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# 35. Particle Detectors at Accelerators

Revised 2024. See the various sections for authors.

<table><tbody><tr><td>35.1</td><td>Introduction</td><td>591</td></tr><tr><td>35.2</td><td>Photon detectors</td><td>591</td></tr><tr><td>35.2.1</td><td>Vacuum photodetectors</td><td>592</td></tr><tr><td>35.2.2</td><td>Gaseous photon detectors</td><td>593</td></tr><tr><td>35.2.3</td><td>Solid-state photon detectors</td><td>593</td></tr><tr><td>35.2.4</td><td>Superconducting photon detectors</td><td>594</td></tr><tr><td>35.3</td><td>Organic scintillators</td><td>594</td></tr><tr><td>35.3.1</td><td>Scintillation mechanism</td><td>594</td></tr><tr><td>35.3.2</td><td>Plastic scintillator practicalities</td><td>595</td></tr><tr><td>35.3.3</td><td>Organic glass scintillators</td><td>596</td></tr><tr><td>35.3.4</td><td>Liquid scintillator practicalities</td><td>596</td></tr><tr><td>35.4</td><td>Inorganic scintillators</td><td>596</td></tr><tr><td>35.5</td><td>Cherenkov detectors</td><td>598</td></tr><tr><td>35.6</td><td>Gaseous detectors</td><td>601</td></tr><tr><td>35.6.1</td><td>Energy loss and charge transport in gases</td><td>601</td></tr><tr><td>35.6.2</td><td>Multi-Wire Proportional and Drift Chambers</td><td>603</td></tr><tr><td>35.6.3</td><td>High Rate Effects</td><td>604</td></tr><tr><td>35.6.4</td><td>Micro-Pattern Gas Detectors</td><td>605</td></tr><tr><td>35.6.5</td><td>Time-projection chambers</td><td>607</td></tr><tr><td>35.6.6</td><td>Transition radiation detectors (TRD's)</td><td>609</td></tr><tr><td>35.6.7</td><td>Resistive-plate chambers</td><td>611</td></tr><tr><td>35.7</td><td>LAr Time Projection Chamber</td><td>613</td></tr><tr><td>35.7.1</td><td>Introduction</td><td>613</td></tr><tr><td>35.7.2</td><td>A Mass of ultra-pure Liquid Argon</td><td>614</td></tr><tr><td>35.7.3</td><td>Charge and Light Signals</td><td>614</td></tr><tr><td>35.7.4</td><td>LAr TPC topologies</td><td>615</td></tr><tr><td>35.7.5</td><td>Data Acquisition and event reconstruction</td><td>615</td></tr><tr><td>35.7.6</td><td>Developments</td><td>617</td></tr><tr><td>35.8</td><td>Semiconductor detectors</td><td>617</td></tr><tr><td>35.8.1</td><td>Signal generation in semiconductors</td><td>617</td></tr><tr><td>35.8.2</td><td>Junction detectors</td><td>618</td></tr><tr><td>35.8.3</td><td>Detectors with structured electrodes</td><td>619</td></tr><tr><td>35.8.4</td><td>Precise timing with silicon detectors</td><td>620</td></tr><tr><td>35.8.5</td><td>Radiation damage in silicon detectors</td><td>621</td></tr><tr><td>35.9</td><td>Low-noise detector readout</td><td>623</td></tr><tr><td>35.9.1</td><td>Principal noise origins</td><td>623</td></tr><tr><td>35.9.2</td><td>Equivalent noise analysis</td><td>623</td></tr><tr><td>35.9.3</td><td>Timing measurements</td><td>626</td></tr><tr><td>35.9.4</td><td>Digital signal processing</td><td>626</td></tr><tr><td>35.9.5</td><td>What to use when?</td><td>626</td></tr><tr><td>35.10</td><td>Calorimeters</td><td>626</td></tr><tr><td>35.10.1</td><td>Introduction</td><td>626</td></tr><tr><td>35.10.2</td><td>Electromagnetic calorimeters</td><td>629</td></tr><tr><td>35.10.3</td><td>Hadronic calorimeters</td><td>630</td></tr><tr><td>35.10.4</td><td>Free electron drift velocities in liquid ionization chambers</td><td>634</td></tr><tr><td>35.11</td><td>Accelerator-based neutrino detectors</td><td>634</td></tr><tr><td>35.11.1</td><td>Introduction</td><td>635</td></tr><tr><td>35.11.2</td><td>Signals and Backgrounds</td><td>635</td></tr><tr><td>35.11.3</td><td>Instances of Neutrino Detector Technology</td><td>635</td></tr><tr><td>35.11.4</td><td>Outlook</td><td>638</td></tr><tr><td>35.12</td><td>Superconducting magnets for collider detectors</td><td>639</td></tr><tr><td>35.12.1</td><td>Solenoid Magnets</td><td>639</td></tr><tr><td>35.12.2</td><td>Properties of collider detector magnets</td><td>639</td></tr><tr><td>35.12.3</td><td>Toroidal magnets</td><td>640</td></tr><tr><td>35.13</td><td>Measurement of particle momenta in a uniform magnetic field</td><td>640</td></tr></tbody></table>

## 35.1 Introduction

This review summarizes the detector technologies employed at accelerator particle physics experiments. Several of these detectors are also used in a non-accelerator context and examples of such applications will be provided. The detector techniques which are specific to non-accelerator particle physics experiments are the subject of Chap. 36. More detailed discussions of detectors and their underlying physics can be found in books by Kolanoski & Wermes [1], Ferbel [2], Kleinknecht [3], Knoll [4], Green [5], Leroy & Rancoita [6], and Gruppen [7].

In Table 35.1 are given typical resolutions and deadtimes of common charged particle detectors. The quoted numbers are usually based on typical devices, and should be regarded only as rough approximations for new designs. The spatial resolution refers to the intrinsic detector resolution, i.e. without multiple scattering. We note that analog detector readout can provide better spatial resolution than digital readout by measuring and averaging the deposited charge in neighboring channels. Quoted ranges attempt to be representative of both possibilities. The time resolution is defined by how accurately the time at which a particle crossed the detector can be determined. The deadtime is the minimum separation in time between two resolved hits on the same channel. Typical performance of calorimetry and particle identification are provided in the relevant sections below.

<table><caption>**Table 35.1:** Typical resolutions and deadtimes of common charged particle detectors. Revised September 2023.</caption><thead><tr><th>Detector Type</th><th>Intrinsinc Spatial Resolution (rms)</th><th>Time Resolution</th><th>Dead Time</th></tr></thead><tbody><tr><td>Resistive plate chamber</td><td>50 µm</td><td>50–1000 ps*</td><td>10 ns†</td></tr><tr><td>Liquid argon TPC</td><td>0.5–1 mm‡</td><td>0.01–1 µs§</td><td>—¶</td></tr><tr><td>Scintillation tracker</td><td>~100 µm</td><td>100 ps/n||</td><td>10 ns</td></tr><tr><td>Bubble chamber</td><td>10–150 µm</td><td>1 ms</td><td>50 ms**</td></tr><tr><td>Wire chambers (proportional and drift chambers)</td><td>50–100 µm</td><td>5–10 ns††</td><td>20–200 ns‡‡</td></tr><tr><td>Micro-pattern gas detector</td><td>30–40 µm</td><td>5–10 ns††</td><td>20–200 ns‡‡</td></tr><tr><td>Silicon strips/pixels</td><td>≤ 10 µm§§</td><td>few ns¶¶‡‡</td><td>≤ 50 ns‡‡</td></tr></tbody></table>

## 35.2 Photon detectors

Revised August 2023 by P. Križan (Ljubljana U; Jozef Stefan Inst.).

Most detectors in high-energy, nuclear, and astrophysics rely on the detection of photons in or near the visible range, 100 nm $\lesssim$ λ $\lesssim$ 1000 nm, or 1 eV $\lesssim$ E $\lesssim$ 10 eV. This range covers scintillation and Cherenkov radiation as well as the light detected in many astronomical observations.

Generally, photodetection involves generating a detectable electrical signal proportional to the (usually very small) number of incident photons. The process involves three distinct steps:

1. generation of a primary photoelectron or electron-hole (e-h) pair by an incident photon by the photoelectric or photoconductive effect,

2. multiplication of the photoelectron or electron-hole pair signal to detectable levels, usually by one or more multiplicative bombardment steps and/or an avalanche process, and,

3. detection of charges induced by secondary electrons.

The important characteristics of a photodetector include the following:

<footnote>*LHC: ~2 mm gap, ~1 ns. HL-LHC: ~1 mm gap, ~350 ps. Timing RPC: ~50 ps</footnote>

<footnote>†Limited by amplifier and discriminator bandwidth, usually around 100 MHz</footnote>

<footnote>‡Detector geometry dependent</footnote>

<footnote>§Using the scintillation signal</footnote>

<footnote>¶No deadtime for medium</footnote>

<footnote>||n = index of refraction.</footnote>

<footnote>**Multiple pulsing time.</footnote>

<footnote>††For fast particles</footnote>

<footnote>‡‡Depending/limited by the amplifying electronics [8]</footnote>

<footnote>§§Depending on electrode pitch, best values around 2–4 µm have been achieved</footnote>

<footnote>¶¶Resolutions < 100 ps are reached in dedicated pixel developments</footnote>
1. quantum efficiency (QE or $\epsilon_Q$): the average number of primary photoelectrons generated per incident photon ($0 \le \epsilon_Q \le 1$; in silicon more than one e-h pair per incident photon can be generated for $\lambda \le 165$ nm),

2. collection efficiency (CE or $\epsilon_C$): the overall acceptance factor other than the generation of photoelectrons ($0 \le \epsilon_C \le 1$),

3. gain ($G$): the number of electrons collected for each photoelectron generated,

4. dark current or dark noise: the electrical signal when there is no incident photon,

5. precision of measuring the intensity $I$ of the incoming light: electronic noise (ENC or $N_e$) and statistical fluctuations in the amplification process compound the Poisson distribution of $n_\gamma$ photons from a given source:

$$ \frac{\sigma(I)}{\langle I \rangle} = \sqrt{\frac{f_N}{n_\gamma \epsilon_Q \epsilon_C} + \left( \frac{N_e}{G n_\gamma \epsilon_Q \epsilon_C} \right)^2}, \quad (35.1) $$

where $f_N$, or the excess noise factor (ENF), is the contribution to the intensity distribution variance due to multiplication statistics [9],

6. dynamic range, linearity and saturation: relation between the number of incident photons and the sensor output in the pulsed mode,

7. time dependence of the response: this includes the transit time, which is the time between the arrival of the photon and the electrical pulse, and the transit time spread, and

8. rate capability: maximal rate of light pulses at which detection is still possible.

The QE is a strong function of the photon wavelength ($\lambda$), and is usually quoted at maximum, together with a range of $\lambda$ where the QE is comparable to its maximum. Spatial uniformity and linearity with respect to the number of photons are highly desirable in a photodetector response.

Optimization of these factors involves many trade-offs and varies widely between applications. For example, while a large gain is desirable, attempts to increase the gain for a given device also increases the ENF and after-pulsing ("echos" of the main pulse). In solid-state devices, a higher QE often requires a compromise in the timing properties. In other types, coverage of large areas by focusing photoelectrons increases the transit time spread.

Other important considerations also are highly application-specific. These include the photon flux and wavelength range, the total area to be covered, and the efficiency required, the volume available to accommodate the detectors, characteristics of the environment such as chemical composition, temperature, magnetic field, ambient background, as well as ambient radiation of different types, mode of operation (continuous or triggered), bias (high-voltage) requirements, power consumption, calibration needs, aging, cost, and so on. Several technologies employing different phenomena for the three steps described above, and many variants within each, offer a wide range of solutions to choose from. The salient features of the main technologies and the common variants are described below. Some key characteristics are summarized in Table 35.2.

### 35.2.1 Vacuum photodetectors

Vacuum photodetectors can be broadly subdivided into three types: photomultiplier tubes, microchannel plate photomultiplier tubes, and hybrid photodetectors.

#### 35.2.1.1 Photomultiplier tubes

A versatile class of photon detectors, vacuum photomultiplier tube (PMT) has been employed by a vast majority of all particle physics experiments to date [9]. Both "transmission-" and "reflection-type" PMTs are widely used. In the former, the photocathode material is deposited on the inside of a transparent window through which the photons enter, while in the latter, the photocathode material rests on a separate surface that the incident photons strike. The cathode material has a low work function, chosen for the wavelength band of interest. When a photon hits

the cathode and liberates an electron (the photoelectric effect), the latter is accelerated and guided by electric fields to impinge on a secondary-emission electrode, or dynode, which then emits several (~5) secondary electrons. The multiplication process is repeated typically about 10 times in series to generate a sufficient number of electrons, which are collected at the anode for delivery to the external circuit. The total gain of a PMT depends on the applied high voltage $V$ as $G = AV^{kn}$, where $k \approx 0.7-0.8$ (depending on the dynode material), $n$ is the number of dynodes in the chain, and $A$ a constant (which also depends on $n$). Typically, $G$ is in the range of $10^5-10^7$; time resolution is $O(1ns)$ but can be as good as $\approx 100$ ps for certain PMT types.

A large variety of PMTs covers a wide span of wavelength ranges from infrared (IR) to extreme ultraviolet (XUV) [10]. They are categorized by the window materials, photocathode materials, dynode structures, and anode configurations. Common window materials are borosilicate glass for IR to near-UV, fused quartz and sapphire (Al₂O₃) for UV, and MgF₂ or LiF for XUV. The choice of photocathode materials include a variety of mostly Cs- and/or Sb-based compounds such as CsI, CsTe, bi-alkali (SbRbCs, SbKCs), multi-alkali (SbNaKCs), GaAs(Cs), GaAsP(Cs), etc. Sensitive wavelengths and peak quantum efficiencies for these materials are summarized in Table 35.3. Typical dynode structures used in PMTs are circular cage, line focusing, box-and-grid, venetian blind, and fine mesh.

Multianode PMTs (MaPMTs) of up to 5 × 5 cm² in size are based on the parallel (side-by-side) arrangement of several dynode channels and anodes in the same tube, requiring advanced micro-machining and processing techniques. Fast PMTs with very large windows—measuring up to 508 mm across—have been developed for detection of Cherenkov radiation in neutrino experiments such as Super-Kamiokande and KamLAND among many others. Specially prepared low-radioactivity glass is used to make these PMTs, and they are also able to withstand the high pressure of the surrounding liquid.

PMTs are vulnerable to magnetic fields—sometimes even the geomagnetic field causes large orientation-dependent gain changes. A high-permeability metal shield is often necessary. However, proximity-focused PMTs, e.g. the fine-mesh types, can be used even in a high magnetic field ($\ge 1$ T) if the direction of electric field of the tube is close to the direction of the external magnetic field. CMS uses custom-made vacuum phototriodes (VPT) mounted on the back face of projective lead tungstate crystals to detect scintillation light in the endcap sections of its electromagnetic calorimeters, which are inside a 3.8 T superconducting solenoid. A VPT employs a single dynode (thus, $G \approx 10$) placed close to the photocathode, and a mesh anode plane between the two, to help it cope with the strong magnetic field, which is not too unfavorably oriented with respect to the photodetector axis in the endcaps (within 25°), but where the radiation level is too high for Avalanche Photodiodes (APDs) like those used in the barrel section.

#### 35.2.1.2 Microchannel plate photomultiplier tubes

A typical microchannel plate photomultiplier tube (MCP-PMT) consists of two or more ~1 mm thick glass plates with densely packed $O(10 \mu m)$-diameter cylindrical holes, or "microchannels", sitting between the transmission-type photocathode and anode planes, separated by $O(1$ mm) gaps. Instead of discrete dynodes, the inner surface of each cylindrical hole with a length-to-diameter ratio of 40-100 serves as a continuous dynode for the entire cascade of multiplicative bombardments initiated by a photoelectron. Gain fluctuations are reduced by operating each of the MCPs in the saturation mode. MCPs are stacked in a "chevron" configuration that alternates their bias angle; this reduces ion and photon feed-back effects and optimizes the overall amplification gain.

