs converted from the incoming photons by the tungsten converters. As shown in Fig. 5, the STK contains of 6 tracking planes each consisting of 2 layers of SSD arranged orthogonally. Each single layer consists of 16 ladders, and each ladder comprises 4 modules bonded end-to-end. The SSDs are glued on the flex part of the Tracker Front-end Hybrid (TFH) board to form a ladder. Each layer of SSD has an active area of 0.55 m$^2$, with a total radiation length of 0.976% $X_0$, spatial resolution $<{80}\,{\upmu \text{m}}$ within ${60}^\circ$ incidence, and a total weight of 154.8 kg.

Fig. 5

(Color online) Left: Exploded view of the STK; Right: The STK single ladder, made by four SSDs. Reproduced from [28]

The readout is performed on one every other strip (corresponding to 384 channels per ladder) in the SSD. The signal sha** and amplification is performed by six VA140 ASIC chips mounted on the TFH [28]. The VA140 is a 64-channel low-noise charge-sensitive amplifier ASIC from the Norwegian IDEAS company. Each channel of the VA140 comprises a charge-sensitive preamplifier, a filter sha** circuit, and a sample and hold circuit. The input charge dynamic range spans from ${-200}\,{\text{fC}}$ to 200 fC, with a sha** time of only ${6.5}\,{\upmu \text{s}}$. This ASIC employs serial readout through a multiplexing circuit and the power consumption is 0.29 mW/channel.

Based on the successful development and operation of DAMPE, the Purple Mountain Observatory of the CAS, together with several institutions, proposed the Very Large Area Gamma-ray Space Telescope (VLAST).As shown in Fig. 6, the VLAST plans to use SSD to build Silicon Tracker and low Energy gamma-ray Detector (STED). The main function is to realize the conversion of high-energy gamma photon-electron pairs, and to achieve high-angular resolution observation of gamma photons through the track measurement of electron pairs. The main technical indicators of STED are [29]:

• Number of detector layers: 8 super layers; (each super layer includes a CsI detection layer and two large silicon micro-strip detection layers);

• Active detection area of each layer: $\ge$ 2.8 m $\times$ 2.8 m;

• Detection energy range: 1 MeV –100 MeV;

• Spatial resolution $< {0.1}^\circ$ (@50 GeV).

Fig. 6

(Color online) The schematic plot of the payload of VLAST. Reproduced from [29]

The VA140 from IDEAS company is also a potential candidate for the readout of the SSD on VLAST. In addition, the IMP is now develo** a readout chip called SiReadout. The first version of the chip is shown in Fig. 7. The preliminary single-channel test indicates that it has a gain of 2.01 mV/fC, power consumption of approximately ${220}\,{\upmu \text{W}}$, a peaking time of ${3.12}\,{\upmu \text{s}}$, linearity error below 1%, and an Equivalent Noise Charge (ENC) of 992 e$^-$ at zero F plus 13.5 e$^-$ per pF.

Fig. 7

(Color online) Microphoto of the first version of SiReadout

Also, the ALPHA Magnetic Spectro-meter (AMS) experiment similarly utilizes SSD to build a magnetic spectrometer to measure momenta, charges and mass of the particles [30], the Fermi Large Area Telescope (Fermi-LAT) builds the LAT tracker to reconstruct the incoming photon direction, etc [31].

2.1.3 Silicon pixel detector

Silicon pixel detector is currently one of the main detectors and is expected to play a significant role in the future due to their exceptional spatial resolution, reduced material budget, low noise, and rapid readout rates. It mainly consists of a densely packed pixel array and peripheral readout circuits, with each pixel containing a charge-sensitive unit for collecting electrons and outputting electrical signals and its front-end signal processing circuit. The distinct signals generated by particles interacting with different pixels offer precise two-dimensional positional information. Silicon pixel detectors can be classified architecturally into monolithic and hybrid types.

Monolithic active pixel sensor The monolithic type integrates the charge-sensitive unit and front-end circuit on a single substrate, minimizing complexities in interface designs. This integration ensures high granularity, a low material budget, and a relatively small equivalent input capacitance. Monolithic Active Pixel Sensor (MAPS) is currently one of the most promising and well-developed technologies among monolithic types.

Fig. 8

(Color online) Left: The array structure of MAPS; Right: The principle of MAPS

MAPS shares the similar detection principle as SSD. As depicted in Fig. 8, a lightly doped P-type epitaxial (EPI) layer grows on a substrate heavily doped with P-type impurities, the Nwell/P-EPI diode is the charge-sensitive unit and the front-end circuit is also on the same substrate connecting to it directly. MAPS typically features pixel sizes ranging from 10–${30}\,{\upmu \text{m}}$, resulting in a position resolution of 3–${7}\,{\upmu \text{m}}$. The readout speed can achieve hundreds of kilohertz, and noise is maintained at approximately 10e$^-$ level. MAPS demonstrates a good balance in resolution, material budget, radiation hardness, readout speed, and power consumption.

The EPI process in MAPS significantly impacts charge collection. The standard EPI process has a thickness of approximately ${10}\,{\upmu \text{m}}$ which causes a small depletion layer, and an electrical resistivity of around 10 $\Omega$ cm, making thermal diffusion the dominant way for charge collection. Therefore, it needs a long time to collect electrons and the collection efficiency is very low. In contrast to that is an HR EPI process with a thickness of up to ${40}\,{\upmu \text{m}}$ and an electrical resistivity that potentially can reach $\sim 1000\, \Omega$ cm. The depletion layer is thicker, and charges can also be collected by drifting. The process of collecting is faster and more efficient. Moreover, it reduces the probability of electron–hole pair recombination, enhancing radiation hardness and improving the Signal-to-Noise Ratio (SNR). In the standard twin-well process (Fig. 9 left), PMOS cannot be used in pixel design because the Nwell where PMOS resides competes with the Nwell of the diode, leading to a reduction in Charge Collection Efficiency (CCE). Hence, the deep Pwell is needed to isolate the two. In addition, applying a reverse bias voltage to the substrate could expand the depletion layer region which means increasing CCE and improving radiation hardness, but it may also cause the peripheral readout circuit on the same substrate not to work properly, so deep Nwell is needed for protection. Simulations can give the preliminary study of charge collection in certain process for specific particles in the early phase of design [32,33,34]. In summary, the prevailing approach for MAPS involves the utilization of a complete quadra-well process (Fig. 9 right) with HR EPI.

Fig. 9

(Color online) Left: twin-well process; Right: quadra-well process

In experimental physics, MAPS finds primary applications as vertex and track detectors in collider experiments. The Heavy Flavor Tracker (HFT) detector in the STAR experiment is the world’s first detector to use MAPS to enhance vertex resolution and extend measurement capabilities in the heavy flavor domain [35]. The HFT detector incorporates MAPS in its innermost two layers (at radii of 2.8 and 8 cm from the beamline) among four concentric cylinders near the STAR interaction point, and these layers feature 400 Ultimate (MIMOSA-28) chips, covering a total silicon area of 0.16 m$^2$, as illustrated in Fig. 10. Every layer costs a global material budget of only 0.5% $X_0$ because the chip on it operates normally with air cooling at room temperature [36].