MCP-PMTs are thin, offer good spatial resolution, have excellent time resolution (~20 ps), and can tolerate magnetic fields up to 0.1 T and axial fields up to 1–2 T. The technology has significantly evolved over the past 10 years [11]. A main breakthrough was the introduction of the atomic layer deposition (ALD) coatings on the MCP surfaces to increase the lifetime (>20 C/cm² of charge accumulated on the anode) and gain. The Large Area Pi-
<table><caption>**Table 35.2:** Representative characteristics of some photodetectors commonly used in particle physics.</caption><thead><tr><th>Type</th><th>λ<br>(nm)</th><th>ε<sub>Q</sub> ε<sub>C</sub></th><th>Gain</th><th>Risetime<br>(ns)</th><th>Single photon<br>time resol. (ps)</th><th>Area<br>(mm<sup>2</sup>)</th><th>1-p.e noise *<br>(Hz/mm<sup>2</sup>)</th><th>HV<br>(V)</th></tr></thead><tbody><tr><td>PMT †</td><td>115–1700</td><td>0.15–0.25</td><td>10<sup>5</sup>–10<sup>7</sup></td><td>0.7–10</td><td>~200</td><td>10–10<sup>5</sup></td><td>10<sup>2</sup>–10<sup>2</sup></td><td>500–3000</td></tr><tr><td>MCP-PMT†</td><td>115–650</td><td>0.01–0.10</td><td>10<sup>3</sup>–10<sup>7</sup></td><td>0.15–0.3</td><td>~20</td><td>1–10<sup>4</sup></td><td>1–10</td><td>500–3500</td></tr><tr><td>HPD†</td><td>115–850</td><td>0.1–0.3</td><td>10<sup>3</sup>–10<sup>4</sup></td><td>O(1)</td><td>~1000</td><td>10–10<sup>5</sup></td><td>10–100</td><td>~2 × 10<sup>4</sup></td></tr><tr><td>HAPD†</td><td>115–850</td><td>0.1–0.3</td><td>10<sup>4</sup>–10<sup>5</sup></td><td>O(1)</td><td>~30</td><td>10–10<sup>5</sup></td><td>~1</td><td>~1 × 10<sup>4</sup></td></tr><tr><td>GPD†</td><td>115–500</td><td>0.15–0.3</td><td>10<sup>3</sup>–10<sup>6</sup></td><td>O(0.1)</td><td>~100</td><td>O(10)</td><td>~1</td><td>300–2000</td></tr><tr><td>APD</td><td>300–1700</td><td>~0.7</td><td>10–10<sup>8</sup></td><td>O(1)</td><td>- ‡</td><td>1–10<sup>3</sup></td><td>O(10<sup>7</sup>) §</td><td>400–1400</td></tr><tr><td>SiPM</td><td>125–1000</td><td>0.15–0.4</td><td>10<sup>5</sup>–10<sup>6</sup></td><td>~1</td><td>~50</td><td>1–36</td><td>10<sup>4</sup>–10<sup>5</sup></td><td>30–60</td></tr></tbody></table>

cosecond Photo-Detector (LAPPD) project [12] is an important attempt to produce at a reasonable cost large (20 by 20 cm²) sensors with a transit time spread of 50-70 ps.

### 35.2.1.3 *Hybrid photon detectors*

Hybrid photon detectors (HPD) combine the sensitivity of a vacuum PMT with the excellent spatial and energy resolutions of a silicon sensor [13]. A single photoelectron ejected from the photocathode is accelerated through a large potential difference of ~20 kV before it impinges on the silicon sensor/anode. The gain nearly equals the maximum number of e-h pairs that could be created from the entire kinetic energy of the accelerated electron: $G \approx \text{eV}/w$, where e is the electronic charge, V is the applied potential difference, and w ≈ 3.7 eV is the mean energy required to create an e-h pair in Si at room temperature. Since the gain is achieved in a single step, one can expect to have the excellent resolution of a simple Poisson statistic with large mean, but in fact it is even better, thanks to the Fano effect discussed in Sec. 35.8.

Low-noise electronics must be used to read out HPDs if one intends to take advantage of the low fluctuations in gain, e.g. when counting small numbers of photons. HPDs can have the same $\epsilon_Q \epsilon_C$ and window geometries as PMTs and can be segmented down to ~50 µm. However, they require rather high biases and will not function in a magnetic field. The exception is proximity-focused devices (⇒ no (de)magnification) in an axial field. With time resolutions of ~10 ps and superior rate capability, proximity-focused HPDs can be an alternative to MCP-PMTs. Applications of HPDs include the CMS hadronic calorimeter and the RICH detector in LHCb. Large-size HPDs with sophisticated focusing may be suitable for future water Cherenkov experiments.

Hybrid APDs (HAPDs) add an avalanche multiplication step following the electron bombardment to boost the gain by a factor of ~50. This affords a higher gain and/or a lower bias voltage, but also increases the detector capacitance and fluctuations in multiplication. The forward RICH detector of Belle II uses a 144-channel device of this type [14].

<table><caption>**Table 35.3:** Properties of photocathode and window materials commonly used in vacuum photodetectors. [10]</caption><thead><tr><th>Photocathode material</th><th>λ (nm)</th><th>Window material</th><th>Peak ε<sub>Q</sub> (λ/nm)</th></tr></thead><tbody><tr><td>CsI</td><td>115–200</td><td>MgF<sub>2</sub></td><td>0.13 (130)</td></tr><tr><td>CsTe</td><td>115–320</td><td>MgF<sub>2</sub></td><td>0.17 (200)</td></tr><tr><td rowspan="2">Bi-alkali</td><td>300–650</td><td>Borosilicate</td><td>0.27 (390)</td></tr><tr><td>160–650</td><td>Synthetic Silica</td><td>0.27 (390)</td></tr><tr><td rowspan="2">"Ultra Bi-alkali"</td><td>300–650</td><td>Borosilicate</td><td>0.43 (350)</td></tr><tr><td>160–650</td><td>Synthetic Silica</td><td>0.43 (350)</td></tr><tr><td rowspan="2">Multi-alkali</td><td>300–850</td><td>Borosilicate</td><td>0.20 (375)</td></tr><tr><td>160–850</td><td>Synthetic Silica</td><td>0.25 (380)</td></tr><tr><td>GaAsP(Cs)</td><td>280–720</td><td>Borosilicate</td><td>0.40 (480–530)</td></tr></tbody></table>

### 35.2.2 *Gaseous photon detectors*

In a gaseous photon detector (GPD) a photoelectron in a suitable gas mixture initiates an avalanche in a high-field region, producing a large number of secondary impact-ionization electrons. In principle the charge multiplication and collection processes are identical to those employed in gaseous tracking detectors such as multiwire proportional chambers (MWPC), micromesh gaseous detectors (Micromegas), or gas electron multipliers (GEM). These are discussed in Sec. 35.6.4.

The devices can be divided into two types depending on the photosensitive material. One type uses solid photocathode materials much in the same way as PMTs. Since it is resistant to gas mixtures typically used in tracking chambers, CsI is a common choice. In the other type, photoionization occurs on suitable molecules vaporized and mixed in the drift volume. Most gases have photoionization work functions in excess of 10 eV, which would limit their sensitivity to wavelengths far too short. However, vapors of tetrakis dimethyl-amine ethylene (TMAE) or triethyl-amine (TEA), which have smaller work functions (5.3 eV for TMAE and 7.5 eV for TEA), are suited for XUV photon detection [15]. Since devices like GEMs offer sub-mm spatial resolution, GPDs are often used as position-sensitive photon detectors. They can be made into flat panels to cover large areas ($O(1 \text{ m}^2)$), can operate in high magnetic fields, and are relatively inexpensive. Many of the ring imaging Cherenkov (RICH) detectors have used GPDs for the detection of Cherenkov light [16–19]. Special care must be taken to suppress the ion-feedback and photon-feedback processes in GPDs. It is also important to maintain high purity of the gas as minute traces of $O_2$ or $H_2O$ can significantly degrade the detection efficiency.

### 35.2.3 *Solid-state photon detectors*

In a phase of rapid development, solid-state photodetectors are competing with vacuum- or gas-based devices for many existing applications and making way for a multitude of new ones. Compared to traditional vacuum- and gaseous photodetectors, solid-state devices are more compact, lightweight, rugged, tolerant to magnetic fields, and often cheaper. They also allow fine pixelization, are easy to integrate into large systems, and can operate at low electric potentials, while matching or exceeding most performance criteria.

Silicon photodiodes (PD) are widely used in high-energy physics as particle detectors and in a large number of applications as photon detectors. The structure is discussed in some detail in Sec. 35.8. In its simplest form, the PD is a reverse-biased p-n junction. Photons with energies above the indirect bandgap energy (wavelengths shorter than about 1050 nm, depending on the temperature) can create e-h pairs (the photoconductive effect), which are collected on the p and n sides, respectively. Often, as in the PDs used for crystal scintillator readout in CLEO, L3, Belle, BaBar, and GLAST, intrinsic silicon is doped to create a p-i-n structure. The reverse bias increases the thickness of the depleted region; in the case of these particular detectors, to full

<footnote>*Normalized to photocathode/sensor area; room temperature operation assumed.</footnote>

<footnote>†These devices often come in multi-anode configurations. In such cases, the area is to be considered on a "per readout-channel" basis.</footnote>

<footnote>‡No single photon detection possible.</footnote>

<footnote>§Since in an APD no single photon detection is possible, dark current is usually quoted instead of the dark count rate; here we assumed a gain of 50 to convert from the dark current to the dark count rate.</footnote>
depletion at a depth of about 100 µm. Increasing the depletion depth decreases the capacitance (and hence electronic noise) and extends the red response. Quantum efficiency can exceed 90%, but falls toward the red because of the decrease of the light absorption probability in silicon; the absorption length reaches 100 µm at 985 nm. However, since $G = 1$, electronic signal amplification is necessary. Optimal low-noise amplifiers are slow, but, even so, noise limits the minimum detectable signal in room-temperature devices to several hundred photons.

In APDs, an exponential cascade of impact ionizations initiated by the original photogenerated $e-h$ pair under a large reverse-bias voltage leads to an avalanche multiplication [20–23], and eventually to breakdown in Geiger-mode APDs. As a result, detectable electrical response can be obtained from low-intensity optical signals down to single photons. Excellent junction uniformity is critical, and a guard ring is generally used as a protection against edge breakdown. Well-designed APDs, such as those used in CMS crystal-based electromagnetic calorimeter, have achieved $\epsilon_Q \epsilon_C \approx 0.7$ with sub-ns response time. The sensitive wavelength window and gain depend on the semiconductor used. The gain is typically 10–200 in linear and up to $10^8$ in Geiger mode of operation. Stability and close monitoring of the operating temperature are important for linear-mode operation, and substantial cooling is often necessary.

One of the most promising recent developments in the field is SiPMs ("Silicon Photomultiplier"), a device consisting of large arrays ($O(10^3)$) of tiny APDs packed over a small area ($O(1 \text{mm}^2)$) and operated in a limited Geiger mode [24–26]. Although each cell only offers a binary output, linearity with respect to the number of photons is achieved by summing the cell outputs. The sum of all cells is proportional to the number of photons received so long as the probability of an individual cell receiving multiple photons during a single time gate is negligible. SiPMs are being adopted as the preferred solution for various purposes including medical imaging, e.g. positron emission tomography (PET). These compact, rugged, and economical devices allow auto-calibration through decent separation of photoelectron peaks and offer gains of $O(10^6)$ at a moderate bias voltage (~30 V). However, the single-photoelectron noise of a SiPM, being the logical "or" of $O(10^3)$ Geiger APDs, is rather large: $O(10-100 \text{kHz/mm}^2)$ at room temperature. Intensive R&D in recent years [27] led to a substantial reduction in dark count rates and in correlated noise levels, resulting in coverage of larger areas and in a wider range of applications. One way to further improve the signal-to-noise ratio in SiPMs is by using dedicated light collectors, either as quartz Winston cone like arrays [28] or suitably designed meta-materials [29]. In this way, photons propagate from a larger entry window to a considerably smaller semiconductor sensor, resulting in an improved signal photon to dark-count ratio. Intense R&D is expected to improve radiation hardness of these sensors. The fabrication of the sensors and the front-end electronics combined in the same process with the goal of making SiPMs extremely easy to use has already been successful (digital SiPMs) [30], and remains a topic of intense R&D.

More solid-state light sensors have either been developed or are potentially interesting for use in HEP experiments. The Run 2 DØ detector used 86000 Visible-light photon counters (VLPC) to read the optical signal from its scintillating-fiber tracker and scintillator-strip preshower detectors. These light sensors utilize the formation of an impurity band only 50 meV below the conduction band in As-doped Si to generate strong ($G \approx 5 \times 10^4$) yet sharp response to single photons with $\epsilon_Q \approx 0.9$ [31–33]. Only a very small bias (~7 V) is needed, but high sensitivity to infrared photons requires cooling below 10 K. Another interesting light sensor that has not yet found its use in HEP instrumentation are quantum dots, realized by nanometer-sized semiconductor 'particles' embedded in a semiconductor bulk.

### 35.2.4 Superconducting photon detectors

In this rapidly developing technology field, three most established technologies are the superconducting nano-wire single photon detector (SNSPD), the transition edge sensor (TES), and the microwave kinetic inductance detector (MKID). An SNSPD consists of a thin (4 nm) and narrow (100-250 nm) superconducting

nanostrip that is current-biased just below its critical current. Absorption of a photon generates a resistive domain in the superconducting nanostrip, which leads to a transient voltage signal that can be detected. SNSPDs offer a unique combination of speed, both in terms of count rate (~GHz) and low timing jitter (< 3 ps [34]), large range of wavelength sensitivity from VUV (120 nm) to mid-IR (10 µm), high detection efficiencies (approaching 100% for UV to near-IR), and low dark count rates (~5-10 Hz), making them appealing for a wide variety of demanding applications.

Examples of present use in particle physics are small nanowire detectors for dark matter and dark photons. Work is in progress that could make these sensors relevant to HEP applications by increasing the area (using 300 mm wafers and larger) and pixel size, coupling via windows to cryogenic stages, and readout of arrays (superconducting electronics for data processing). While the performance of these sensors is impressive, an application in large accelerator-based detectors would require an extensive R&D program because of the severe cryogenic requirements.

## 35.3 Organic scintillators

Revised August 2023 by S. C. Eno (U. Maryland) and Matthieu Hamel (Paris-Saclay U. CEA, LIST).

Organic scintillators produce light when transversed by a charged particle. They can be broadly categorized into four types: single crystal, liquid, plastic, and a recently emerged glass [35]. The most useful scintillators produce photons with wavelengths between 370-750 nm (ultraviolet to red), typically peaking at 425 nm [36] via a series of processes that are initialized when charged particles interact with the material via both excitation and ionization/recombination (see Sec. 34.2 of this Review). Typical photon yields are about 1 photon per 100 eV of energy deposit [37], although the collected and transduced signal can be much lower. Methods to guide the light towards the photon-electron converter, such as diffusive paint, reflectors, photonic crystals, or light guides, may be required to optimize light yield.

Organic scintillators have found use in a wide variety of detectors [38]. Plastics are mostly used in collider detectors, and liquids in neutrino experiments. Ease of fabrication into desired shapes and low cost has made plastic scintillator ideal for large detectors. In the form of scintillating fiber, it has found widespread use in tracking and calorimetry. Demand for large volume detectors (e.g. neutrino detectors: MiniBooNE, NOvA) has led to increased use of liquid scintillator, which can be very low cost.

### 35.3.1 Scintillation mechanism

Plastic and liquid scintillators are based on an aromatic "matrix" such as benzene. The p electrons form both "pi" and "sigma" bonds between the atoms; the pi bonds are responsible for scintillation. Scintillation is produced via standard photophysical interactions, shown schematically in Fig. 35.1. While there have been claims of delayed light production on long time scales (labeled "phosphorescence" in the figure), this is still a subject of active debate in the community. As aromatic molecules scintillate in the ultraviolet (UV), useful scintillators have one or several fluorophores dissolved into the matrix as dopants. Common fluorophores include 2,5-diphenyloxazole, p-terphenyl, 9,10-diphenylanthracene (9,10-DPA), 1,4-bis(2-methylstyryl)benzene (bis-MSB) and 1,4-bis(5-phenyl-2-oxazolyl)benzene (POPOP). Each molecule has its own role: the matrix (whether liquid or plastic) is where most of the radiation/matter interaction occurs. After radiation interaction, ions may recombine giving birth to excited molecules (excitons). Excitons in the matrix are transferred to a "primary fluorophore", whose concentration is typically 1-3 weight % in commercial plastic and liquid scintillators. This concentration is large enough to ensure exciton transfer – primarily via the Förster mechanism, a resonant dipole-dipole interaction which decreases at sixth the power of the distance between molecules. The concentration, however, can be up to the solubility limit. Transfer via the Förster mechanism increases both speed and light output
<figure><img src="image_198.png" /><figcaption>**Figure 35.1:** Schematic of scintillation mechanism. Schematic of typical excitation and de-excitation of matrix modules.</figcaption></figure>

of the organic scintillator. To reduce reabsorption of the emitted light by the matrix or the primary fluorophore, and the resulting shortened attenuation length, a “secondary fluorophore” is also used to shift the light to longer wavelengths. Transfer from the primary to the secondary is generally radiative. Typical secondary concentrations in plastic and liquids are 0.01-0.2 weight %. The chain of emission and absorption from the matrix to the subsequent fluorophores is shown in Fig. 35.2. Scintillators with

<figure><img src="image_199.png" /><figcaption>**Figure 35.2:** Schematic of scintillation mechanism. Typical emission and absorption spectra for the matrix, the primary, and the secondary fluorophore.</figcaption></figure>

two fluorophores typically have absorption lengths of several meters. The longest attenuation lengths require a third fluorophore: when the matrix is transparent up to 1 cm, adding a primary fluorophore increases the light transmission up to ≈ 10 cm, whereas the ternary cocktail is transparent up to 2 m and longer [39].

For most scintillators, decay times are in the ns range; rise times are much faster. Sub-ns timing resolutions have been achieved [40].

Organic scintillators do not respond linearly to the ionization density. Very dense ionization tracks, with large $dE/dx$, emit less light than expected compared to minimum-ionizing particles. A widely used semi-empirical model by Birks posits that recombination and quenching effects between the excited molecules reduce

the light yield [41]. These effects are more pronounced the greater the density of the excited molecules. Birks' formula is

$$ \frac{d\mathcal{L}}{dx} = \mathcal{L}_0 \frac{dE/dx}{1 + k_B dE/dx}, \qquad (35.2) $$

where $\mathcal{L}$ is the luminescence, $\mathcal{L}_0$ is the luminescence at low specific ionization density, and the product $k_B$ is known as Birks' constant, which must be determined for each scintillator by measurement. The value of $k_B$ for polystyrene is 0.126 mm/MeV, which is large enough to play an important role in compensation in scintillator-based calorimetry. The high hydrogen content of plastic, which enhances the neutron interaction cross section, as well as its large mass stopping power, also contributes to calorimetry compensation. In the case of large $dE/dx$ values (e.g. with alpha particles), ion recombination may lead to the creation of triplet excited states instead of singlet excited states. If two triplet states are close enough (typically in the order of 10Å), then triplet-triplet annihilation may occur following the Dexter process [42], leading to delayed fluorescence. This phenomenon is useful for $\alpha/\beta$ or neutron/$\gamma$ discrimination and is more efficient in liquid scintillators than in plastics due to the molecular motion.

Extensive research searching for new efficient molecules that can act as matrix, primary, or secondary fluorophores, is ongoing [43]. Other chemical modifications can affect the scintillator emission wavelength and decay time, or be used e.g. as stabilizers or to enhance thermal neutron sensitivity. Other parameters that can be modified are the density and the effective atomic number.

### 35.3.2 Plastic scintillator practicalities

Most commercial plastic scintillators use either polystyrene (PS) or poly(vinyltoluene) (PVT) as matrix. A variety of manufacturing techniques [43] are used in the production of plastic scintillator. Cast plastic has the highest light yield, while extruded scintillator is less expensive and allows creation of the scintillator and coating with a diffusive reflector in a single process. In the last couple of years, 3D printing of plastic scintillator has emerged as a reliable production method. The technique has been applied towards plastics for pulse-shape discrimination (PSD) [44]. However, large-scale production (10+ liters) has not yet been achieved. Plastic scintillator is also used to produce scintillating, wavelength-shifting, and clear fibers. These fibers can be useful to guide light to photodetectors, and as the active element in the type of calorimeter pioneered by the RD52/DREAM collaboration [45]. They have even been used in the construction of trackers [46, 47].

Plastic scintillators are reliable, robust, and convenient. However, exposure to solvent vapors, high temperatures, mechanical flexing, irradiation, or rough handling will cause degradation. The surface is a particularly fragile region and can “craze” – develop microcracks which degrade transmission of light by total internal reflection. Crazing is particularly likely where oils, solvents, or fingerprints have contacted the surface or when mechanical stresses are present. The light yield is influenced by several environmental factors: it decreases with the partial pressure of oxygen [48] and increases with increasing magnetic field. In particular, the combination of elevated temperature with relative humidity accelerates aging. This apparent fogging is typically observed in radiation portal monitors, which are exposed to harsh environmental conditions. The aging can become irreversible after multiple cycles. Recently the T2K collaboration reported a 10-year light-yield measurement showing damage due to aging [49].

Plastics are susceptible to radiation damage [50]. At high enough dose, the visible color of the plastic can change to yellow or (at high enough dose) even brown. During irradiation, broken atomic bonds (“radicals”) absorb light, generally strongly in the UV, with tails to longer wavelengths. Because of this, shifting the light to longer wavelengths reduces the decrease in light output and in attenuation length due to radiation effects. Radicals produce mostly temporary damage that “anneals” when the irradiation ends, as the bonds can reform. Radicals can also polymerize via cross linking, and this leads to a permanent reduction in light yield [51]. In an inert atmosphere at room temperature, the bond reformation timescale is on the order of a month. Oxygen, which
diffuses into the plastic during radiation to a depth that scales as the inverse square root of dose rate, can quickly bind to the radicals, reducing but not eliminating temporary damage at the price of a small increased permanent damage [52–54]. After irradiation, oxygen, if present, will diffuse through the entire sample, leading to oxide formation and speeding the annealing process. The decrease in light output due to permanent damage depends on the dose rate. Lower dose rates show large light losses for the same dose. The ratio of the light output to the unirradiated light output can roughly be parameterized as an exponential. For dose rates typical of current collider detectors at the Large Hadron Collider (from a few $10^{-3}$ to 10 Gy/hr), an exponential dose constant of tens of kGy is observed.

### 35.3.3 Organic glass scintillators

Starting in 2016, extensive research by Sandia National Laboratories lead to a new organic scintillator family: organic glasses (OGSs) [55]. Whereas polymers are long-chain molecules built from a standard unit called a monomer, OGSs consist of small organic molecules. In addition, polymers such as PS or PVT require dopants, when OGSs are intrinsically good scintillators. This new material has the useful properties present in inorganic single crystals (light yield, PSD properties, along with fast-timing properties), without the poor mechanical characteristics seen in single crystals. The maintenance of the amorphous state of these bulk optical materials was achieved mainly either by using molecules with high configurational disorder or by introducing compositional disorder. OGSs can be prepared in medium to large scales when they are blended with polymers, or pixelated for neutron detection systems, and they can eventually be loaded with heavy elements.

### 35.3.4 Liquid scintillator practicalities

Liquid scintillators have been used in large scale neutrino experiments 36.3.1.1 due to their low cost. They can hermetically fill any vessel shape. Liquid scintillators are also, due to the mobility of the molecules, much less susceptible to radiation damage.

Care must be taken to avoid dissolved water, solvents such as isopropyl alcohol, and oxygen, which reduce light yield. As they can dissolve many materials (e.g. plastics, adhesives, paints..) care must be taken in their handling. Flammability concerns limit their use in practical experiments in intense radiation fields.

## 35.4 Inorganic scintillators

Revised August 2023 by C.L. Woody (BNL) and R.-Y. Zhu (HEP California Inst. of Technology).

Inorganic crystals form a class of scintillating materials with much higher densities than organic plastic scintillators (typically ~ 4–8 g/cm³) with a variety of different properties for use as scintillation detectors. Due to their high density and high effective atomic number, they can be used in applications where high stopping power or a high conversion efficiency for electrons or photons is required. These include total absorption electromagnetic calorimeters (see Sec. 35.10.2), which consist of a totally active absorber (as opposed to a sampling calorimeter), as well as serving as gamma ray detectors over a wide range of energies. Many of these crystals also have very high light output, and can therefore provide excellent energy resolution down to very low energies (~ few hundred keV).

Some crystals are intrinsic scintillators in which the luminescence is produced by a part of the crystal lattice itself. However, other crystals require the addition of a dopant, typically fluorescent ions such as thallium (TI) or cerium (Ce) which is responsible for producing the scintillation light. However, in both cases, the scintillation mechanism is the same. Energy is deposited in the crystal by ionization, either directly by charged particles, or by the conversion of photons into electrons or positrons which subsequently produce ionization. This energy is transferred to the luminescent centers which then radiate scintillation photons. The light yield LY in terms of the number of scintillation photons produced per MeV of energy deposit in the crystal can be expressed as [56]

$$LY = 10^6 S \cdot Q/(\beta \cdot E_g), \quad (35.3)$$

where $\beta \cdot E_g$ is the energy required to create an e-h pair expressed as a multiple of the band gap energy Eg (eV), S is the efficiency of energy transfer to the luminescent center and Q is the quantum efficiency of the luminescent center. The values of $\beta$, $S$ and $Q$ are crystal dependent and are the main factors in determining the intrinsic light yield of the scintillator. The decay time of the scintillator is mainly dominated by the decay time of the luminescent center.

Table-35.4 lists the basic properties of some commonly used inorganic crystals. NaI(Tl) is one of the most common and widely used scintillators, with an emission that is well matched to a bialkali photomultiplier tube, but it is highly hygroscopic and difficult to work with, and has a rather low density. CsI(Tl) and CsI(Na) have high light yield, low cost, and are mechanically robust (high plasticity and resistance to cracking). However, they need careful surface treatment and are slightly and highly hygroscopic respectively. Pure CsI has identical mechanical properties as CsI(Tl), but a faster emission at shorter wavelength and a much lower light yield.

Undoped BaF₂ has a fast component with a less than 0.6 ns decay time, and is the fastest known scintillator. However, it also has a slow component with a much longer decay time (~ 630 ns). Bismuth gemanate (Bi₄Ge₃O₁₂ or BGO) has a high density, and consequently a short radiation length $X_0$ and Molière radius $R_M$. Similar to CsI(Tl), BGO's emission is well-matched to the spectral sensitivity of silicon photodiodes, and it is easy to handle and not hygroscopic. Lead tungstate (PbWO₄ or PWO) has a very high density, with a very short $X_0$ and $R_M$, but its intrinsic light yield is rather low.

Cerium doped lutetium oxyorthosilicate (Lu₂SiO₅:Ce, or LSO:Ce) [57] and cerium doped lutetium-yttrium oxyorthosilicate (Lu₂(1-x)Y₂xSiO₅, LYSO:Ce) [58] are dense crystal scintillators which have a high light yield and a fast decay time. Only the properties of LSO:Ce are listed in Table-35.4 since the properties of LYSO:Ce are similar to that of LSO:Ce except a slightly lower density than LSO:Ce depending on the yttrium fraction (typically 5 to 10%) in LYSO:Ce. This material is also featured with excellent radiation hardness [59, 60], so is expected to be used where extraordinary radiation hardness is required.

Also listed in Table-35.4 are other fluoride crystals such as PbF₂ as a Cherenkov material and CeF₃, which have been shown to provide excellent energy resolution in calorimeter applications. Table-35.4 also includes cerium doped lanthanum tri-halides, such as LaBr₃ [61] and CeBr₃ [62], which are brighter and faster than LSO:Ce, but they are highly hygroscopic and have a lower density. The FWHM energy resolution measured for these materials coupled to a PMT with bi-alkali photocathode for 0.662 MeV $\gamma$-rays from a $^{137}$Cs source is about 3%, and has recently been improved to 2% by co-doping with cerium and strontium [63], which is the best among all inorganic crystal scintillators. For this reason, LaBr₃ and CeBr₃ are expected to be used in applications where a good energy resolution for low energy photons are required, such as homeland security.

Beside the crystals listed in Table-35.4, a number of new crystals are being developed that may have potential applications in high energy or nuclear physics. Of particular interest is the family of yttrium and lutetium perovskites and garnet, which include YAP (YAlO₃:Ce), LuAP (LuAlO₃:Ce), YAG (Y₃Al₅O₁₂:Ce) and LuAG (Lu₃Al₅O₁₂:Ce) and their mixed compositions. These have been shown to be linear over a large energy range [64], and have the potential for providing good intrinsic energy resolution.

Aiming at the best jet-mass resolution inorganic scintillators are being investigated for HEP calorimeters with dual readout for both Cherenkov and scintillation light to be used at future lepton colliders. These materials may be used for an electromagnetic calorimeter [65] or a homogeneous hadronic calorimetry (HHCAL) detector concept, including both electromagnetic and hadronic parts [66, 67]. Because of the unprecedented volume (70 to 100 m³) foreseen for the HHCAL detector concept the materials must be (1) dense (to minimize the leakage) and (2) cost-effective. It should also be UV transparent (for effective collection of the Cherenkov light) and allow for a clear discrimination between the Cherenkov and scintillation light. The preferred scintillation light
<table><caption>**Table 35.4:** Properties of several inorganic crystals. Most of the notation is defined in Sec. 6 of this Review.</caption><thead><tr><th>Parameter:</th><th>ρ</th><th>MP</th><th>X<sub>0</sub>*</th><th>R<sub>M</sub>*</th><th>dE/dx*</th><th>λ<sub>I</sub>*</th><th>τ<sub>decay</sub></th><th>λ<sub>max</sub></th><th>n<sup>†</sup></th><th>Relative yield<sup>‡</sup></th><th>Hygro- scopic?</th><th>d(LY)/dT</th></tr><tr><th>Units:</th><th>g/cm<sup>3</sup></th><th>°C</th><th>cm</th><th>cm</th><th>MeV/cm</th><th>cm</th><th>ns</th><th>nm</th><th></th><th></th><th></th><th>%/°C<sup>§</sup></th></tr></thead><tbody><tr><td>NaI(Tl)</td><td>3.67</td><td>651</td><td>2.59</td><td>4.13</td><td>4.8</td><td>42.9</td><td>245</td><td>410</td><td>1.85</td><td>100</td><td>yes</td><td>-0.2</td></tr><tr><td>BGO</td><td>7.13</td><td>1050</td><td>1.12</td><td>2.23</td><td>9.0</td><td>22.8</td><td>300</td><td>480</td><td>2.15</td><td>21</td><td>no</td><td>-0.9</td></tr><tr><td>BaF<sub>2</sub></td><td>4.89</td><td>1280</td><td>2.03</td><td>3.10</td><td>6.5</td><td>30.7</td><td>&lt;0.6<sup>f</sup></td><td>220<sup>f</sup></td><td>1.50</td><td>36<sup>s</sup></td><td>no</td><td>-1.9<sup>s</sup></td></tr><tr><td>CsI(Tl)</td><td>4.51</td><td>621</td><td>1.86</td><td>3.57</td><td>5.6</td><td>39.3</td><td>1220</td><td>550</td><td>1.79</td><td>165</td><td>slight</td><td>0.4</td></tr><tr><td>CsI(Na)</td><td>4.51</td><td>621</td><td>1.86</td><td>3.57</td><td>5.6</td><td>39.3</td><td>690</td><td>420</td><td>1.84</td><td>88</td><td>yes</td><td>0.4</td></tr><tr><td>CsI(pure)</td><td>4.51</td><td>621</td><td>1.86</td><td>3.57</td><td>5.6</td><td>39.3</td><td>30<sup>s</sup></td><td>310</td><td>1.95</td><td>3.6<sup>s</sup></td><td>slight</td><td>-1.4</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>6<sup>f</sup></td><td></td><td></td><td>1.1<sup>f</sup></td><td></td><td></td></tr><tr><td>PbWO<sub>4</sub></td><td>8.30</td><td>1123</td><td>0.89</td><td>2.00</td><td>10.1</td><td>20.7</td><td>30<sup>s</sup></td><td>425<sup>s</sup></td><td>2.20</td><td>0.3<sup>s</sup></td><td>no</td><td>-2.5</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>10<sup>f</sup></td><td>420<sup>f</sup></td><td></td><td>0.077<sup>f</sup></td><td></td><td></td></tr><tr><td>LSO(Ce)</td><td>7.40</td><td>2050</td><td>1.14</td><td>2.07</td><td>9.6</td><td>20.9</td><td>40</td><td>402</td><td>1.82</td><td>85</td><td>no</td><td>-0.2</td></tr><tr><td>PbF<sub>2</sub></td><td>7.77</td><td>824</td><td>0.93</td><td>2.21</td><td>9.4</td><td>21.0</td><td>-</td><td>-</td><td>-</td><td>Cherenkov</td><td>no</td><td>-</td></tr><tr><td>CeF<sub>3</sub></td><td>6.16</td><td>1460</td><td>1.70</td><td>2.41</td><td>8.42</td><td>23.2</td><td>30</td><td>340</td><td>1.62</td><td>7.3</td><td>no</td><td>0</td></tr><tr><td>LaBr<sub>3</sub>(Ce)</td><td>5.29</td><td>783</td><td>1.88</td><td>2.85</td><td>6.90</td><td>30.4</td><td>20</td><td>356</td><td>1.9</td><td>180</td><td>yes</td><td>0.2</td></tr><tr><td>CeBr<sub>3</sub></td><td>5.23</td><td>722</td><td>1.96</td><td>2.97</td><td>6.65</td><td>31.5</td><td>17</td><td>371</td><td>1.9</td><td>165</td><td>yes</td><td>-0.1</td></tr></tbody></table>

is thus at a longer wavelength, and not necessarily bright or fast. Dense crystals, scintillating glasses and ceramics offer a very attractive implementation for this detector concept [68].