Fig. 10

(Color online) Left: Schematic view of the HFT inside the TPC inner field cage, reproduced from [36]; Right: MIMOSA28 on its PCB. Reproduced from [37]

The Ultimate chip, designed by the IPHC, fabricated by ${0.35}\,{\upmu \text{m}}$ HR OPTO process (400 $\Omega$ cm), features a pixel array of 928 $\times$ 960 pixels with a pixel pitch of ${20.7}\,{\upmu \text{m}}$, providing a sensitive area of approximately 3.8 cm$^2$. Its pixel includes a sensing diode for charge collection as well as an amplification circuit and a Correlated Double Sampling (CDS) circuit for signal extraction and noise removal. Each pixel column is terminated with a high precision discriminator and is read out in a rolling shutter mode at 5 MHz. The discriminator’s outputs are processed through an integrated zero suppression logic and the sparsified data are sent out to the acquisition via two 160 Mbps LVDS outputs. The Ultimate demonstrated a MIPs detection efficiency near to 100%, a fake hit rate of less than 10$^{-4}$, and power consumption maintained at 150 mW/cm$^2$ [37].

The ALICE Inner Tracking System 2 (ITS2) stands as the world’s largest detection system employing MAPS. As illustrated in Fig. 11 left, the detector layout features concentric 7 layers with radii ranging from 23 mm to 400 mm. These layers consist of over 24120 ALICE Pixel Detector (ALPIDE) chips (Fig. 11 right) [38], forming a 10 m$^2$ active detection area with a total of 12.5 $\times 10^9$ pixels.

Fig. 11

(Color online) Left: Layout of the ITS2 detector, reproduced from [39]; Right: The ALPIDE chip. Reproduced from [40]

ALPIDE is fabricated using the TowerJazz 180 nm quadra-well HR CMOS process ($>1\, \text{k}\Omega$ cm), and features 512 $\times$ 1024 pixels with the pitch of ${28}\,{\upmu \text{m}}$, providing a sensitive area of 30 mm $\times$ 13.8 mm [41]. Its pixel includes an octagon collection diode which achieves nearly 100% CCE and a distinctive front-end circuit consisting of a continuously active discriminating amplifier and a multiple-event memory, which yields an ENC of less than 10 e$^-$. The in-pixel multiple-event memory is read out asynchronously through a priority encoder circuit in each double column. This is fast and power efficient as the expected occupancy is low and only hit pixels are read out in a hit-driven mode. Data are collected at the periphery and shipped off the detector by means of a high-speed serial link [42]. Extensive beam tests confirm that ALPIDE achieves a detection efficiency exceeding 99%, a false hit probability below the required 10$^{-6}$ level, and a spatial resolution better than the desired ${5}\,{\upmu \text{m}}$. Even after exposure to a TID of 2.7 Mrad and a non-ionizing energy loss (NIEL) flux of 1.7$\times$10$^{13}$ (1 MeV neq/cm$^2$), surpassing the anticipated detector lifetime, it sustains performance and provides a readout rate of 100 kHz with a power density of less than 40 mW/cm$^2$ [43].

MAPS also plays a crucial role in high-resolution beam telescopes for tracking charged particles, exemplified by the Desy II beam telescope. The first generation adopted the EUDET-type framework, employing MIMOSA-26, which provided outstanding spatial resolution and a lower material budget. Achieving a distribution resolution of ${1.83}\,{\upmu \text{m}}$ for a 6 GeV electron or positron beam on the Device Under Test (DUT), the rolling shutter readout operated at a frequency of approximately 10k frames per second. As MIMOSA-26 production ceased and updating became unfeasible, a new beam telescope was constructed based on ALPIDE technology (Fig. 12). This telescope features a sensitive area of 414 mm$^2$, a trigger rate of up to 100 kHz, and significantly reduced noise levels compared to the previous telescope. This enhancement allows for more efficient beam utilization and a cleaner tracking environment. The spatial resolution remains in the micron range (approximately ${5}\,{\upmu \text{m}}$ at 6 GeV), with a low fake hit rate [44].

Fig. 12

(Color online) Design of the ALPIDE beam telescope system. Reproduced from [44]

MAPS is increasingly pivotal in proton and heavy-ion imaging, particularly in the burgeoning field of ion beam radiotherapy. Unlike traditional photon radiation, ion beams exhibit a Bragg peak, a concentrated dose deposition, whose depth can be finely adjusted by altering the beam energy. This feature enhances protection for healthy tissues [45]. Proton and heavy-ion imaging research contributes to refining treatment plans for proton/heavy-ion therapy [46]. Current methods of making particle therapy treatment plans rely on converting X-ray CT HU value into Relative Stop** Power (RSP) of proton/heavy ions, which led to inevitable range uncertainties. However, the Bergen proton CT (PCT) system (Fig. 13), incorporating a Digital Tracking Calorimeter (DTC), can directly measure the RSP to address this problem.

Fig. 13

(Color online) Principle of the Bergen proton CT. Reproduced from [47]

The DTC comprises 43 layers, each equipped with 108 ALPIDE chips, which feature the first two layers as tracking layers for acquiring the position information of incoming particles and the subsequent 41 layers as a digital calorimeter. As a particle traverses the detector, it deposits energy in the sensitive layer, generating a 3D digital hit map along its path. The final prototype has a measuring area of 27 cm $\times$ 16.6 cm, which is adequate for imaging the human head [47].

Another compact full digital system that utilizes the MAPS with a similar structure to Bergen PCT but for heavy-ion imaging is the Hi’CT proposed by IMP (Fig. 14). The simulation results achieve less than 1% deviation in Relative Stop** Power (RSP) and better image quality of CATPHAN phantoms. The real-time imaging capability of Hi’CT may reduce target deviations caused by organ or respiratory movement, achieving optimized treatment effectiveness and improved quality of life for patients [48].

Fig. 14

(Color online) Conceptual design of the Hi’CT. Reproduced from [48]

MAPS technology has advanced with the adoption of stitching technique in wafer-level chip manufacturing. The stitching technique is the way to continue the scaling of technology in the semiconductor industry because of the reticle size limitation [49]. It is achieved by dividing the reticle into sections that could individually be exposed and aligned with neighboring sections [50]. As Fig. 15 left shows, the design reticle gets subdivided in sub-frames that correspond to sub-frames of the photomasks. During the photolithographic patterning of wafers, these are selectively exposed to adjacent locations according to a pre-established pattern. This requires very accurate translations and alignment of the wafers between each exposure. The peripheral structures along the outer edges of the core array and at the four corners are designed in dedicated sub-frames of the reticle. The red lines in the figure indicate the dicing lanes. With a judicious design of the geometries in the reticle sub-frames, large chips with diagonals approaching the wafer diameter become feasible, provided their core area can be constructed as an array of sub-units regularly repeating in space. Interconnections across the sub-units are made with the joining of wiring geometries at the abutment boundaries [51].