The fast scintillation light provides timing information about electromagnetic interactions and showers, which may be used to mitigate pile-up effects and/or for particle identification since the time development of electromagnetic and hadronic showers, as well as minimum ionizing particles, are different. The timing information is primarily determined by the scintillator rise time and decay time, and the number of photons produced. For fast timing, it is important to have a large number of photons emitted in the initial part of the scintillation pulse, e.g. in the first ns, since one is often measuring the arrival time of the particle in the crystal using the leading edge of the light pulse. A good example of this is BaF₂, which has ~10% of its light in its fast component with a decay time of less than 0.6 ns. Recent investigation shows that doping with yttrium in BaF₂ reduces its slow component significantly, while keeping its ultrafast scintillation component unchanged [69, 70]. The light propagation can spread out the arrival time of the scintillation photons at the photodetector due to time dispersion [71]. The time response of the photodetector also plays a major role in achieving good time resolution with fast scintillating crystals.

Table-35.4 gives the light yield of other crystals relative to NaI(Tl) and their dependence to the temperature variations. The light output was measured for 1.5 X₀ cube crystal samples with a Tyvek paper wrapping and a full end face coupled to a photodetector [72]. The quantum efficiency of the photodetector is taken out to facilitate a direct comparison of crystal's light yield. However, the measured light output produced by a scintillator is usually quoted in terms of the number of photoelectrons per MeV produced by a given photodetector. The relationship between the light yield (LY) in number of photons/MeV produced (N<sub>photons</sub>/MeV) and the light output (LO) in number of photoelectrons/MeV detected involves the factors for the light collection efficiency (LCE) and the quantum efficiency (QE) of the photodetector:

$$LO = LY \cdot LCE \cdot QE. \qquad (35.4)$$

LCE depends on the size and shape of the crystal sample, and includes effects such as the transmission of scintillation light within the crystal (i.e., the bulk attenuation length of the material), scattering from within the crystal, reflections and scattering from the crystal surfaces, and re-bouncing back into the crystal by wrapping materials. These factors can vary considerably depending on the sample, but can be in the range of ~10–60%. The inter-

nal light transmission depends on the intrinsic properties of the material, e.g. the density and type of the scattering centers and defects that can produce internal absorption within the crystal, and can be highly affected by factors such as radiation damage, as discussed below.

The quantum efficiency depends on the type of photodetector used to detect the scintillation light, which is typically ~15–30% for photomultiplier tubes and higher for silicon photodetectors for visible wavelengths. The response of the detector is usually highly wavelength dependent and should be matched to the particular crystal of interest to give the highest quantum yield at the wavelength corresponding to the peak of the scintillation emission. Fig. 35.3 shows the quantum efficiency for a Hamamatsu R2059 PMT with bi-alkali cathode and quartz window, and the particle detection efficiency (PDE) for a Hamamatsu S14160-3015ps multi-pixel photon counter (MPPC), which is also called silicon photomultiplier (SiPM), as a function of wavelength. Also shown in the figure are emission spectra of three crystal scintillators, BGO, LSO:Ce/LYSO:Ce and CsI(Tl), and the numerical values of the emission weighted quantum efficiency. The area under each emission spectrum is proportional to crystal's light yield, as shown in Table-35.4, where the quantum efficiencies of the photodetector has been taken out. Results with different photodetectors can be significantly different. For example, the response of CsI(Tl) relative to NaI(Tl) with a standard photomultiplier tube with a bi-alkali photo-cathode, e.g. Hamamatsu R2059, would be 45 rather than 165 because of the photomultiplier's low quantum efficiency at longer wavelengths. For scintillators which emit in the UV, a detector with a quartz window should be used.

For very low energy applications (typically below 1 MeV), non-proportionality of the scintillation light yield may be important. It has been known for a long time that the conversion factor between the energy deposited in a crystal scintillator and the number of photons produced is not constant. It is also known that the energy resolution measured by all crystal scintillators for low energy γ-rays is significantly worse than the contribution from photo-electron statistics alone, indicating an intrinsic contribution from the scintillator itself. Precision measurement using low energy electron beam shows that this non-proportionality is crystal dependent [73]. Recent study on this issue also shows that this effect is also sample dependent even for the same crystal [74]. Further work is therefore needed to fully understand this subject.

One important issue related to the application of a crystal scintillator is its radiation hardness. Stability of its light output, or the ability to track and monitor the variation of its light output

<footnote>*Numerical values calculated using formulae in this review.</footnote>

<footnote>†Refractive index at the wavelength of the emission maximum.</footnote>

<footnote>‡Relative light yield measured for samples of 1.5 X₀ cube with a Tyvek paper wrapping and a full end face coupled to a photodetector. The quantum efficiencies of the photodetector are taken out.</footnote>

<footnote>§Variation of light yield with temperature evaluated at the room temperature.</footnote>

<footnote>f = fast component, s = slow component</footnote>
<figure><img src="image_200.png" /><figcaption>Figure 35.3: The quantum efficiency for a Hamamatsu R2059 PMT with bi-alkali cathode and quartz window and the particle detection efficiency (PDE) for a Hamamatsu S14160-3015ps multi-pixel photon counter (MPPC), which is also called silicon photomultiplier (SiPM), are shown as a function of wavelength. Also shown in the figure are emission spectra of three crystal scintillators, BGO, LSO and CsI(Tl), and the numerical values of the emission weighted quantum efficiencies. The area under each emission spectrum is proportional to crystal's light yield.</figcaption></figure>

in a radiation environment, is required for high resolution and precision calibration [75]. All known crystal scintillators suffer from ionization dose induced radiation damage [76], where a common damage phenomenon is the appearance of radiation induced absorption caused by the formation of color centers originated from the impurities or point defects in the crystal. This radiation induced absorption reduces the light attenuation length in the crystal, and hence its light output. For crystals with high defect density, a severe reduction of light attenuation length may cause a distortion of the light response uniformity, leading to a degradation of the energy resolution. Additional radiation damage effects may include a reduced intrinsic scintillation light yield (damage to the luminescent centers) and an increased phosphorescence (afterglow). For crystals to be used in a high precision calorimeter in a radiation environment, its scintillation mechanism must not be damaged and its light attenuation length in the expected radiation environment must be long enough so that its light response uniformity, and thus its energy resolution, does not change.

While radiation damage induced by ionization dose is well understood [77], investigation is on-going to understand radiation damage caused by hadrons, including both charged hadrons [78] and neutrons [79]. Two additional fundamental processes may cause defects by hadrons: displacement damage and nuclear breakup. While charged hadrons can produce all three types of damage (and it's often difficult to separate them), neutrons can produce only the last two, and electrons and photons only produce ionization damage. Studies on hadron induced radiation damage to lead tungstate [80] show a proton-specific damage component caused by fragments from fission induced in lead and tungsten by particles in the hadronic shower. The fragments cause a severe, local damage to the crystalline lattice due to their extremely high energy loss over a short distance [80]. Recent investigation also sees evidence of neutron-specific damage in various crystals [79].

Most of the crystals listed in Table-35.4 have been used in high energy or nuclear physics experiments when the ultimate energy resolution for electrons and photons is desired. Examples are the Crystal Ball NaI(Tl) calorimeter at SPEAR, the L3 BGO calorimeter at LEP, the CLEO CsI(Tl) calorimeter at CESR, the KTeV CsI calorimeter at the Tevatron, and the BaBar, BELLE

and BES III CsI(Tl) calorimeters at PEP-II, KEK and BEPC II, respectively. Because of their high density and relative low cost, PWO calorimeters are used by CMS and ALICE at LHC, by CLAS and PrimEx at CEBAF and by PANDA at GSI, and is planned to be used for the Backward Endcap Calorimeter for the ePIC experiment at the EIC. Similarly, PbF₂ calorimeters are used by the A4 experiment at MAINZ and by the g-2 experiment at Fermilab. A CsI calorimeter is being built for the Mu2e experiment at Fermilab. An LYSO:Ce calorimeter is being built for the COMET experiment at J-PARC, and an LYSO:Ce crystal-based precision timing layer is being built for the CMS experiment for the HL-LHC.

## 35.5 Cherenkov detectors

Revised August 2023 by J. Schwiening (GSI Darmstadt).

Although devices using Cherenkov radiation are often thought of as only particle identification (PID) detectors, in practice they are used over a much broader range of applications including; (1) fast particle counters; (2) hadronic PID; (3) electromagnetic calorimeters (EMC); and (4) tracking detectors performing complete event reconstruction. Examples of applications from each category include; (1) the BaBar luminosity detector [81] and the Quartic fast timing counter for the ATLAS Forward Proton Detector, designed to measure small angle scatters at the LHC [82]; (2) the hadronic PID detectors at the B factory detectors—DIRC in BaBar [83], and the modern Imaging Aerogel and TOP counters at Belle II [84]; (3) the CMS Hadron Forward calorimeter based on Cherenkov light emitted in quartz fibers embedded in a steel absorber [85]; and (4) large water Cherenkov counters such as Super-Kamiokande [86].

Cherenkov counters contain two main elements; (1) a radiator through which the charged particle passes, and (2) a photodetector. As Cherenkov radiation is a weak source of photons, light collection and detection must be as efficient as possible. The refractive index $n$ and the particle's path length through the radiator $L$ appear in the Cherenkov relations allowing the tuning of these quantities for particular applications. One or more of the properties of Cherenkov radiation discussed in the Passages of Particles through Matter section (Sec. 34 of this Review) are utilized in Cherenkov detectors: the prompt emission of a light pulse; the existence of a velocity threshold for radiation; and the dependence of the Cherenkov cone half-angle $\theta_c$ and the number of emitted photons on the velocity of the particle $v_p$ and the refractive index $n$ of the medium. The Cherenkov angle can be calculated as

$$ \cos \theta_c = \frac{1}{n(E)\beta}, \qquad (35.5) $$

where $\beta = v_p/c$ with $c$ being the speed of light, and $E$ the photon energy. The number of photoelectrons ($N_{p.e.}$) detected in a given device with radiator of length $L$ is

$$ N_{p.e.} = L \frac{\alpha^2 z^2}{r_e m_e c^2} \int \epsilon(E) \sin^2 \theta_c(E) dE, \qquad (35.6) $$

where $\epsilon(E)$ is the efficiency for collecting the Cherenkov light and transducing it into photoelectrons, and $\alpha^2/(r_e m_e c^2) = 370 \text{ cm}^{-1}\text{eV}^{-1}$. The quantities $\epsilon$ and $\theta_c$ are functions of the photon energy. As the typical energy dependent variation of the index of refraction is modest, a quantity called the Cherenkov detector quality factor $N_0$ can be defined as

$$ N_0 = \frac{\alpha^2 z^2}{r_e m_e c^2} \int \epsilon dE, \qquad (35.7) $$

so that, taking the charge number $z = 1$ (the usual case in high-energy physics),

$$ N_{p.e.} \approx LN_0 \langle \sin^2 \theta_c \rangle. \qquad (35.8) $$

This definition of the quality factor $N_0$ is not universal, nor, indeed, very useful for those common situations where $\epsilon$ factorizes as $\epsilon = \epsilon_{coll}\epsilon_{det}$ with the geometrical photon collection efficiency
($\epsilon_{\text{coll}}$) varying substantially for different tracks while the photon detector efficiency ($\epsilon_{\text{det}}$) remains nearly track independent. In this case, it can be useful to explicitly remove ($\epsilon_{\text{coll}}$) from the definition of $N_0$. A typical value of $N_0$ for a photomultiplier (PMT) detection system working in the visible and near UV, and collecting most of the Cherenkov light, is about $100 \text{ cm}^{-1}$. Practical counters, utilizing a variety of different photodetectors, have values ranging between about 30 and $180 \text{ cm}^{-1}$. Radiators can be chosen from a variety of transparent materials (Sec. 34 of this Review and Table 6). In addition to refractive index, the choice requires consideration of factors such as material density, radiation length and radiation hardness, transmission bandwidth, absorption length, chromatic dispersion, optical workability (for solids), availability, environmental impact, and cost. When the momenta of particles to be identified is high, the refractive index must be set close to one, so that the photon yield per unit length is low and a long particle path in the radiator is required. In recent years, the gap in refractive index that has traditionally existed between gases and liquid or solid materials has been partially closed with transparent silica aerogels with indices that range between about 1.003 and 1.26. Due to the potential ability to tune the refractive index to the exact requirements of an experiment, metamaterials, including photonic crystals, are being investigated as radiators for future Cherenkov counters [87].

Cherenkov counters may be classified as either imaging or threshold types, depending on whether they do or do not make use of Cherenkov angle ($\theta_c$) information. Imaging counters may be used to track particles as well as identify them. The recent development of very fast photodetectors such as micro-channel plate PMTs (MCP-PMT) (see 35.2 of this Review) also potentially allows very fast Cherenkov based time of flight (TOF) detectors of either class [87]. The track timing resolution of imaging detectors can be extremely good as it scales approximately as $\frac{1}{\sqrt{N_{\text{p.e.}}}}$.

Threshold Cherenkov detectors [88], in their simplest form, make a yes/no decision based on whether the particle is above or below the Cherenkov threshold velocity $\beta_t = 1/n$. A straightforward enhancement of such detectors uses the number of observed photoelectrons (or a calibrated pulse height) to discriminate between species or to set probabilities for each particle species [89]. This strategy can increase the momentum range of particle separation by a modest amount (to a momentum some 20% above the threshold momentum of the heavier particle in a typical case).

Careful designs give $\langle \epsilon_{\text{coll}} \rangle \gtrsim 90\%$. For a photomultiplier with a typical bialkali cathode, $\int \epsilon_{\text{det}} dE \approx 0.27 \text{ eV}$, so that

$$N_{\text{p.e.}}/L \approx 90 \text{ cm}^{-1} \langle \sin^2 \theta_c \rangle \quad (\text{i.e., } N_0 = 90 \text{ cm}^{-1}). \quad (35.9)$$

Suppose, for example, that $n$ is chosen so that the threshold for species a is $p_t$; that is, at this momentum species a has velocity $\beta_a = 1/n$. A second, lighter, species b with the same momentum has velocity $\beta_b$, so $\cos \theta_c = \beta_a/\beta_b$, and

$$N_{\text{p.e.}}/L \approx 90 \text{ cm}^{-1} \frac{m_a^2 - m_b^2}{p_t^2 + m_a^2}. \quad (35.10)$$

For $K/\pi$ separation at $p = p_t = 1(5) \text{ GeV/c}$, $N_{\text{p.e.}}/L \approx 16(0.8) \text{ cm}^{-1}$ for $\pi$'s and (by design) 0 for K's.