Fig. 15

(Color online) Left: Principles of stitching, reproduced from [51]; Right: Layout of the ITS3 Inner Barrel. Reproduced from [52]

The upgrade of ALICE’s ITS3 (Fig. 15 right) is prepared to utilize stitching technology to manufacture a kind of single MAPS on a 12-inch silicon wafer, achieving dimensions of 27 cm $\times$ 9 cm. ITS3 is expected to significantly reduce the material budget from 0.35%$X_0$ to 0.05%$X_0$ because the new MAPS will be capable of self-bending without the need for complex support and cooling systems. Simultaneously, ITS3 can place the innermost layer at a radial distance of only 18 mm from the interaction point. These features will enhance the resolution of impact parameters to twice that of all momenta and significantly improve tracking efficiency at low transverse momentum [52]. In addition, large scientific facilities such as the Electron-Ion Collider in China (EicC), the Electron-Ion Collider (EIC), and the Nuclotron-based Ion Collider Facility (NICA) are also preparing to adopt wafer-scale MAPS implemented with stitching technology.

As mentioned before, reverse bias can enlarge the depletion layer region, but normal CMOS processes typically have a maximum bias substrate voltage of 5 V [53]. High voltage (HV) CMOS technology is starting to be used in MAPS to improve sensor properties. Unlike the quadra-well process mentioned earlier, in the HV CMOS process, the deep Nwell is used to protect the entire circuit except for the charge-sensitive unit, which is another kind of diode composed of EPI and the deep Nwell itself as shown in Fig. 16. Such a design can even achieve a 100% fill-factor [54]. A typical example is ALTASpix3,originally designed for the upgrade of the ATLAS tracking experiment and a option for the silicon tracking detector of the Circular Electron Positron Collider (CEPC). Its deep Nwell connects to the positive power supply rail at 1.8 V and the maximum voltage of the substrate is around 66 V, corresponding to a depleted region of approximately ${30}\,{\upmu \text{m}}$ [55].

Fig. 16

(Color online) The principle of HV MAPS. Reproduced from [55]

The Silicon-On-Insulator (SOI) CMOS technology has also been used to significantly enhance radiation hardness for MAPS design. SOI wafers are composed of a thin Silicon film (device layer) on top of an insulating layer (buried oxide) that is manufactured on a standard Silicon substrate. In traditional SOI technologies, the substrate serves solely as a mechanical support for the silicon film. In detector applications, as shown in Fig. 17, the substrate has high resistivity and is utilized for creating the sensor (a matrix of fully depleted diodes) monolithically coupled to the readout electronics integrated in the silicon film above the insulating layer [56]. Laboratory laser testing of SOI CMOS pixel detectors has demonstrated excellent TID tolerance up to 1 Gray [57].

Fig. 17

(Color online) The principle of HV MAPS. Reproduced from [56]

One consideration to address limitations in pixel size is constructing circuit chips in three-dimensional (3D) structures [58]. One method is 3D stacking, illustrated in Fig. 18, employing Through-Si Via (TSV) for vertical communication.

Fig. 18

(Color online) Schematic cross-section of the two tiers (sketch not to scale). Reproduced from [59]

Another method, known as 3D detectors, decouples electrode distance and substrate thickness. It allows to place the electrodes perpendicular to the silicon wafer penetrating through the substrate. Therefore, in contrast to standard planar detectors, the depletion region laterally grows between the electrodes [60], as depicted in Fig. 19.

Fig. 19

(Color online) Left: Schematic cross-sections of planar sensor; Right: 3D sensor. emphasizing the decoupling of active thickness ($\Delta$) and collection distance (L) in 3D sensors. Reproduced from [61]

Nuclear physics experiments also require MAPS to have the capability for time and energy measurements beyond position only. Time measurement is needed to address the high counting rate requirements, such as the China Hyper-Nuclear Spectrometer (CHNS) and precise monitoring of heavy ion beams, which may require counting rates as high as 10$^6$ to 10$^8$ counts per second, corresponding to a time precision of 10 ns to ${1}\,{\upmu \text{s}}$. Energy measurement contributes to position resolution and particle identification. For example, the B$\rho$-DE-TOF (magnetic rigidity-ionization energy loss-time of flight) method, which combines momentum generated by trajectory curvature and the Bethe-Bloch formula, is mainly used in the identification of particles in medium to high energy radioactive beams and the identification of reaction products on secondary targets. According to the relationship between ionization energy loss $\Delta E$ and particle charge number Z, and velocity v: $\Delta E \propto Z^2/v^2$, using $\Delta E$ combined with TOF measurement can realize particle identification [62]. Meanwhile, for real-time monitoring of heavy ion beams at facilities such as the Heavy Ion Research Facility in Lanzhou (HIAF), the spatial resolution can be improved by calculating the center of mass of large clusters using energy information [63]. It can also provide calibration for time measurements.

MAPS development in China started in the 2010s and has grown rapidly. The representing ones for MIPs detection are the MIC series [64] from Central China Normal University (CCNU), the Taichupix [65] and Jadepix [66] from the Institute of High Energy Physics (IHEP) of the CAS, the SuPix from Shandong University [71]

5 Cherenkov detector

5.1 The principles of the Cherenkov detector

A uniformly moving charged particle traversing through a homogeneous medium with a refractive index of n, and with a velocity surpassing the phase velocity of light in the medium c/n, initiates a coherent superposition of electromagnetic radiation emitted during the de-excitation process of the medium’s atoms or molecules. This phenomenon gives rise to the formation of a Cherenkov light cone along the direction of particle motion. The relationship between the Cherenkov radiation angle ($\theta _\text{C}$) and the velocity of the charged particle is expressed as:

$$\begin{aligned} \cos \theta _\text{C}=1/(n\beta )=c/(nv). \end{aligned}$$

(14)

Since the momentum of the charged particle can be reconstructed from its trajectory in a magnetic field (tracking reconstruction), and its velocity (or $\beta =v/c$) can be obtained from measuring the Cherenkov radiation angle, the combination of these two parameters allows for the determination of the charged particle’s mass, facilitating Particle IDentification (PID). The detector exhibits a rapid response, robust radiation tolerance, and the capability to discriminate particles over a wide range of momenta.