For limited path lengths $N_{\text{p.e.}}$ will usually be small. The overall efficiency of the device is controlled by Poisson fluctuations, which can be especially critical for separation of species where one particle type is dominant. Moreover, the effective number of photoelectrons is often less than the average number calculated above due to additional equivalent noise from the photodetector (see the discussion of the excess noise factor in 35.2 of this Review). It is common to design for at least 10 photoelectrons for the high velocity particle in order to obtain a robust counter. As rejection of the particle that is below threshold depends on not seeing a signal, electronic and other background noise, especially overlapping tracks, can be important. Physics sources of light production for the below threshold particle, such as decay to an above threshold particle, scintillation light, or the production of delta rays in the radiator, often limit the separation attainable, and need to be

carefully considered. Well designed, modern multi-channel counters, such as the ACC at Belle [90], can attain adequate particle separation performance over a substantial momentum range.

Imaging counters make the most powerful use of the information available by measuring the ring-correlated angles of emission of the individual Cherenkov photons. They typically provide positive ID information both for the “wanted” and the “unwanted” particles, thus reducing mis-identification substantially. Since low-energy photon detectors can measure only the position (and, perhaps, a precise detection time) of the individual Cherenkov photons (not the angles directly), the photons must be “imaged” onto a detector so that their angles can be derived [91]. Typically the optics map the Cherenkov cone onto (a portion of) a distorted “circle” at the photodetector. Though the imaging process is directly analogous to familiar imaging techniques used in telescopes and other optical instruments, there is a somewhat bewildering variety of methods used in a wide variety of counter types with different names. Some of the imaging methods used include (1) focusing by a lens or mirror; (2) proximity focusing (i.e., focusing by limiting the emission region of the radiation); and (3) focusing through an aperture (a pinhole). In addition, the prompt Cherenkov emission coupled with the speed of some modern photon detectors allows the use of (4) time imaging, a method which is little used in conventional imaging technology, and may allow some separation with particle TOF. Finally, (5) correlated tracking (and event reconstruction) can be performed in large water counters by combining the individual space position and time of each photon together with the constraint that Cherenkov photons are emitted from each track at the same polar angle (Sec. 36.3.1 of this Review).

In a simple model of an imaging PID counter, the fractional error on the particle velocity ($\delta_{\beta}$) is given by

$$\delta_{\beta} = \frac{\sigma_{\beta}}{\beta} = \tan \theta_c \sigma(\theta_c), \quad (35.11)$$

where

$$\sigma(\theta_c) = \frac{\langle \sigma(\theta_i) \rangle}{\sqrt{N_{\text{p.e.}}}} \oplus C, \quad (35.12)$$

and $\langle \sigma(\theta_i) \rangle$ is the average single photoelectron resolution, as defined by the optics, detector resolution and the intrinsic chromaticity spread of the radiator index of refraction averaged over the photon detection bandwidth. C combines a number of other contributions to resolution including, (1) correlated terms such as tracking, alignment, and multiple scattering, (2) hit ambiguities, (3) background hits from random sources, and (4) hits coming from other tracks. The actual separation performance is also limited by physics effects such as decays in flight and particle interactions in the material of the detector. In many practical cases, the performance is limited by these effects.

For a $\beta \approx 1$ particle of momentum (p) well above threshold entering a radiator with index of refraction (n), the number of $\sigma$ separation ($N_{\sigma}$) between particles of mass $m_1$ and $m_2$ is approximately

$$N_{\sigma} \approx \frac{|m_1^2 - m_2^2|}{2p^2\sigma(\theta_c)\sqrt{n^2 - 1}}. \quad (35.13)$$

In practical counters, the angular resolution term $\sigma(\theta_c)$ varies between about 0.1 and 5 mrad depending on the size, radiator, and photodetector type of the particular counter. The range of momenta over which a particular counter can separate particle species extends from the point at which the number of photons emitted becomes sufficient for the counter to operate efficiently as a threshold device (~20% above the threshold for the lighter species) to the value in the imaging region given by the equation above. For example, for $\sigma(\theta_c) = 2$ mrad, a fused silica radiator ($n = 1.474$), or a fluorocarbon gas radiator ($C_5F_{12}$, $n = 1.0017$), would separate $\pi/K$'s from the threshold region starting around 0.15(3) GeV/c through the imaging region up to about 4.2(18) GeV/c at better than $3\sigma$.

Many different imaging counters have been built during the last several decades [87]. Among the earliest examples of this class of counters are the very limited acceptance Differential Cherenkov
detectors, designed for particle selection in high momentum beam lines. These devices use optical focusing and/or geometrical masking to select particles having velocities in a specified region. With careful design, a velocity resolution of $\sigma_{\beta}/\beta \approx 10^{-4}-10^{-5}$ can be obtained [88].

Practical multi-track Ring-Imaging Cherenkov detectors (generically called RICH counters) are a more recent development. RICH counters are sometimes further classified by 'generations' that differ based on historical timing, performance, design, and photodetection techniques. Prototypical examples of first generation RICH counters are those used in the DELPHI and SLD detectors at the LEP and SLC Z factory $e^{+}e^{-}$ colliders [87]. They have both liquid ($C_6F_{14}$, $n = 1.276$) and gas ($C_5F_{12}$, $n = 1.0017$) radiators, the former being proximity imaged with the latter using mirrors. The phototransducers are a TPC/wire-chamber combination. They are made sensitive to photons by doping the TPC gas (usually, ethane/methane) with ~0.05% TMAE (tetrakis(dimethylamino)ethylene). Great attention to detail is required, (1) to avoid absorbing the UV photons to which TMAE is sensitive, (2) to avoid absorbing the single photoelectrons as they drift in the long TPC, and (3) to keep the chemically active TMAE vapor from interacting with materials in the system. In spite of their unforgiving operational characteristics, these counters attained good $e/\pi/K$ separation over wide momentum ranges (from about 0.25 to 20 GeV/c) during several years of operation at LEP and SLC. Related but smaller acceptance devices include the OMEGA RICH at the CERN SPS, and the RICH in the balloon-borne CAPRICE detector [87]. Despite their excellent match to the radiator requirement for gaseous RICHes, saturated fluorocarbons may soon need to be replaced due to their high global warming impact. Possible alternatives for a similar refractive index include hydrofluoroolefins or Argon, pressurized at a few bar [87].

Later generation counters [87] generally operate at much higher rates, with more detection channels, than the first generation detectors just described. They also utilize faster, more forgiving photon detectors, covering different photon detection bandwidths. Radiator choices have broadened to include materials such as lithium fluoride, fused silica, and aerogel.

Vacuum-based photodetection systems (e.g., single or multi-anode PMTs, MCP-PMTs, or hybrid photodiodes (HPD)) have become increasingly common (see 35.2 of this Review). They handle high rates, and can be used with a wide choice of radiators. Examples include (1) the SELEX RICH at Fermilab, which mirror focuses the Cherenkov photons from a neon radiator onto a camera array made of ~2000 PMTs to separate hadrons over a wide momentum range (to well above 200 GeV/c for heavy hadrons); (2) the NA62 RICH at CERN, which uses a 17 m long tank filled with neon gas as radiator and spherical mirrors to focus the photons on two arrays of 2000 PMTs to separate pions from muons for momenta between 15 and 35 GeV/c; (3) the CBM RICH under construction at FAIR where the Cherenkov photons, produced in about 30 m³ of CO₂ radiator gas, are mirror-focused on arrays of multi-anode PMTs (MaPMTs) with a total of about 55,000 pixels, to identify electrons with momenta up to 10 GeV/c; and (4) the LHCb detector now running at the LHC. It uses two separate counters. One volume contains $C_4F_{10}$ (originally in combination with aerogel, which was removed in 2015) while the second volume contains $CF_4$. Photons are mirror-focused onto arrays of photon detectors to cover a $\pi/K$ separation momentum range between 1 and 150 GeV/c. Additional upgrades, including the replacement of the HPDs by MaPMTs and improved readout electronics, were performed to deal with increases in luminosity.

Other fast detection systems that use solid cesium iodide (CsI) photocathodes or triethylamine (TEA) doping in proportional chambers are useful with certain radiator types and geometries. Examples include (1) the CLEO-III RICH at CESR that uses a LiF radiator with TEA doped proportional chambers; (2) the ALICE detector at the LHC that uses proximity focused liquid ($C_6F_{14}$ radiators and solid CsI photocathodes (similar photodetors have been used for several years by the HADES and COMPASS detectors), and the hadron blind detector (HBD) in the PHENIX detector at RHIC that couples a low index $CF_4$ radiator

to a photodetector based on electron multiplier (GEM) chambers with reflective CsI photocathodes [87].

Recent technological advances in the production of aerogel with improved transparency in the UV range and finely tuned refractive indices enable several new RICH designs. The innovative hybrid geometry of the CLAS12 RICH, with complex photon paths that feature multiple passes through the aerogel tiles, is only possible due to the improved scattering length of the aerogel. It minimizes the material inside of the detector acceptance as well as the size and cost of the photon sensor array. Beam tests have demonstrated that the counter will be able to provide clean $\pi/K$ separation up to 8 GeV/c. The forward endcap Aerogel RICH (ARICH) for the Belle II upgrade at KEKB, designed to provide clean $\pi/K$ separation for momenta up to 3.5 GeV/c, is an example of the so-called focusing aerogel approach [92]. The radiator is a dual-layer aerogel, with a thickness of 20 mm for each layer and increasing refractive indices of $n = 1.045$ and $n = 1.055$ along the particle path. The Cherenkov ring images from the two layers overlap on the array of Hybrid Avalanche Photo Detectors (HAPDs), which provide efficient single photon detection in the 1.5 T magnetic field.

A DIRC (Detection [of] Internally Reflected Cherenkov [light]) is a distinctive, compact RICH subtype first used in the BaBar detector [83]. A DIRC “inverts” the usual RICH principle for use of light from the radiator by collecting and imaging the total internally reflected light rather than the transmitted light. It utilizes the optical material of the radiator in two ways, simultaneously: as a Cherenkov radiator and as a light pipe. The magnitudes of the photon angles are preserved during transport by the flat, rectangular cross section radiators, allowing the photons to be efficiently transported to a detector outside the path of the particle where they may be imaged in up to three independent dimensions (the usual two in space and, due to the long photon paths lengths, one in time). Because the index of refraction in the radiator is large ($n \sim 1.47$ for fused silica), the momentum range with good $\pi/K$ separation goes up to 4–5 GeV/c. It is plausible, but difficult, to extend it up to about 10 GeV/c with an improved design.

The BaBar experiment at the asymmetric PEP-II $e^{+}e^{-}$ collider studied CP violation in $\Upsilon(4S)$ decays. Excellent pion/kaon separation for particle momenta up to 4 GeV/c was required. The BaBar DIRC used 4.9 m long, rectangular bars made from synthetic fused silica as radiator and light guide. The photons were imaged via a “pin-hole” through an expansion region filled with 6000 liters of purified water onto an array of 10 752 densely packed photomultiplier tubes placed at a distance of about 1.2 m from the bar end. During more than 8 years of operation, the BaBar DIRC achieved $\pi/K$ separation of 2.5 standard deviations or more up to 4 GeV/c momentum. For a pion identification rate around 85% the DIRC provided a kaon misidentification rate well below 1% up to 3 GeV/c.

The next generation of DIRC detectors [93] takes advantage of the new, very fast, pixelated photodetectors becoming available, such as MaPMTs and MCP-PMTs. They typically utilize either time imaging or lens/mirror-focused optics, or both, leading not only to a precision measurement of the Cherenkov angle, but in some cases, to a precise measurement of the particle time of flight, and/or to correction of the chromatic dispersion in the radiator. Examples [87] include (1) the Belle II Time of Propagation (TOP) counter that emphasizes precision timing for both Cherenkov imaging and TOF to perform $\pi/K$ separation of at least 3 standard deviations up to 4 GeV/c; (2) the DIRC upgrade of the GlueX experiment at Jefferson Lab that places four de-commissioned BaBar DIRC modules, coupled to upgraded optics and readout, perpendicular to the beamline, the first application of a DIRC in a detector endcap; (3) the high-performance DIRC for the ePIC detector at the EIC, to be installed in 2030, that will combine lens focusing with fast photon time imaging and is expected to provide more than 3 standard deviations $\pi/K$ separation up to 6 GeV/c; and (4) the TORCH counter being developed for an LHCb upgrade in 2033 which uses DIRC imaging for individual photons with fast photon detectors to provide $\pi/K$ separation up to 10 GeV/c via particle TOF with a precision of
10-15 ps per track over a flight path length of 9.5 m.

## 35.6 Gaseous detectors

### 35.6.1 Energy loss and charge transport in gases

Revised November 2021 by F. Sauli (CERN) and M. Titov (IRFU, CEA, Université Paris-Saclay).

Gas-filled detectors use the localized ionization produced by charged particles, generally after charge multiplication. The statistics of ionization processes, having asymmetries in the ionization trails, affect the coordinate determination deduced from the measurement of drift time, or of the center of gravity of the collected charge. For thin gas layers, the width of the energy loss distribution can be larger than its average, requiring multi-sampling devices or truncated mean analysis to achieve good particle identification. In the truncated mean method for calculating $\langle dE/dx \rangle$, the ionization measurements along the track length are broken into many samples and then a fixed fraction of high-side (and sometimes also low-side) values are rejected [94].

<table><caption>**Table 35.5:** Properties of noble and molecular gases at normal temperature and pressure (NTP: 20° C, one atm). $E_X$, $E_I$: first excitation, ionization energy; $W_I$: average energy for creation of ion pair; $dE/dx|_{min}$, $N_P$, $N_T$: differential energy loss, primary and total number of electron-ion pairs per cm, for unit charge minimum ionizing particles. Values often differ, depending on the source, and those in the table should be taken only as approximate.</caption><thead><tr><th>Gas</th><th>Density, mg cm<sup>-3</sup></th><th>E<sub>x</sub> eV</th><th>E<sub>I</sub> eV</th><th>W<sub>I</sub> eV</th><th>dE/dx|<sub>min</sub> keV cm<sup>-1</sup></th><th>N<sub>P</sub> cm<sup>-1</sup></th><th>N<sub>T</sub> cm<sup>-1</sup></th></tr></thead><tbody><tr><td>H<sub>2</sub></td><td>0.084</td><td>10.8</td><td>13.6</td><td>37</td><td>0.34</td><td>5.2</td><td>9.2</td></tr><tr><td>He</td><td>0.179</td><td>19.8</td><td>24.6</td><td>41.3</td><td>0.32</td><td>3.5</td><td>8</td></tr><tr><td>Ne</td><td>0.839</td><td>16.7</td><td>21.6</td><td>37</td><td>1.45</td><td>13</td><td>40</td></tr><tr><td>Ar</td><td>1.66</td><td>11.6</td><td>15.7</td><td>26</td><td>2.53</td><td>25</td><td>97</td></tr><tr><td>Xe</td><td>5.495</td><td>8.4</td><td>12.1</td><td>22</td><td>6.87</td><td>41</td><td>312</td></tr><tr><td>CH<sub>4</sub></td><td>0.667</td><td>8.8</td><td>12.6</td><td>30</td><td>1.61</td><td>28</td><td>54</td></tr><tr><td>C<sub>2</sub>H<sub>6</sub></td><td>1.26</td><td>8.2</td><td>11.5</td><td>26</td><td>2.91</td><td>48</td><td>112</td></tr><tr><td>iC<sub>4</sub>H<sub>10</sub></td><td>2.49</td><td>6.5</td><td>10.6</td><td>26</td><td>5.67</td><td>90</td><td>220</td></tr><tr><td>CO<sub>2</sub></td><td>1.84</td><td>7.0</td><td>13.8</td><td>34</td><td>3.35</td><td>35</td><td>100</td></tr><tr><td>CF<sub>4</sub></td><td>3.78</td><td>10.0</td><td>16.0</td><td>35-52</td><td>6.38</td><td>52-63</td><td>120</td></tr></tbody></table>

The energy loss of charged particles and photons in matter is discussed in Sec. 34. Every ionization process is a quantum mechanical transition initiated by the Coulomb field of the particle and the field created by neighbouring polarizable atoms; the average energy losses are described by the Bethe-Bloch formula with Sternheimer's density effect corrections. The fluctuations caused by Rutherford scattering on quasi-free electrons follow a Landau distribution and the influence of atomic shells is described by the photoabsorption ionization (PAI) model, which allows simulation of each energy transfer [95], with relaxation cascades and simulation of delta-electrons [96]. Table 35.5 provides values of relevant parameters in some commonly used gases at NTP for unit-charge minimum-ionizing particles (MIPs) [97] [98]. When an ionizing particle passes through the gas it creates electron-ion pairs; often the ejected electrons have sufficient energy to further ionize the medium. The number of pairs is known as cluster-size distribution, because the secondary electrons are created in the immediate vicinity of the primary encounter and, together with the primary electrons, form clusters of one, several, or sometimes many, electron-ion pairs. As shown in Table 35.5, the total number of pairs ($N_T$) is a few times larger than the number of primaries ($N_P$). For different conditions and for mixtures, and neglecting energy transfer processes (e.g. Penning effect), one can scale the density, $N_P$, and $N_T$ with temperature and pressure assuming a perfect gas law.