Currently, two commonly used Cherenkov detectors have been developed: the Ring-Imaging CHerenkov detector (RICH) and the Detector of Internally Reflected Cherenkov light (DIRC), as illustrated in Fig. 88. RICH detector directly measures the Cherenkov radiation angle excited by charged particles within the radiator material. On the other hand, DIRC detector determines the Cherenkov angle indirectly by measuring the exit angle and time of Cherenkov light after multiple internal reflections within a radiator material, commonly fused silica. The advantages of RICH detector include the ability to discriminate particles over a wide range of momenta by replacing radiators with different refractive indices. However, its drawbacks are the larger volume of the optical imaging system, complex structure, and higher cost. In comparison, DIRC detector features a more compact structure with a thickness typically ranging from 1 to 2 cm, resulting in a smaller spatial requirement for the detector. However, one limitation of DIRC detector is its smaller momentum coverage compared to RICH detector. For instance, the state-of-the-art high-performance DIRC (hpDIRC) in the Electron-Ion Collider (EIC) is expected to achieve a maximum momentum of $\sim$ 6 GeV/c at 3$\sigma \pi$/K separation [370]. Based on the momentum distribution characteristics of final-state particles produced in electron-nucleon collisions, it is common practice to employ RICH detector in the endcap region and DIRC detector in the barrel region, as exemplified by the design of Belle II [371, 372].

Fig. 88

(Color online) Principles of the Cherenkov detector: different charged particles induce Cherenkov lights with different Cherenkov angles in the quartz radiator (upper); Imaging of Cherenkov rings for different charged particles (lower). Reproduced from [373]

5.2 The development of RICH

The RICH detector was invented as early as the early 1980s and has been utilized in experiments such as E605 [374], WA69 [375], and WA82 [376]. Following over a decade of development and iterations, the third generation of RICHes, constructed in the mid-1990s, demonstrated outstanding performance in experiments such as SELEX [377], HERMES, and HERA-B. With advancements in novel photodetector devices and high-speed readout electronics, the significance of the new generation of RICHes in high-energy particle physics experiments has become increasingly prominent [378].

HERA-B was an experiment conducted at the HERA electron-proton collider to study B mesons and D mesons produced in the interaction of 920 GeV/c protons with a fixed target. The RICH detector in this experiment utilized C$_4$F$_{10}$ gas as the radiator, and the spherical mirror was split into two halves, tilted at 9$^{\circ }$ in opposite directions (Fig. 89), to ensure that the photon detector only captured Cherenkov light cones and avoided interference from other particles. The upper and lower photon detector modules of the RICH detector consisted of Hamamatsu R5900-M16, Hamamatsu R5900-M4, and other devices, including a telescope system to enhance the efficient collection of photons [379]. The detector was capable of achieving a 3$\sigma$ separation for $\pi$/K particles with momenta of $\sim$ 50 GeV/c [380].

Fig. 89

Side view of the RICH. Rays emitted by a particle and their paths to the photon detector are indicated. Reproduced from [379]

The HERMES experiment employed a dual-radiator RICH (dRICH), utilizing C$_4$F$_{10}$ gas and a silica aerogel wall to extend the momentum detection range. This configuration enabled the discrimination of $\pi$/K/p particles in the momentum range of 2 to 15 GeV [381]. Interestingly, this approach was initially proposed by the LHCb experiment. In LHCb, the RICH 1 detector employed a combination of C$_4$F$_{10}$ gas and aerogel for particles in the polar angle range of 25 to 300 mrad and momentum range of 2 to 40 GeV/c. RICH 2 detector only used gaseous CF4 for PID in the polar angle range of 15 to 100 mrad and momentum range of 15 to 100 GeV/c [382]. Nevertheless, during its RUN I phase, it was observed that RICH 1 detector couldn’t effectively differentiate particles from these two radiators, and the presence of aerogel reduced the reconstruction rate. Consequently, during RUN II, the aerogel was removed [383]. The photon detectors of the RICH detector utilized the Hybrid Photon Detector (HPD) [384], which was developed in collaboration with Hamamatsu Photonics and specifically designed for the LHCb RICH system. They were subsequently upgraded in 2019–2020 to Hamamatsu’s R13742 MaPMTs and R13743 MaPMTs [385].

The BELLE II experiment, in order to increase photon yield without compromising resolution, adopted a near-focusing RICH scheme with a dual-layer aerogel radiator. This scheme employed aerogel layers for focusing, where the refractive index of the upstream aerogel was slightly lower than that of the downstream aerogel (1.045 and 1.055). The photon detectors, utilizing the Hybrid Avalanche Photo Detector (HAPD) [386] jointly developed with Hamamatsu Photonics, achieve a 3$\sigma$ separation of $\pi$/K up to $\sim$ 4 GeV/c [387].

The main scientific objectives of the currently under construction EIC involve investigating the spin and flavor structure of nucleons and atomic nuclei, as well as researching Quantum Chromodynamics (QCD) in extreme parton density regimes. It is the world’s first collider with polarized electron and light-ion beams, capable of generating heavier, non-polarized ion beams, up to uranium. As shown in Fig. 90, the electron endcap, hadron endcap, and barrel regions of the EIC employ Cherenkov detectors for PID, specifically utilizing module RICH (mRICH), dRICH, and DIRC [388, 389](see the following section for DIRC details).

Fig. 90

(Color online) Top view of the current layout of the full acceptance JLab EIC detector with all subsystems. The detector is divided into three regions: an electron end-cap to the left, a hadronic end-cap to the right, and a barrel region in the middle. Reproduced from [389]

The radiator of the dRICH detector consists of aerogel, C$_2$F$_6$ gas, and an acrylic filter with a thickness of < 300 nm(to absorb the majority of Rayleigh scattered photons generated within the aerogel). This RICH detector is designed for comprehensive hadron identification ranging from 3 to 50 GeV/c ($\pi$/K/p), as well as for electron identification up to $\sim$ 15 GeV/c (e/$\pi$).

The mRICH detector not only needs to provide hadron identification capabilities within a momentum range from 3 to 10 GeV/c but also requires a compact design to accommodate the spatial constraints of the EIC experiment. Each mRICH module is self-containing (see left in Fig. 91), encapsulating an aerogel radiator, a focusing Fresnel lens with $n = 1.47$ refractive index and 6”(15.24 cm) focal length, and pixelated photon sensors within a box of approximately 14 cm $\times$ 14 cm $\times$ 25 cm. As shown on the right side of Fig. 91, the Fresnel lens focuses photons emitted parallelly by the aerogel to converge at a point with relatively larger angles. This process generates a clearer and more compact Cherenkov ring, thus achieving better separation capabilities without the need for a large photon detection area. The photon detectors for this RICH detector are currently under discussion and evaluation. It is anticipated that the choice will be between the Hamamatsu H13700 and Silicon PhotoMultiplier (SiPM).

Fig. 91

(Color online) The GEANT4 mRICH model and simulated events (left) and its working principle (right). Reproduced from [388]

5.3 The development of DIRC

The DIRC detector was first proposed and successfully implemented by the BABAR collaboration [390]. The DIRC detector structure in the BABAR experiment, as shown in Fig. 92, utilized highly polished, bar-shaped quartz (synthetic fused silica) as its radiator. This material is resistant to ionizing radiation damage, has a long ultraviolet light attenuation length, and exhibits low dispersion within the Cherenkov light wavelength range. To prevent photon loss due to internal reflection at the quartz-water interface and to reduce the required size of the detection surface, the end of the quartz bar is connected to a wedge-shaped quartz light guide. The light guide’s distal end is a water-filled expansion volume, referred to as the Stand-Off Box (SOB). The SOB’s annular surface is equipped with an array of 10752 PhotoMultiplier Tubes (PMTs), along with hexagonal-shaped “light catchers” to maximize the detection area. The PMTs are connected to front-end electronics outside the SOB, comprising a total of 168 DIRC Front-end Boards (DFBs), each processing signals from 64 PMTs.

Fig. 92

Schematic of the DIRC fused silica radiator bar and imaging region. Reproduced from [390]

Due to the use of 6,000 ls of ultra-pure water as the light guide medium in the BABAR DIRC, which was sensitive to electromagnetic and neutron backgrounds and also voluminous, the canceled SUPERB project proposed a new structure called Focused DIRC (FDIRC). This system replaced the light guide in the BABAR with a precise optical focusing system, reducing the detector’s volume to 1/25th of the BABAR DIRC and improving the response speed by a factor of 10 [391].

The subsequent BELLE-II experiment developed a simple DIRC-like detector, Time Of Propagation counter (TOP), capable of separating $\pi$/K/p under 4 GeV/c. This device placed position-sensitive photodetectors (MCP-PMT arrays [392]) directly at the rear of the bars, precisely measuring the exit position and flight time of photons for three-dimensional image reconstruction (x, y, and time). Although the performance of this design is comparable to that of BABAR’s, it achieves this goal with a very small expansion volume and a compact readout. Furthermore, its radiator used wide bars (plates), significantly reducing costs compared to the thin bars used in BABAR [372].

JLab’s GlueX experiment repurposed some BABAR DIRC quartz bars, along with MAPMTs and electronics from the CLAS12 RICH, to construct the GlueX DIRC. This design also drew inspiration from the FDIRC concept, with the difference being that its radiator used distilled water instead of quartz, and it utilized three planar mirror segments to approximate a cylindrical mirror. This design was capable of achieving 3$\sigma$ separation of $\pi$/K/p up to about 4 GeV/c [393].

The PANDA experiment [394], aiming to address various issues related to strong interactions and planning its first antiproton physics experiment in 2025, features one of the most representative DIRCs. The barrel DIRC detector [371] in this experiment employed a triple-lens system composed of a layer of lanthanum crown glass (NLaK33) and two layers of synthetic fused quartz. This triple-layer lens operated without any air gap, minimizing photon loss during the transition from the lens to the expansion volume. Inspired by the FDIRC, the expansion volume part utilized 16 compact fused silica prisms instead of the large water tank of the BABAR DIRC, making it easier to integrate and less susceptible to harmful radiation from the accelerator. Due to improvements in the lens and expansion volume, the system employs 48 radiators, each 2400 mm long and 53 mm wide, significantly reducing polishing costs compared to BABAR’s. Additionally, developments in electronics have been key to its performance improvements. Its photodetectors used 6.5 mm $\times$ 6.5 mm MCP-PMTs, capable of operating in a strong magnetic field (1 T), with a single-photon timing resolution of 30–40 ps and a gain of about 10$^6$. Based on TRB3 technology [395] for readout and using the DiRICH system’s front-end electronics, the system achieves a timing precision of 100 ps. Overall, the DIRC works between ${22}^\circ$ and ${140}^\circ$ and can distinguish $\pi$/K below a momentum of 3.5 GeV/c.

The endcap of this experiment also utilized a DIRC, named the Endcap Disc DIRC (EDD) [396]. Although the basic concept of EDD was proposed as early as 1996 [397], it was first realized in the PANDA endcap. The EDD was divided into four independent quadrants, each consisting of a 20 mm thick fused silica radiator disk. Together, these disks form a dodecagon with a diamond-shaped notch at the center. Each quadrant comprises a radiator and 24 ReadOut Modules (ROMs). Each ROM contained three bars, three 16 mm Focusing Element Lenses (FELs), MCP-PMT, and a front-end electronics board. As shown in Fig. 93, the Cherenkov photons emitted within the radiator are ultimately detected by the MCP-PMTs at the edges, allowing for the determination of the Cherenkov angle and azimuthal angle through algorithms.

Fig. 93

(Color online) a A charged particle traverses the radiator plate and emits Cherenkov photons (the paths are exemplified by dashed lines) at certain angles. b, c The azimuthal angle is determined from the position of the prism where the photon is registered. Reproduced from [396]

As stated in the previous section, the DIRC will be used in the barrel region of the EIC. This DIRC detector will expand the momentum coverage of the PANDA DIRC, allowing for 3$\sigma$ separation of $\pi$/K, e/$\pi$, and p/K at 6 GeV/c, 1.8 GeV/c, and 10 GeV/c, respectively. Its fundamental structure is similar to the PANDA barrel DIRC, with the primary difference lying in its adoption of smaller pixelated photon sensors. Specific aspects related to these photon sensors and reconstruction algorithms are still under discussion and evaluation [370].

5.4 Summary

Over the past forty years, driven by the particle identification demands in accelerator-based particle physics experiments, Cherenkov detectors have experienced continuous advancements. These advancements are fueled both by structural innovations, such as dual-radiator structure, DIRC structure, and the optical structure of FDIRCs, as well as by improvements in device performance, including smoother quartz radiators, smaller photon pixel detectors, higher precision timing technologies, and superior image reconstruction methods. Its development has not only contributed to the prosperity of particle physics experiments but has also led to the progress of practical fields such as cosmic ray detection, industrial metal inspection, and medical imaging.

6 Transition radiation detector

6.1 Introduction

Transition Radiation (TR) refers to the electromagnetic waves generated when ultrarelativistic charged particles traverse interfaces between different media. Its existence was predicted by Ginzburg and Frank in 1945 [398], and Goldsmith and Jelley confirmed optical range TR in 1959 [399]. In its initial decades, TR research primarily focused on understanding its fundamental physics and experimental measurements [400,401,402,403,404,405]. Due to the easy self-absorption of low-energy photons, TR photons in the X-ray range are more readily detected experimentally, with measured TR photon energies ranging from a few keV to several tens of keV. Consequently, gas detectors have become the preferred choice for Transition Radiation Detectors (TRD). The substantial difference in the average ionization energy deposition between TR photons and charged particles in gas has led to the extensive use of TRD in accelerator experiments [406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428] and astroparticle physics experiments [429,430,431,432,433] for charged particle identification. Particularly, TRD demonstrates advantages in particle discrimination at GeV and higher energies, expanding the physical limits of Cherenkov detectors. Additionally, TR intensity depends on the Lorentz factor of the incident charged particles, enabling TRD to measure the Lorentz factors of high-energy charged particles [434,435,436,437,438,439]. Here, we first introduce the fundamental principles of TR, briefly outline past TRD experiments, and discuss the latest applications and developments in TRD.