The probability for a released electron to have an energy $E$ or larger follows an approximate $1/E^2$ dependence (Rutherford law),

shown in Fig. 35.4 for Ar at NTP (dotted line, left scale). More detailed estimates taking into account the electronic structure of the medium are shown in the figure, for three values of the particle velocity factor $\beta\gamma$ [99]. The dot-dashed line provides, on the right scale, the practical range of electrons (including scattering) of energy $E$. As an example, about 0.6% of released electrons have 1 keV or more energy, substantially increasing the total ionization loss. The practical range of 1 keV electrons in argon (dot-dashed line, right scale) is 70 $\mu$m and this can contribute to the error in the coordinate determination.

<figure><img src="image_201.png" /><figcaption>**Figure 35.4:** Probability of single collisions in which released electrons have an energy $E$ or larger (left scale) and practical range of electrons in Ar at NTP (dot-dashed curve, right scale) [99].</figcaption></figure>

Garfield++ [100], together with HEED [96], Degrad [101], Magboltz [102, 103], SRIM, ANSYS, COMSOL, and neBEM [104] software packages represent the core simulation tools for microscopic modelling of gaseous detector response. The number of electron-ion pairs per primary ionization, or cluster size depends little on the medium; it can be computed with the programs mentioned above or experimentally measured. For example, there is about 1% probability for primary clusters to contain ten or more electron-ion pairs in argon [105].

Once released in the gas, and under the influence of an applied electric field, electrons and ions drift in opposite directions and diffuse towards the electrodes. The electron-molecule collision cross sections are determined by the details of atomic and molecular structure and depends strongly on the electron energy and therefore on the electric field $E$ for most gases. High values of the total electron scattering cross section reduce the electron diffusion and increase the drift velocity; a large inelasticity implies that high fields are required to raise the electron energy. For noble gases, the inelastic cross section is zero until the electrons reach the first excitation and ionization energies $O(10 \text{ eV})$; on the contrary, for molecular gases, like $CH_4$, inelastic channels, involving rotational and vibrational levels, open up at energies above $\sim 0.1 \text{ eV}$. Large drift velocities are achieved by adding polyatomic gases (usually hydrocarbons $C_xH_y$, $CO_2$, $CF_4$) having large inelastic component at moderate energies of a few eV; this results in the electron "cooling" into the energy range of the Ramsauer-Townsend minimum (at $\sim 0.5 \text{ eV}$) of the elastic ("momentum-transfer") cross-section in Ar [98]. Under these circumstances, it is not surprising that the addition of very small quantities of one gas to another can dramatically modify the average electron energy and alter the dependence of the drift velocity ($v_d$) on $E/P$ and temperature; this has a particularly strong effect for noble gases, as illustrated in Fig. 35.5 for Ar. Carbon tetrafluoride ($CF_4$) has the largest drift velocity and the lowest electron diffusion among known gases due to the sizeable Ramsauer-Townsend dip in the elastic cross-section which coincides with a very large vibrational modes. Another principal role of the polyatomic gas is to absorb the ultraviolet photons emitted by the excited noble gas atoms. Addition of molecular gases (hydrocarbons or $CO_2$) are widely used in the proportional counters as a quencher) to noble gas allows to dissipate a good fraction of energy through rotational and vibrational radiationless transitions without the creation of photons or ions. On the
contrary, $CF_4$ has a small quenching cross-section of excited Ar states and light emission in $CF_4$ (from the far UV to the visible light) is a complex process, involving the creation of $CF_3^+$ excited states [106].

Extensive collections of experimental data [107] and theoretical calculations based on transport theory permit evaluation of drift and diffusion properties in pure gases and their mixtures; modern compilations of the electron-molecule cross sections are available at the open-access website LXCAT [108]. Fig. 35.5 and Fig. 35.6 show drift velocity and transverse diffusion for some commonly used gases at NTP, computed with the Magboltz program [102, 103]. For different conditions, the horizontal axis must be scaled inversely with the gas density. Standard deviations for longitudinal ($\sigma_L$) and transverse diffusion ($\sigma_T$) are given for one cm of drift, and scale with the square root of the drift distance.

In a simple approximation, gas kinetic theory provides the drift velocity $v_d$ as a function of the mean collision time $\tau$ and the electric field $E$: $v_d = eE\tau/m_e$ (Townsend's expression). In the presence of an external magnetic field, the Lorentz force acting on electrons between collisions deflects the drifting electrons and modifies the drift properties. The electron trajectories, velocities and diffusion parameters can be computed with Magboltz. The friction force model provides an approximate expression for the vector drift velocity $v$ as a function of electric and magnetic field vectors $E$ and $B$, of the Larmor frequency $\omega = eB/m_e$, and of the mean collision time $\tau$ (more precise calculation is available in Magboltz, which computes drift velocity by tracing electrons at the microscopic level through numerous collisions with gas molecules):

$$v = \frac{e}{m_e} \frac{\tau}{1 + \omega^2 \tau^2} \left( E + \frac{\omega \tau}{B} (E \times B) + \frac{\omega^2 \tau^2}{B^2} (E \cdot B)B \right) \quad (35.14)$$

To a good approximation, and for moderate fields, one can assume that the energy of the electrons is not affected by $B$, and use for $\tau$ the values deduced from the drift velocity at $B=0$ (the Townsend expression). For $E$ perpendicular to $B$, the drift angle relative to the electric field vector is $\tan \theta_B = \omega\tau$ and $v = (E/B)(\omega\tau/\sqrt{1+\omega^2\tau^2})$. For parallel electric and magnetic fields, drift velocity and longitudinal diffusion are not affected, while the transverse diffusion can be strongly reduced: $\sigma_T(B) = \sigma_T(B=0)/\sqrt{1+\omega^2\tau^2}$. As an example, the dotted line in Fig. 35.6 represents $\sigma_T$ for the classic Ar/CH$_4$ (90:10) mixture at 4 T. Large values of $\omega\tau \sim 20$ at 5 T are consistent with the measurement of diffusion coefficient in Ar/CF$_4$/iC$_4$H$_{10}$ (95:3:2). This reduction is exploited to substantially improve spatial resolution in the Drift (Sec. 35.6.2) and Time Projection Chambers (Sec. 35.6.5).

<figure><img src="image_202.png" /><figcaption>Figure 35.5: Computed electron drift velocity as a function of electric field in several gases at NTP and $B=0$ [102, 103].</figcaption></figure>

In some mixtures containing molecules with electronic affinity, electrons can be captured to form negative ions. Capture cross sections vary considerably with an energy and, hence, the electric field; as a consequence, the three-body electron attachment coefficients may differ significantly for the same additive in different mixtures. As an example, at moderate fields (up to 1 kV/cm)

the addition of 0.1% of oxygen to an Ar/CO$_2$ mixture results in an electron capture probability about twenty times larger than in Ar/CH$_4$. Among common molecules, the largest electron affinities are found for the halogenides, O$_2$ and H$_2$O. The attachment probability in O$_2$ or H$_2$O is large at low fields and electron energies close to thermal, but decreases at increasing fields. On the contrary, $CF_4$ is not electronegative at low and moderate fields, but has a large electron capture cross section at fields above ~8 kV/cm, before reaching the avalanche field strengths. Depending on the mixture and detector geometry, some signal reduction and energy resolution loss is expected in this gas.

If the electric field is increased sufficiently, electrons gain enough energy between collisions to excite and ionize molecules. Above a gas-dependent threshold, the mean free path for ionization, $\lambda_i$, decreases exponentially with the field; its inverse, $\alpha = 1/\lambda_i$, is named the first Townsend coefficient. In wire chambers, most of the increase of avalanche particle density occurs very close to the anode wires, and a simple electrostatic consideration shows that the largest fraction of the detected signal is due to the motion of positive ions receding from the wires. The electron component, although very fast, contributes very little to the signal. This determines the characteristic shape of the detected signals in the proportional mode: a fast rise followed by a gradual increase. The slow component, the so-called “ion tail” that limits the time resolution of the detector, is usually removed by differentiation of the signal. In uniform fields, $N_0$ initial electrons multiply over a length $x$ forming an electron avalanche of size $N = N_0 e^{\alpha x}$; $N/N_0$ is the gain of the detector. Fig. 35.7 shows examples of Townsend coefficients for several gas mixtures, computed with Magboltz [102, 103].

<figure><img src="image_203.png" /><figcaption>Figure 35.6: Electron longitudinal diffusion ($\sigma_L$) (dashed lines) and transverse diffusion ($\sigma_T$) (full lines) for 1 cm of drift at NTP and $B=0$. The dotted line shows $\sigma_T$ for the P10 mixture at 4 T [102, 103].</figcaption></figure>

<figure><img src="image_204.png" /><figcaption>Figure 35.7: Computed first Townsend coefficient $\alpha$ as a function of electric field in several gases at NTP [102, 103].</figcaption></figure>
Additional ionizing energy transfer mechanisms due to the excited noble gas atoms, called collisional Penning energy transfers, occur when the excitation energy of a noble gas is higher than the ionization potential of an admixture gas. The energy transfer rate, probability that an excited atom ionizes a quenching agent, is a priori not known for a mixture but can be extracted from the fits of the experimental gas gain data [109] using the Magboltz simulations [102, 103]. In the gain calculations, the Penning adjusted Townsend coefficient is defined in terms of the total production frequencies of the noble gas excitations and direct ionizations of the mixture. Systematic gas gain measurements for varying mixing ratios and pressures are critical for determining the efficiency of the different mechanisms involved in the transfers. Collisional energy transfer mostly scales linearly with the gas pressure and the fraction of quenching gas in the mixture, while ionization by photons emitted from excitations is independent of the medium [110]. In addition, collisional Penning transfers of some higher excited states can occur before they decay at atmospheric pressure and are not restricted to metastable states of the excited noble gas. For example, the impact of the Penning effect on gas gain is roughly a factor 10 in Ar-CO₂ mixtures and exceeding a factor of 100 in Ar-C₂H₂ mixtures [110].

Positive ions released by the primary ionization or produced in the avalanches drift and diffuse under the influence of the electric field. Negative ions may also be produced by electron attachment to gas molecules. The drift velocity of ions in the fields encountered in gaseous detectors (up to few kV/cm) is typically about three orders of magnitude smaller than for electrons. The ion mobility $\mu$, the ratio of drift velocity to electric field, is constant for a given ion type up to very high fields. Values of ions mobility at NTP are given in Table 35.6 [111]. For different temperatures and pressures, the mobility can be scaled inversely with the density assuming an ideal gas law. Both the longitudinal and transverse diffusion of ions are proportional to the square root of the drift time, with a coefficient that depends on temperature but not on the ion mass. It has been historically assumed that, due to a very effective charge transfer mechanism, only ions with the lowest ionization potential survive after a short path in the mixture. However, recent experimental data suggests that the signal ions, in e.g. CO₂-quenched mixtures of Ar and Ne are CO₂⁺·(CO₂)ₙ cluster ions, and not CO₂⁺ or noble gas ions [112]. Since the cluster ions are slower than the initial ions, the signals induced by ion motion are altered. The effect can be present in constant-field detectors and TPCs (see Sec. 35.6.5), and might affect devices such as Micromegas (see Sec. 35.6.4) and drift tubes. A negative-ion TPC can be used to expand the reach of directional dark matters searches [113].

<table><caption>**Table 35.6:** Mobility of ions in gases and mixtures at NTP [111].</caption><thead><tr><th>Gas</th><th>Mobility μ<br>(cm² V⁻¹ s⁻¹)</th></tr></thead><tbody><tr><td>He</td><td>10.4</td></tr><tr><td>Ne</td><td>4.7</td></tr><tr><td>Ar</td><td>1.54</td></tr><tr><td>Ar/CH₄</td><td>1.87</td></tr><tr><td>Ar/CO₂</td><td>1.72</td></tr><tr><td>CH₄</td><td>2.26</td></tr><tr><td>CO₂</td><td>1.09</td></tr></tbody></table>

### 35.6.2 Multi-Wire Proportional and Drift Chambers

Revised November 2021 by F. Sauli (CERN) and M. Titov (IRFU, CEA, Université Paris-Saclay).

Single-wire counters that detect the ionization produced in a gas by a charged particle, followed by charge multiplication and collection around a thin (typically 20 – 50 µm diameter) wire, have been used for decades. Good energy resolution is obtained in the proportional amplification mode, while very large saturated pulses can be detected in the streamer and Geiger modes [114].

Modern fully electronic devices, multiwire proportional chambers (MWPCs) [115, 116] introduced in the late 1960’s, detect, localize and measure energy deposit by charged particles over large areas. A mesh of parallel anode wires at a suitable potential, inserted between two cathodes, acts almost as a set of independent proportional counters (see Fig. 35.8a). Electrons released in the gas volume drift towards the anodes and produce avalanches in the increasing field. Analytic expressions for the electric field can be found in many textbooks. The fields close to the wires $E(r)$, in the drift region $E_D$, and the capacitance $C$ per unit length of anode wire are approximately given by

$$E(r) = \frac{CV_0}{2\pi\epsilon_0 r} \qquad E_D = \frac{CV_0}{2\epsilon_0 s} \qquad C = \frac{2\pi\epsilon_0}{\pi(\ell/s) - \ln(2\pi a/s)}, \qquad (35.15)$$

where $r$ is the distance from the center of the anode, $s$ the wire spacing, $\ell$ and $V_0$ the distance and potential difference between anode and cathode, and $a$ the anode wire radius.

Because of electrostatic forces, anode wires are in equilibrium only for a perfect geometry. Small deviations result in forces displacing the wires alternatively below and above the symmetry plane, sometimes with catastrophic results [117]. These displacement forces are countered by the mechanical tension of the wire, up to a maximum unsupported stable length, $L_M$ [118], above which the wire displaces:

$$L_M = \frac{s}{CV_0} \sqrt{4\pi\epsilon_0 T_M} \qquad (35.16)$$

The maximum tension $T_M$ depends on the wire diameter and modulus of elasticity. Table 35.7 gives approximate values for tungsten and the corresponding maximum stable wire length under reasonable assumptions for the operating voltage ($V_0 = 5$ kV) [119]. Internal supports and spacers can be used in the construction of longer detectors to overcome limits on the wire length imposed by Eq. (35.16).

<table><caption>**Table 35.7:** Maximum tension $T_M$ and stable unsupported length $L_M$ for tungsten wires with spacing $s$, operated at $V_0 = 5$ kV. No safety factor is included.</caption><thead><tr><th>Wire diameter (μm)</th><th>T<sub>M</sub> (newton)</th><th>s (mm)</th><th>L<sub>M</sub> (cm)</th></tr></thead><tbody><tr><td>10</td><td>0.16</td><td>1</td><td>25</td></tr><tr><td>20</td><td>0.65</td><td>2</td><td>85</td></tr></tbody></table>

Traditionally, several simplifying assumptions are made in such analytical calculations: electrostatic force acting on the wire does not change during wire movements, or varies linearly with the displacement, the wire shape is parabolic; only one wire moves at a time. Therefore, for complicated electrode geometries the approximations listed above are not applicable. The advantage of numerical integrations using Garfield++ program is to simulate the collective movement of all wires, which are difficult analytically, and to consider all forces acting on a wire: forces between anode wire and other electrodes (wires, cathode) and a gravitational force [120].

Detection of charge on the wires over a predefined threshold provides the transverse coordinate to the wire with an accuracy comparable to that of the wire spacing. The coordinate along each wire can be obtained by measuring the ratio of collected charge at the two ends of resistive wires. The cathode planes can be fabricated in the form of group of wires or isolated strips, which are often patterned in orthogonal directions. Making use of the charge profile induced by avalanches on segmented cathodes, the so-called electronic center-of-gravity (COG) method allows localization of tracks to sub-mm accuracy. Due to the statistics of energy loss and asymmetric ionization clusters, the position accuracy is ~ 50 µm rms for fast particles perpendicular to the wire plane, but degrades to ~ 250 µm at 30° to the normal [121].