6.2 Transition radiation

When an ultrarelativistic charged particle passes through the interfaces of different media, the polarized electric field of the charged particle changes, resulting in the outward radiation of electromagnetic waves, i.e., traversing radiation [400,401,402,403,404,405]. For single interface, the differential equation of the transition radiation intensity with energy and angle is expressed as:

$$\begin{aligned} \begin{aligned}&\left( \frac{\text{d}^2W_\text{TR}}{\text{d}\theta \text{d}w}\right) _\text{interface}\\&\quad = \frac{2\alpha h \theta ^3Z^2}{\pi ^2}\left( \frac{1}{1/\gamma ^2+\theta ^2+\xi _1^2}-\frac{1}{1/\gamma ^2+\theta ^2+\xi _2^2}\right) ^2. \end{aligned} \end{aligned}$$

(15)

Here, $\theta$ is the angle between the exit direction of the TR photon and the direction of motion of the incident charged particle, $\omega$ is the frequency of the TR photon, $\alpha$ = 1/137 is the fine structure constant, h is Planck’s constant, Z is the charge of the incident charged particle, $\gamma$ is the Lorentz factor of the incident charged particle, $\xi _{1,2} = \omega _\text{p1,p2}/\omega$, $\omega _\text{p1,p2}$ is the plasma frequency of the two media, $\omega _{\text{p}i} \approx 28.8\sqrt{\bar{\rho Z}/{\bar{A}}}$, $\rho$ is the density of the medium, ${\bar{Z}}$ and ${\bar{A}}$ respectively denote the average atomic number and the average atomic weight of the substance. Integral of $\theta$, there is:

$$\begin{aligned} \begin{aligned}&\left( \frac{\text{d}W_\text{TR}}{\text{d}\omega }\right) _\text{interface}\\&\quad = \frac{2\alpha hZ^2}{\pi }\left[ \frac{\omega _\text{p1}^2+\omega _\text{p2}^2+2\omega ^2/\gamma ^2}{\omega _\text{p1}^2-\omega _\text{p2}^2}\right. \\&\left. \quad \ln \left( \frac{1/\gamma ^2+\omega _\text{p1}^2/\omega ^2}{1/\gamma ^2+\omega _\text{p2}^2/\omega ^2}\right) -2\right] . \end{aligned} \end{aligned}$$

(16)

The differential of TR intensity with photon energy is shown in Fig. 94, where there is a clear cutoff at the high energy end of the TR photon, with a cutoff energy of $\omega _\text{cutoff} = \gamma \omega _\text{p1}$. Integral of $\omega$, there is:

$$\begin{aligned} W_\text{TR,interface}= & {} \int \left( \frac{\text{d}W_\text{TR}}{\text{d}\omega }\right) \text{d}\omega \nonumber \\= & {} \frac{\alpha \hbar Z^2\gamma }{3}\frac{(\omega _\text{p1}-\omega _\text{p2})^2}{\omega _\text{p1}+\omega _\text{p2}}. \end{aligned}$$

(17)

Obviously, the TR intensity is proportional to the $\gamma$ of the incident particle and the square of its charge $Z^2$.

Fig. 94

TR spectrum of a single interface and a single foil. Reproduced from [439]

The TR of a single foil is coherent due to the existence of two interfaces, and the differential representation of its radiation intensity with the TR photon exit angle and frequency is given as:

$$\begin{aligned} \left( \frac{\text{d}^2W_\text{TR}}{\text{d}\theta \text{d}\omega }\right) _\text{foil}=\left( \frac{\text{d}^2W_\text{TR}}{\text{d}\theta \text{d}\omega }\right) _\text{interface} \times 4\sin ^2\left( \frac{l_1}{d_1}\right) . \end{aligned}$$

(18)

where $4\sin ^2(l_1/d_1)$ is the interference term. $l_1$ is the thickness of the foil, $d_1$ is the thickness of the formation zone of the foil material. For both dielectric materials, the formation zone thickness is defined as (c is the speed of light):

$$\begin{aligned} d_i=\frac{4c}{\omega }\left( \frac{1}{\gamma ^2}+\theta ^2+\frac{\omega _{\text{p}i}^2}{\omega ^2}\right) ^{-1}. \end{aligned}$$

(19)

The TR energy spectrum of a single foil is given in Fig. 94. The energy corresponding to the rightmost coherent peak, $\omega _\text{max peak}$ = l$_1\omega _\text{p1}^2$/2$\pi$ is an important basis for TRD design.

For a radiator with N layers foil, the TR photon yield is a superposition of the yields of 2N interfaces, taking into account the self-absorption of TR photons by the radiator material, which is expressed as:

$$\begin{aligned} \begin{aligned} \left( \frac{\text{d}^2W_\text{TR}}{\text{d}\theta \text{d}\omega }\right) _{N \text{foil}}&=\left( \frac{\text{d}^2W_\text{TR}}{d\theta d\omega }\right) _\text{interface}4\sin ^2\left( \frac{l_1}{d_1}\right) \\&\quad \times \frac{\sin ^2[N(l_1/d_1+l_2/d_2)]}{\sin ^2(l_1/d_1+l_2/d_2)}\times N_\text{eff}(\omega ). \end{aligned} \end{aligned}$$

(20)

Here, $l_1$ and $l_2$ denote the thicknesses of the foil and the gap, respectively, $d_1$ and $d_2$ denote the thicknesses of the formation zones of the foil and the gap material, respectively. $N_\text{eff}$($\omega$) denotes the absorption term of the N layers foil for TR photons, denoted as:

$$\begin{aligned} N_\text{eff}(\omega )=\frac{1-\exp \{-N[\sigma _1(\omega )l_1+\sigma _2(\omega )l_2]\}}{1-\exp \{-[\sigma (\omega )l_1+\sigma _2(\omega )l_2]\}}. \end{aligned}$$

(21)

where $\sigma _{1,2}$($\omega$) denotes the absorption length of the two materials for photons with $\omega$ frequency, respectively.

TR characteristics can be briefly summarized as a few points: (1) TR photon energy from the radiator exit mainly in the X-ray energy region; (2) TR photon yield of single interface is very low, with the same order of magnitude as $\alpha$; (3) The N layers foil-stacked radiator has coherence, and its TR photon yield is about 2N times of the single interface; (4) The angle between the exit direction of the TR photon and the direction of motion of the incident charged particle is very small, and the most probable emission angle is $\theta _\text{MPV} \approx$ 1/$\gamma$; (5) Relativistic charged particles with same charge Z and same Lorentz factor $\gamma$ have the same TR intensity, and their radiation yield is proportional to the square of the charge of the incident charged particle $Z^2$, while is also proportional to the Lorentz factor $\gamma$.

6.3 briefly consideration for TRD design

The radiators in TRD come in two types: regular and irregular. Regular radiators tend to yield higher levels of TR photons compared to irregular radiators of the same thickness. However, irregular radiators offer a more stable mechanical structure, making them easier to fabricate. Avakian [440] extensively researched the relationship between TR yield and radiator parameters. An efficient TRD requires a high TR photon yield, with the number of interface layers in the radiator (foil layers, denoted as N) being a primary influencing factor. Opting for a foil material with a higher plasma frequency can enhance TR photon yield but necessitates a balance between foil density and self-absorption issues.

The energy range of TR photons depends on both the material and thickness of the radiator. In multi-layer foil radiators, several coherent peaks are present within the TR spectrum [441]. In practical applications, the focus is typically on the most energetic peak within the coherent spectrum. TRDs are employed for particle identification and $\gamma$ measurements, and their measurement range is determined by radiator parameters. The TR intensity varies with $\gamma$, resulting in threshold and saturation effects [404], expressed as $\gamma _\text{thr} \approx$ 2.5$\hbar \omega _\text{p1}l_1$ and $\gamma _\text{sta} \approx$ 3.0$\hbar \omega _\text{p1}\sqrt{l_1l_2}$, respectively. For particle identification requirements in accelerators ranging from tens to hundreds of GeV/c, optimal radiator parameters often involve plastic foil thicknesses in the tens of micrometers and gas gap dimensions in the millimeter range.

For detectors used to measure TR, the most prevalent ones currently are straw tubes [426] and MWPC [427]. Straw tubes are typically made from materials like polyimide or Mylar coated with aluminum, with diameters ranging from a few mm to several cm, often assembled in rows to form modules. MWPC are more suitable for large-area applications. The choice of working gas directly influences the detection efficiency of TR photons, where Xenon stands out as the optimal choice, although Argon has seen use in NUSEX and MACRO experiments. For measurements in higher energy ranges, considering new types of detectors becomes necessary, such as the Compton scattering TRD proposed by the ACCESS experiment [442].

The readout electronics vary based on different applications. A classic example is the difference between the readout electronics in the ALICE experiment’s TRD, which adopts a slow readout method, and those in the ATLAS experiment, which, due to high collision luminosity, requires a fast readout system. TRDs used for measuring TR emission angles require electronics with two-dimensional readout capabilities, such as those utilizing the Timepix3 chip-based readout for TRD [443].

6.4 ALICE TRD

The TRD in the ALICE experiment not only facilitates e/$\pi$ discrimination but also enables track reconstruction [427]. Comprising 522 readout chambers, it encircles the central part of ALICE, dividing it into 18 sections. Each section consists of 6 layers, with 5 readout chambers per layer. These chambers comprise radiators and MWPCs. The radiators consist of polypropylene fibers and two layers of Rohacell foam HF71, totaling 4.7 cm. Each readout chamber is divided into a 3.0 cm drift region and a 0.7 cm amplification region. The working gas is Xe/CO$_2$ (85%/15%), and its detector module is depicted in Fig. 95.

Fig. 95

(Color online) Cross-sectional diagram of the ALICE TRD module. Reproduced from [427]

According to ionization signals, the ALICE TRD can reconstruct particle tracks with a position resolution of up to 700 $\upmu$m. As depicted in Fig. 96, for particles with a momentum of 1 GeV/c and a 90% electron efficiency, employing the simplest algorithm, LQ1D, arrives a $\pi$ rejection factor of 70. When incorporating the timing information of its signal, the rejection factor reaches 410.

Fig. 96

(Color online) The e/$\pi$ identification ability of ALICE TRD. Reproduced from [427]

6.5 AMS-02 TRD

The particle identification capability of the TRD is closely linked to the intensity of the TR signals it detects. One effective method to enhance the TR signal strength involves increasing the number of modules within the TRD. The AMS-02 experiment [432, 444, 445] utilizes a 20-layered TRD, as depicted in the experimental setup shown in Fig. 97. Each single TRD layer consists of 2.0 cm thick irregular radiators and straw tubes with a 0.6 cm diameter. The radiators contain fibers with a diameter of 10 $\upmu$m, and the straw tubes, measuring 2 m in length, have walls comprised of two layers of aluminum-coated Kapton film, each ${72}\,{\upmu \text{m}}$ thick. The operating gas is a mixture of Xe/CO$_2$ (80%/20%) at a pressure of 0.9 bar. Every 16 straw tubes constitute a module, illustrated in Fig. 98, resulting in a total of 5248 straw tubes across the 20 layers. Additionally, the intermediate 12 layers facilitate three-dimensional reconstruction of particle trajectories. To ensure gas stability during operations, a gas circulation system carrying 48 kg of Xenon and 5 kg of CO$_2$ is deployed in orbit.

Fig. 97

(Color online) Schematic diagram of the AMS-02 experimental setup. Reproduced from [444]

Fig. 98

(Color online) AMS-02 TRD module cross-sectional view of straw tubes (top) and physical representation (bottom). Reproduced from [444]

The probability density function is constructed using the maximum likelihood method for the deposition energies of electrons and protons, and the beam test and on-orbit results for TRD particle identification are shown in Fig. 99, for protons with a rejection factor higher than 10$^3$ at 90% electron efficiency.

Fig. 99

(Color online) Particle identification capability of AMS-02 TRD tested and in-orbit results. Reproduced from [445]

6.6 TRACER TRD

The TRACER experiment utilizes TRD as a cosmic ray energy measurement instrument for high-Z cosmic ray nuclei spectra [437]. The TR intensity is directly proportional to the square of the charged particle’s charge, resulting in better measurement resolution with higher charge values. The schematic diagram of TRACER, shown in Fig. 100, consists of four TRD layers, each comprising a radiator and rear-facing double-layered straw tubes. The first layer employs a thick-type radiator with an average fiber diameter of ${17}\,{\upmu \text{m}}$ and a thickness of 17.8 cm. The subsequent three layers are thin-type with fibers approximately ${4.5}\,{\upmu \text{m}}$ in diameter and each layer is 11.25 cm thick. This design advantageously allows high-energy TR photons produced in the first layer’s radiator to partially pass through the first TRD straw tubes and be detected by the subsequent three layers, exploiting this “feedthrough effect” to enhance the measured TR signal intensity. The straw tubes are made of aluminum-coated mylar foil, 2 cm in diameter and 200 cm in length, with a working gas mixture of Xenon and CH$_4$. The initial two balloon flight tests (T99, LDB1) utilized Xe/CH$_4$ (50%/50%) at a pressure of 0.5 bar, while the third flight test LDB2 employed Xe/CH$_4$ (90%/10%) at a pressure of 1.0 bar. Additionally, a 3000 L gas circulation system was carried to ensure the stability of the working gas. During the LDB2 flight test, a resolution of 8% was achieved for cosmic ray iron nuclei at 1500 GeV/amu.