Drift chambers, developed in the early '70's, can be used to estimate the space coordinate perpendicular to the wires by exploiting the arrival time of electrons at the anodes if the time of interaction is known [122]. The distance between anode wires (e.g.
<figure><img src="image_205.png" /><figcaption>**Figure 35.8:** Electric field lines and equipotentials in (a) a multiwire proportional chamber and (b) a drift chamber.</figcaption></figure>

Au-plated W) is usually several cm, allowing coverage of large areas at reduced cost. In the original design, a thicker wire (the field wire, often from Cu-Be or Al) at the proper voltage, placed between the anode wires, removes the low-field region at the midpoint between anodes and improves charge collection (Fig. 35.8b). In some drift chamber designs, and with the help of suitable voltages applied to field-shaping electrodes, the electric field structure is adjusted to improve the linearity of space-to-drift-time relation, resulting in better spatial resolution [123].

Drift chambers can reach a longitudinal spatial resolution from timing measurement of order 100 µm (rms) or better for minimum ionizing particles, depending on the geometry and operating conditions. However, a degradation of resolution is observed [124] due to primary ionization statistics for tracks close to the anode wires, caused by the spread in arrival time of the nearest ionization clusters. The effect can be reduced by operating the detector at higher pressures. Sampling the drift time on rows of anodes led to the concept of multiple arrays such as the multi-drift module [125] and the JET chamber [126]. A measurement of drift time, together with the recording of charge sharing from the two ends of the anode wires provides the coordinates of segments of tracks. An ultimate drift chamber design is the Time Projection Chamber (TPC) concept [127], which provides 3D precision tracking with low material budget and enables particle identification through differential energy loss dE/dx measurement or cluster counting $dN_{cl}/dx$ techniques. In all cases, a good knowledge of electron drift velocity and diffusion properties is required. This has to be combined with the knowledge of the electric fields in the structures [103]. Accumulation of ions in the gas volume may induce gain reduction and field distortions, especially for long drift distances in TPC (see Sec. 35.6.5). An important major innovation is related to the replacement of MWPC with Micro-Pattern Gaseous Detectors (MPGD) (see Sec. 35.6.4) for the TPC endplate readout, which offers many advantages: reduced track-angle, and negligible $E \times B$ track distortion effects, narrower pad response function (PRF), and intrinsic suppression of Ion Back Flow (IBF). For an overview of detectors exploiting the drift time for coordinate measurement see Refs. [118, 128].

Multiwire and drift chambers have been operated with a variety of gas fillings and operating modes, depending on experimental requirements. The so-called “Magic Gas,” a mixture of argon, isobutane and Freon [116], permits very high and saturated gains (~ $10^6$). This gas mixture was used in early wire chambers, but was found to be susceptible to severe aging processes. DAFNE’s KLOE Drift Chamber and the recent version of it developed for

the MEG2 experiment [129] are the precursors of the next generation of ultralight central trackers for future colliders. Since the main contribution in terms of radiation length is related to tungsten wires, high transparency can be achieved thanks to the development of new wire materials (e.g. carbon monofilaments) and novel approaches for the wiring and assembly procedures. Drift chambers have been operated with a light helium/hydrocarbon mixtures, which are not reliable for long-term, high-rate operation [130]. Dedicated R&D is necessary to find an alternative hydrocarbon-free mixture adapted to the desired performance at future colliders.

Although very powerful in terms of performance, multi-wire structures have reliability problems when used in harsh or hard-to-access environments, since a single broken wire can disable the entire detector. Introduced in the 1980s, straw and drift tube systems make use of large arrays of proportional counters encased in individual enclosures, each acting as an independent wire counter [131]. Techniques for low-cost mass production of these detectors have been developed for large experiments, such as the Transition Radiation Tracker and the Drift Tubes arrays for CERN’s LHC experiments [132]. The state-of-the-art NA62 straw tracker utilizes new construction techniques of ultrasonic welding to close the straw and to keep them straight and withstand the vacuum pressure without breaking [133]. Future efforts for straw detectors, e.g. COMET Phase-II at JPARC or Mu2e-II at Fermilab, will focus on ultra-thin wall development, long and thin wire handling, precise mechanics and innovative designs.

### 35.6.3 High Rate Effects

Revised November 2021 by F. Sauli (CERN) and M. Titov (IRFU, CEA, Université Paris-Saclay).

The production of positive ions in the avalanches and their slow drift before neutralization result in a rate-dependent accumulation of positive charge in the detector. This may result in significant field distortion, gain reduction and degradation of spatial resolution. As shown in Fig. 35.9 [134], the proportional gain drops above a charge production rate around $10^9$ electrons per second and mm of wire, independently of the avalanche size. For a proportional gain of $10^4$ and 100 electrons per track, this corresponds to a particle flux of $10^3 s^{-1} mm^{-1}$ (1 kHz/mm² for 1 mm wire spacing). For the description of rate effects in MPGD, see Sec. 35.6.4.

<figure><img src="image_206.png" /><figcaption>**Figure 35.9:** Charge rate dependence of normalized gas gain $G/G_0$ (relative to zero counting rate) in proportional thin-wire detectors [134]. Q is the total charge in single avalanche; N is the particle rate per wire length.</figcaption></figure>

Although almost any gas can be used to operate wire chambers, $CF_4$-based mixtures have been preferred due to their properties. Their main advantage for the use in large volume detectors are high drift velocity, low diffusion, non-flammability and low sensitivity to neutrons; also they do not form polymers in avalanches.

However, the problem of greenhouse gases, such as $CF_4$, could become a fundamental limitation for their future applications in
gaseous detectors; due to the EU regulations their prices might go up and future availability is unknown. Performance studies of several eco-friendly mixtures have been initiated, together with a better understanding of their long-term ageing effects [135] (see also Sec. 35.6.4).

Ageing phenomena (formation of polymer deposits on the electrodes) constitute one of the most complex and serious potential problems which could limit or severely impair the use of gaseous detectors in unprecedented harsh radiation environments and lead to operational instabilities [136] [130]. The process has been extensively investigated, often with conflicting results. Several causes have been identified, including organic pollutants and silicone oils. Addition of small amounts of water in many (but not all) cases has been shown to extend the lifetime of the detectors. Addition of fluorinated gases (e.g., $CF_4$) or oxygen may result in an etching action that can overcome polymer formation, or even eliminate already existing deposits. However, the issue of long-term survival of gas detectors with these gases is controversial. Under optimum operating conditions, a total collected charge of a few coulombs per cm of wire can usually be reached before noticeable degradation occurs. This corresponds, for one mm spacing and at a gain of $10^4$, to a total particle flux of $\sim 10^{14}$ MIPs/cm$^2$.

### 35.6.4 Micro-Pattern Gas Detectors

Revised November 2021 by F. Sauli (CERN) and M. Titov (IRFU, CEA, Université Paris-Saclay).

Despite various improvements, position-sensitive detectors based on wire structures are limited by basic diffusion processes and space charge effects to localization accuracies of 50–100 µm [137]. Industrial advances in microelectronics and photolithographic technology on flexible and standard PCB substrates has favored the invention, in the last years of the 20th century, of novel Micro-Pattern Gaseous Detectors (MPGD) [138–140]. Since the very beginning, the goal was the development of novel devices with high rate capability (up to $10^6$ Hz/mm$^2$) and excellent spatial resolution (down to 30 µm), single photo-electron time resolution in the ns-range, large sensitive area and dynamic range, superior radiation hardness and low-cost for large area coverage. Nowadays, a broad family of MPGD technologies are being developed and optimized for numerous applications, such as [141,142]: Micro-Strip Gas Chamber (MSGC), Gas Electron Multiplier (GEM), Micro-Mesh Gaseous Structure (Micromegas), THick GEMs (THGEM), also referred to in the literature as Large Electron Multipliers (LEM), Resistive Plate WELL (RPWELL), GEM-derived architecture (μ-RWELL), Micro-Pixel Gas Chamber (μ-PIC), and an integrated readout of gaseous detectors (Gridpix) using solid-state pixel chips (e.g. Medipix or Timepix).

The MSGC concept, invented in 1988, was the first of the microstructure gas chambers [138]. It consists of a set of tiny parallel metal strips laid on a thin resistive support, alternatively connected as anodes and cathodes and resembles a multi-anode proportional counter. Through an accurate and simple photolithography process, the anode strips can be made very narrow ($\sim 10$ µm) with a typical pitch (distance between strips) of $\sim 100$ µm. When appropriate potentials are applied to the electrodes, electrons released in the drift volume move toward the strips and multiply in the high-field region. Owing to the small anode-to-cathode distance, the fast removal of positive ions by nearby cathode strips reduces space charge build-up, and improves significantly the rate capability, compared to wire counter. Despite their promising performance, experience with MSGCs has raised serious concerns about their long-term behavior. There are several major processes, particularly at high rates, leading to the MSGC operational instabilities: substrate charging-up and time-dependent distortions of the electric field, surface deposition of polymers (“aging”) during sustained irradiation, and destructive micro-discharges under exposure to heavily ionizing particles [143]. The physical parameters used to manufacture and operate these detectors (substrate material, metal of strips, type and purity of the gas mixture) appeared to play dominant roles in determining the medium- and long-term stability. The problems encountered inspired the development of novel structures, using modern photolithographic

<figure><img src="image_207.png" /><figcaption>**Figure 35.10:** Schematic view and typical dimensions of the hole structure in the GEM amplification cell. Electric field lines (solid) and equipotentials (dashed) are shown. Electron trajectories do not strictly follow the field lines as drifting electrons scatter isotropically with gas molecules and diffuse transversally.</figcaption></figure>

processes: GEM, Micromegas and others, having increased reliability and radiation hardness.

A GEM detector consists of a thin-foil copper-insulator-copper sandwich chemically perforated to obtain a high density of holes in which avalanches occur [139, 144]. The hole diameter is typically between 25 µm and 150 µm, while the corresponding distance between holes varies between 50 µm and 200 µm. The central insulator is usually (in the original design) a polyimid foil, with a thickness of 50 µm. Application of a potential difference between the two metal sides of the GEM generates the electric fields indicated in Fig. 35.10. Each hole acts as an independent proportional counter. Electrons released by the primary ionization particle in the upper conversion region (above the GEM foil) drift into the holes, where charge multiplication occurs in the high electric field (50–70 kV/cm), and are transferred into the gap below the GEM. Systematic measurements with cascaded multi-GEM structures confirm that the gains and charge transfer processes are predictable from electrostatic considerations and avalanche development models; an overall gas gain well above $10^4$ can be reached in the presence of highly ionizing particles, while strongly reducing the risk of discharges [145]. Other important parameters such as attachment, diffusion depend on the gas mixture composition and $E/P$. The majority of the charges created in the avalanche process follow the field lines and are collected by the metallic electrodes; owing however to diffusion, some may deposit on the dielectric surfaces, modifying the field and affecting gain and transparency of the structures [146]. This effect is known as “charging-up” effect; its time constant and amplitude depend largely on the shape of the holes.

The micro-mesh gaseous structure (Micromegas) is a thin parallel-plate avalanche counter, as shown in Fig. 35.11 [140]. It consists of a drift region and a narrow multiplication gap (25–150 µm) between a thin metal grid (micromesh) and the read-out electrode (strips or pads of conductor printed on an insulator board). Electrons from the primary ionization drift through the mesh into the narrow multiplication gap, where they are amplified. The electric field is mostly homogeneous in both the drift (electric field $\sim 1$ kV/cm) and amplification (50–70 kV/cm) regions and exhibits a funnel-like shape close to the openings of the micromesh: field lines are compressed into a small diameter of the order of a few microns, depending on the electric field ratio between the two gaps. In the narrow multiplication region, small variations of the amplification gap are approximately compensated by an inverse variation of the Townsend coefficient from
<figure><img src="image_208.png" /><figcaption>**Figure 35.11:** Schematic drawing of the Micromegas detector.</figcaption></figure>

the electric field, resulting in a more uniform gain. The transverse size of the electron avalanche due to diffusion is of the order of 10–15 µm, depending on the gas mixture, the electric field, and the gap width, giving rise to excellent spatial resolution (12 µm for MIPs) [147]. Most positive ions are quickly removed by the micromesh; this prevents space-charge accumulation and induces very fast signals (~100 ns length) due to electrons with a (fast) tail due to ions. Efforts have been also focused on producing Micromegas detector using innovative manufacturing techniques - the "Bulk" and "MicroBulk" technologies [148].

The absence of space-charge effects in GEMs at the highest rates reached so far, thanks to its fine-pitch structure of a few hundred microns, improves the maximum rate capability by more than two orders of magnitude compared to MWPC (see Fig.35.12) [149] [150]. Even larger rate capability has been reported for Micromegas [151].

<figure><img src="image_209.png" /><figcaption>**Figure 35.12:** Normalized gas gain as a function of particle rate for MWPC [149] and GEM [150].</figcaption></figure>

The fine granularity and high-rate capability of GEM and Micromegas can be fully exploited by using high-density pixel readout with a size corresponding to the intrinsic width of the detected avalanche charge. An elegant solution is the use of a CMOS pixel ASIC, assembled directly below the GEM or Micromegas amplification structure. Modern wafer post-processing technology allows an integration of a small-scale micromesh grid directly on top of a Timepix chip, thus forming an integrated MPGD readout, called GridPix concept (see Fig.35.13) [152]. With this arrangement, avalanche electrons are collected on the metalized input pads, exposed to the gas and signals are induced at the input gate of a charge-sensitive preamplifier. Every pixel is then directly connected to the amplification and digitization circuits, integrated in the underlying CMOS layers. A thin insulating layer, e.g. a few µm of silicon nitride, is usually deposited on top of CMOS ASIC to protect against destructive discharges across the O(50 µm) amplification gap. The GridPix concept provides the high granularity needed to resolve individual electron clusters (separated by an average distance of a few hundred microns) and to determine energy loss by the cluster counting technique, rather

than by the charge measurement, with a precision of better than 3%. Despite the enormous challenges, real breakthrough was the development of the TPC readout endplate with a 160 GridPix ASICs, each 2 cm², corresponding to 10.5 million pixels, demonstrating for the first time the feasibility of large-area MPGD with CMOS pixel readout [153]. New structures, where a GEM foil is facing the Medipix chip, forming the GEMpix detector, are in use for medical applications [154] as well as for monitoring the radioactive waste [155].

<figure><img src="image_210.png" /><figcaption>**Figure 35.13:** Photo of the Micromegas ('GridPix') detector. The grid holes can be accurately aligned with readout pixels of Timepix CMOS chip. The insulating pillars are centered between the grid holes, thus avoiding dead regions.</figcaption></figure>

Gaseous detectors represent the most cost-effective solution to cover very large areas with photosensitive elements. MPGD-based gaseous photomultipliers, conceived with the aim to overcome the limitations of MWPCs, with semi-transparent or reflective photocathodes (PC), allow to minimize PC aging due to the ion and photon feedback and to avoid secondary effects causing electrical instability. For RICH applications requiring large-area coverage and moderate spatial resolution, coarser macro-patterned structures (e.g. THGEM with typical thickness of 0.4–1 mm and hole spacing of 0.7–1.2 mm) offer an interesting cheaper solution [156]. These are derived from the GEM design, scaling up ~10-fold geometrical parameters, and can be mass-produced with standard PCB technology and mechanical drilling of large number of holes: some millions per square meter. Systematic studies to find the optimal electrostatic configuration revealed that the presence of a rim, a circular region around the holes where metal is etched away, plays a major role in THGEM performance. A small or zero rim allows to achieve better gain stability in time and under irradiation, while large rims permit to attain larger maximum gain and to reduce discharges, at the cost of significant charging up of the insulating surface, which modify the electric field. Therefore, in spite of the enhanced gain performance, the use of large rim THGEMs must be avoided to guarantee stable detector performance [157]. MPGDs are now in operation for single photon detection in the COMPASS RICH where a hybrid architecture formed by two THGEM layers (one covered by CsI-PC) and a Micromegas, acting as a third amplification stage, has been adopted.