Fig. 100

TRACER schematic drawing. Reproduced from [437]

6.7 Newest implementations of TRDs

In recent years, there have been new applications and developments of TRDs. With the development of new chips for pixels, which made it possible to measure the fine structure of TR emission angles, and a silicon pixel-based TRD based on the TimePix3 chip [443] made fine measurements of the distribution of TR emission angles. In order to measure the distribution of TR emission angles, the TR photons with different exit directions must be separated in the detector. By adding helium tubes between the radiator and the pixel detector to increase the movement distance of the TR photons, the TR photons are able to be separated in the pixel detector, and the distribution of the TR photons with the angle is reconstructed by the cluster algorithm, a typical measurement result is shown in Fig. 101.

Fig. 101

(Color online) Distribution of TR photon emission angles measured by silicon pixel TRD. Reproduced from [443]

Besides the classic TRDs based on straw tubes and MWPC, in recent years, TRDs based on Thick Gas Electron Multiplier (THGEM) have been developed and applied [439, 446]. Using the THGEM as a replacement for the traditional anode wires for electron multiplication helps avoid issues related to wire aging. Figure 102 illustrates a side-on TRD based on a double-layers THGEM [439]. The radiator consists of 300 layers of stacked polypropylene foils with a thickness of ${20}\,{\upmu \text{m}}$ and ${500}\,{\upmu \text{m}}$ air gaps, providing an effective area of 5 cm $\times$ 5 cm. The detector comprises a TPC utilizing a double-layers THGEM for electron multiplication, operating with an Ar/CO$_2$ (93%/7%) gas mixture at a pressure of 1 atmosphere and a gas thickness of 5.1 cm. The radiator is installed on the side of the TPC. This TRD prototype is designed for high-energy cosmic ray detection facility to calibrate cosmic ray energies in the TeV range. A typical TR spectrum from electronic beam tests of this TRD prototype is shown in Fig. 103.

Fig. 102

(Color online) Schematic diagram of THGEM-based TRD. Reproduced from [439]

Fig. 103

(Color online) Ionization and TR spectra of side-on TRD prototype measured by electron beam. Reproduced from [447]

7 Readout technology

7.1 Introduction

Readout system plays a pivotal role in physics experiments. As shown in Fig. 104, the readout system architecture mainly consists of the Front-End (FE) part, the Back-End (BE) part, and the Data Acquisition (DAQ) software. However, the scale of readout system varies significantly among various physics experiments.

Fig. 104

(Color online) Schematic of a readout system

The electronics in the FE part handle the detector signal and extract the critical physical information. The BE part typically comprises the data readout blocks, the clock and synchronization blocks, and the trigger blocks. It provides high-bandwidth links for transmitting data and other signals and, in some cases, resources for online data processing algorithms. The DAQ software generally facilitates human-computer interaction to control the overall system and store the data.

The boost of modern physics experiments allows physicists to explore the universe but brings new challenges to data acquisition, in particular, higher radiation levels, higher channel density, significantly more data, and accurate measurement of the original detector signal. This chapter will discuss some state-of-the-art techniques in data acquisition to face these challenges in physics experiments.

7.2 Waveform digitization

The waveform of the detectors’ output contains the most comprehensive and detailed physical information. The waveform area of the signal represents the energy deposited by the particles in the detector. The leading edge of the signal waveform carries the time information of the particle hitting the detector. Traditionally, energy measurement consists of a charge-sensitive amplifier, sha** circuit, and analog-to-digital converters (ADCs). Time measurement consists of fast amplifiers, discriminators, and time-to-digital converters (TDCs). Waveform digitization technology directly sample and digitize the waveform of the detector output signal at high speed. The traditional charge integration and sha** are no longer carried out, and the particle’s energy and time information is obtained digitally. According to Shannon’s law of sampling, as long as the sampling rate is high enough, the original pulse waveform can be reconstructed without distortion. The waveform digitization technology can conveniently obtain time and energy information simultaneously, eliminates the pile-up effect caused by the traditional charge integral amplification, and has a short dead time. Hence, it suits physical experiments with high luminosity and event rate. In addition, the waveform digitization technology allows physicists to employ possible digital processing methods. One common way to realize waveform digitization is to use fast-commercial ADCs. Later, a new technique uses the switching capacitor array (SCA) ASIC to achieve ultra-high-speed analog sampling and digitize the waveforms using ADC inside or outside the ASIC. All in all, increasing the sampling rate is a core of the waveform digitization technology.

As the fastest type of ADC, the Flash ADC plays a primary role in waveform digitization. An N-bit flash ADC consists of 2N resistors and 2N-1 comparators arranged as in Fig. 105. Each comparator has a reference voltage from the resistor string, which is 1 LSB higher than the one below it in the chain.

Fig. 105

6-bit flash ADC architecture. Reproduced from [448]

As early as 1985, European scientists used 100 MSPS flash ADCs [449] for the signal readout of the vertex detector in the UA2 experiment at CERN. A typical example application is the MAGIC telescope [450]. The analog signals from the detector are continuously digitized by 8-bit 300 MHz Flash ADCs. This system has been working in Magic experiments until January 2007. Since then, the readout system has been upgraded with 2 GHz 10-bit ADCs [451, 453] uses is a 16-channel, 14-bit pipeline ADC (AD9249) [454] with a sampling rate of 65 MHz to realize waveform digitization. For the MAPS in heavy-ion physics, a regional 12-bit 40-Msps pipeline ADC has been designed to convert the analog signals from the pixels into digital data [455]. Time-interleaved ADC (TI-ADC) is a multi-channel data-parallel acquisition technique that breaks high-speed and high-accuracy bottlenecks. However, calibrating the various mismatch factors (gain, clock phase/skew, offset) is essential. Common correction algorithms are within FPGAs: gain and offset errors are corrected by adders and multipliers, and the time-skew error is corrected based on a fully parallel correction method [456]. Another new approach to calibration is using an additive-neural network-based digital calibration algorithm for nonlinear amplitude and phase distortion [457, 458].

Over the last decade or so, due to the development of the Switched Capacitor Array (SCA) has been an excellent solution for waveform digitization because of its low power consumption and high channel density at affordable costs compared to high-speed ADCs. Figure 106 is the schematic of a SCA circuit. The SCA, controlled by a high-speed domino ring chain, samples, and stores the input voltage signal. The fast SCA ASIC typically combines with low-speed ADCs for analog-to-digital conversion. Various SCA ASICs have been designed for physics experiments, and the sampling rate ranges from GHz to MHz. The GHz sampling SCA chips are mainly used for fast scintillation or Cherenkov light detectors. The DRS4 [459] chip from the Paul Scherrer Institute is a radiation-hard SCA fabricated in a 250 nm process. The DRS4 has nine differential input channels, each with 1024 sampling cells. This ASIC can provide up to 5 GHz sampling speed, and the signal-to-noise ratio allows a resolution equivalent to more than 11 bits, and 4 ps timing resolution. The DRS4 has been used in MAGIC-II [460], PADME [505]