Lately, closed geometry THGEM-based structures (RPWELL) [158], in common with some MPGDs invented at the end of the last century – C.A.T. and WELL, with resistive anodes have been developed, combining THGEM and RPC properties. This concept consists of a single-faced THGEM, copper-clad on its top side only, mounted directly on top of a resistive film deposited on a thin insulating sheet. Compared to THGEM with an induction gap, higher gains could be achieved in RPWELL for lower applied voltage across the THGEM electrode, due to the larger electric field within the closed holes. Another promising GEM-derived architecture is that of the μ-RWELL [159], with its ~ seven-fold smaller pitch with respect to the RPWELL. Two different layouts for resistive stage have been studied: the simplest one is based on
a single-resistive Diamong-Like Carbon (DLC) layer, and grounding by edges (2D charge evacuation for low-rates $O(kHz/cm^2)$) and a more sophisticated scheme using double-resistive layer with a through-vias between them and the grounding done by means of the readout electrodes (3D charge evacuation for high-rate $O(MHz/cm^2)$ applications) [160]. The $\mu$-PIC structure is an industrially produced PCB including anode strips on one side and orthogonal cathode strips on the other one. A regular pattern of uncoated regions is present along the cathode strips; an electric conductor buried in the thin PCB substrate transfers the anode voltage to a "dot" at the center of each of the uncoated cathode zones. Electron avalanches occur under the high-electric field around the point-like anodes; the electric field near cathode edges is weaker than in MSGCs, resulting in a lower discharge probability. A resistive coating of the cathode strips (e.g. using DLC layers) ensures tolerance to occasional discharges [161].

A big step in the direction of large-size applications has been obtained both with conceptual consolidation and industrial and cost-effective manufacturing of MPGDs by developing new fabrication techniques: resistive Micromegas (to suppress destructive sparks in hadron environments) [162] and single-mask and self-stretching GEM techniques (to enable production of large-size foils and significantly reduce detector assembly time) [163]. Scaling up of MPGDs to very large single unit detectors of $O(m^2)$, has facilitated their use in the High Luminosity LHC upgrades: Micromegas will instrument an area of $O(1000m^2)$ in the New Small Wheel of the ATLAS Muon endcaps, while GEMs be used in the CMS Muon system and for the ALICE TPC readout. Exploiting the Micromegas, GEM, and $\mu$-RWELL ability to measure both position and arrival time of the charge released in the drift gap, a novel $\mu$-TPC concept has been developed; it permits achieving nearly constant spatial resolution over a wide range of particle incident angles and allows 3D track reconstruction with a single MPGD layer [164]. Although normally used as planar detectors, GEM, Micromegas, and $\mu$-RWELL can be bent to form cylindrically curved ultra-light inner tracking systems, without support and cooling structures [165].

The consolidation of the better-established technologies has been accompanied with flourishing of novel ones, often specific to well-defined applications. Modern technologies have been also derived from Micromegas and GEM concepts, hybrid approaches combining different elements in a single device, gaseous with non-gaseous detectors, as is the case for optical read-out. MPGD hybridization, a strategy aiming to strengthen the detector performance, remains a valid asset for addressing future experimental challenges such as high granularity and picosecond-precision timing (e.g. PICOSEC-Micromegas concept [166]). A clear direction for future developments is that of resistive materials and related detector architectures. Their usage improves detector stability, making possible a higher gain in a single multiplication layer. Recent DLC resistive layers studies are the key ingredients for increasing the rate capability of MPGDs [167]. Future developments call for novel materials as well as for new fabrication techniques. Contributions to the detector concepts are required in several domains: resistive materials, solid-state photon and neutron converters, innovative nanotechnology components. Material studies can contribute to requirements related to low out-gassing, radiation hardness, radio-purity, converter robustness, and eco-friendly gases. The development of the next generation of MPGDs can largely profit from emerging technologies as those related to MicroElectroMechanical Systems (MEMS), sputtering, novel photoconverters, 3D printing of amplifying structures and cooling circuits, etc. Nowadays, many intensive MPGD R&D activities and their diversified applications are pursued within the world-wide CERN-RD51 collaboration [168].

### 35.6.5 Time-projection chambers

Revised August 2023 by C. Lippmann (GSI Darmstadt).

The Time Projection Chamber (TPC) concept was invented by David Nygren in the 1970's [169]. It consists of a cylindrical or square field cage that is filled with a gaseous (or liquid) detection medium. Charged particles produce tracks of ionization electrons

<figure><img src="image_211.png" /><figcaption>Figure 35.14: Schematic view of the ALICE TPC [170, 171]. The drift volume with 5 m diameter is divided into two halves, each providing 2.5 m drift length. The amplification stage has recently been upgraded from wire planes to GEMs.</figcaption></figure>

that drift in a uniform electric field towards a position-sensitive amplification stage which provides a 2D projection of the particle trajectories. The third coordinate can be calculated from the arrival times of the drifted electrons. The start for this drift time measurement is usually derived from an external detector, e.g. a fast interaction trigger detector.

This section focuses on the gas-filled TPCs that are often used in particle or nuclear physics experiments at accelerators on account of their low material budget. For neutrino physics (Sec. 35.11) or for detecting rare events (Sec. 36.4), on the contrary, usually high density and large active mass are required, and a liquid detection medium is favored.

The TPC enables full 3D measurements of charged particle tracks, which gives it a distinct advantage over other tracking detector designs which record information only in two-dimensional detector planes and have less overall segmentation. The track points recorded in a TPC are basically adjacent, which facilitates the track finding enormously. This advantage is often exploited for pattern recognition in events with large numbers of particles, e.g. heavy-ion collisions. Two examples of modern large-volume gaseous TPCs are shown in (Figure 35.14) and (Figure 35.15).

Identification of the charged particles crossing the TPC is possible by simultaneously measuring their momentum and specific energy deposit through ionisation ($dE/dx$). The momentum, as well as the charge sign, are calculated from a helix fit to the particle trajectory in the presence of a magnetic field (typically parallel to the drift field). For this application, precise spatial measurements in the plane transverse to the magnetic field are most important. The specific energy deposit is estimated from many charge measurements along the particle trajectory (e.g. one measurement per anode wire or per row of readout pads). As the charge collected per readout segment depends on the track angle and on the ambient conditions, the measured values are corrected for the effective length of the track segments and for variations of the gas temperature and pressure. The most probable value of the corrected signal amplitudes for a given track provides the best estimator for the specific energy deposit (see Sec. 34.2.3); it is usually approximated by the truncated mean, i.e. the average of the 50%–70% smallest values. The resulting particle identification performance is illustrated in (Figure 35.16), for the ALICE TPC.

The dependence of the achievable energy resolution on the number of measurements $N$, on the thickness of the sampling layers $t$, and on the gas pressure $P$ can be estimated using an empirical formula [173]:

$$ \sigma_{dE/dx} = 0.41 N^{-0.43} (tP)^{-0.32}. \qquad (35.17) $$

Typical values at nominal pressure are $\sigma_{dE/dx} = 4.5$ to 7.5%, with $t = 0.4$ to 1.5 cm and $N = 40$ up to more than 300. The
<figure><img src="image_212.png" /><figcaption>Figure 35.15: One of the 3 TPC modules for the near detector of the T2K experiment [172]. The size is 2 × 2 × 0.8 m³. Micromegas devices are used for gas amplification and readout.</figcaption></figure>

record, with an unprecedented energy resolution of 3%, is held by the PEP-4/9 TPC [174], due to the high gas pressure of 8.5 bar.

The greatest challenges for a large TPC are due to the length of the drift of up to a few meters. In particular, it can make the device sensitive to small distortions in the electric field. Such distortions can arise from a number of sources, e.g. imperfections in the field cage construction or the presence of ions in the drift volume. The electron drift in a TPC in the presence of a magnetic field is defined by Eq. (35.14). The $E \times B$ term of Eq. (35.14) vanishes for perfectly aligned electric and magnetic fields, which can however be difficult to achieve in practice. Furthermore, the electron drift depends on the $\omega\tau$ factor, which is defined by the gas mixture and the magnetic field strength. The electrons will tend to follow the magnetic field lines for $\omega\tau > 1$, or the electric field lines for $\omega\tau < 1$. The former mode of operation makes the TPC less sensitive to non-uniformities of the electric field, which is usually desirable.

The drift of the ionization electrons is superposed with a random diffusion motion which degrades their position information. The ultimate resolution of a single position measurement is limited to around

$$ \sigma_x = \frac{\sigma_D \sqrt{L}}{\sqrt{n}}, \qquad (35.18) $$

where $\sigma_D$ is the transverse diffusion coefficient for 1 cm drift, L is the drift length in cm and n is the effective number of electrons collected. Without a magnetic field, $\sigma_{D,B=0} \sqrt{L}$ is typically a few mm after a drift of L = 100 cm. However, in a strong magnetic field parallel to the drift field, a large value of $\omega\tau$ can significantly reduce diffusion:

$$ \frac{\sigma_{D,B>0}}{\sigma_{D,B=0}} = \frac{1}{\sqrt{1 + \omega^2 \tau^2}}. \qquad (35.19) $$

This factor can reach values of up to 10. In practice, the final resolution limit due to diffusion typically lies around $\sigma_x = 100 \ \mu\text{m}$.

The drift and diffusion of electrons depend strongly on the gas mixture. The optimal gas mixture varies according to the environment in which the TPC operates. In all cases, the oxygen concentration must be kept very low (few ten parts per million in a large TPC) in order to avoid electron loss through attachment.

Ideally, the drift velocity should depend only weakly on the electric field at the nominal operating condition. The classic Ar/CH₄ (90:10) mixture, known as P10, has a drift velocity maximum of

<figure><img src="image_213.png" /><figcaption>Figure 35.16: Energy deposit versus momentum measured in the ALICE TPC.</figcaption></figure>

5 cm/µs at an electric field of only 125 V/cm (Figure 35.5). In this regime, the electron arrival time is not affected by small variations in the ambient conditions. Moreover, low electric fields simplify the design and operation of the field cage. The mixture has a large transverse diffusion at $B=0$, but this can be reduced significantly in a strong magnetic field due to the relatively large value of $\omega\tau$.

For some applications organic gases like CH₄ are not desirable since they may cause aging. An alternative is to replace CH₄ with CO₂. An Ar/CO₂ (90:10) mixture has a low transverse diffusion at all magnetic field strengths, but does not provide a saturated drift velocity for the typical electric fields used in TPCs (up to a few 100 V/cm). As a consequence, it is quite sensitive to the ambient conditions. Freon admixtures like CF₄ can be an attractive option for a TPC as well, since the resulting gas mixtures provide high drift velocities at low electric fields. However, the use of CF₄ always needs to be thoroughly validated for compatibility with all materials of the detector and the gas system.

Historically, the amplification stages used in gaseous TPCs have been planes of anode wires operated in proportional mode. The performance is limited by effects related to the feature size (wire spacing) of a few mm. Since near the wires the electric and magnetic fields are not parallel, the incoming ionisation electrons are displaced in the direction of the wires ("wire $E \times B$ effect"), which degrades the resolution. The smaller feature sizes of Micro-Pattern Gas Detectors (MPGDs) like GEMs and Micromegas lead to many advantages as compared to wire planes (see Sec. 35.6.4). In particular, $E \times B$ effects in the amplification stage are much smaller. Moreover, the signal induction process in MPGDs leads to a very narrow pad response, allowing for a much finer segmentation, which improves the separation for two very close tracks. Combinations of MPGDs with silicon sensors have resulted in the highest granularity readout systems so far (see Sec. 35.6.4). These devices make it possible to count the number of ionization clusters along the length of a track, which can, in principle, improve the particle identification capability. However, the big challenge for such a system is the huge number of readout channels for a TPC of a typical size.

The accumulation of the positive ions created by the ionization from the particle tracks can lead to time-dependent distortions of the drift field. Due to their low drift velocity, ions from many events may coexist in the drift volume. To reduce the effect of such a build-up of space charge, Argon can be replaced by Neon as the main component of the gas mixture. Neon features a lower number of ionisation electrons per unit of track length (see 35.5) and a higher ion mobility (see 35.6).

Of greater concern are the ions produced in the gas amplification stage. In order to prevent them from entering the drift volume, large TPCs built until now have a gating grid. The gating
grid can be switched to transparent mode (usually in the presence of an interaction trigger) to allow the ionization electrons to pass into the amplification region. After all electrons have reached the amplification region, it is usually closed such that it is rendered opaque to electrons and ions. For triggered operation, a combination of a MPGD and a gating structure may be an attractive solution. However, a gating grid implies a principal rate limitation to a few kHz.

A next generation of TPCs (e.g. ALICE [171], sPHENIX [175]) has been developed for applications where a triggered operation would lead to unacceptable data loss. The employed readout schemes are based on MPGDs, as these can be optimised in order to drastically reduce the ion back-flow. Extensive work has been carried out during the 2010's to design such readout structures. In ALICE and sPHENIX ion back-flow values below 1% are achieved with a thorough adjustment of the various fields in a quadruple GEM system. Similar levels of ion back-flow can be reached with Micromegas detectors [176].

### 35.6.6 Transition radiation detectors (TRD's)

Revised July 2021 by P. Nevski (BNL) and A. Romaniouk (Innsbruck U.; MEPhI Moscow).

Transition radiation (TR) x-rays are produced when a highly relativistic particle ($\gamma \gtrsim 10^3$) crosses a refractive index interface, as discussed in Sec. 34.7. Since the TR yield is about a few % per boundary crossing, radiation from multiple surface crossings (e.g., a stack of foils) is used in practical detectors. The x-rays, ranging from a few keV to a few dozen keV or more, are emitted in a forward direction at small angles (within few mrad) to the particle trajectory. The TR intensity for a single boundary crossing always increases with $\gamma$, but, for multiple boundary crossings, interference leads to saturation above a Lorentz factor $\gamma_{sat} = 0.6 \omega_1 \sqrt{\ell_1 \ell_2}/c$ [177], where $\omega_1$ is the radiator material plasma frequency, $\ell_1$ is its thickness, and $\ell_2$ the spacing between material elements. The probability density function of TR is a fairly complex function of $\gamma$, radiator parameters, photon energy ($\omega$) and its emission angle ($\theta$). For well defined radiator parameters a measured two-dimensional distribution of photon energy vs its reconstructed emission angle is in very good agreement with the theory predictions [178].

Integration over the angle yields the TR spectrum, which typically features many maxima (see Sec. 34.7). Most of the TR energy is emitted near the last maximum of the spectra determined by radiator material parameters at $\omega_{max} = \ell_1\omega_1^2/2\pi c$. The effective TR photon emission starts at about $\gamma_{thr} = \ell_1\omega_1/c$. By varying radiator parameters one may optimize the particle separation for a given range of the $\gamma$-factor. The angular distribution of TR photons has a few maxima and extends up to $\theta_{max} = (1/\gamma^2 + \omega_1^2/\omega^2)^{1/2}$ [179]. For a single foil the largest part of the TR energy is emitted around the most probable angle $\theta = (1/\gamma^2 + \omega_2^2/\omega^2)^{1/2}$, where $\omega_2$ is the plasma frequency of the gas surrounding the radiator material elements. However, in case of multiple interfaces, interference effects may significantly change this angle and more realistic expression for the angle which corresponds to the last interference maximum of the energy spectra is $\theta \approx \sqrt{1.4\pi^2/\gamma_{sat}^2 - 1/\gamma^2}$ [178]. The higher is the gamma-factor, the larger is the angle of the first interference maximum. It reaches almost its asymptotic limit at $\gamma = \gamma_{sat}$. This effect is illustrated in Fig. 35.17 [178] which shows two-dimensional distribution of the TR photon energy versus the reconstructed production angle obtained in 20 GeV electron beam with the radiator containing a stack of foils of 15.5 $\mu$m thickness spaced by 210 $\mu$m (the left plot) using a Si-pixel detector. TR produced by 20 GeV electrons is emitted mostly around $\theta \sim 0.9$ mrad. All features of this distribution are well reproduced with MC simulations (the right plot).

The simplified numerical expressions can be used for practical estimation of the main TR production parameters [178]: $\theta \sim 1.2/\omega_1\sqrt{\ell_1\ell_2}$, $\gamma_{thr} \sim 3 \times 10^3 \omega_1\ell_1$, $\gamma_{sat} \sim 3 \times 10^3 \omega_1\sqrt{\ell_1\ell_2}$ and $\omega_{max} = 0.65 \ell_1\omega_1^2$, where $\theta$ in mrad, $\omega_1$ in eV, $\omega_{max}$ in keV and $\ell_1$ and $\ell_2$ in mm.

In the simplest concept, a detector module might consist of a

low-Z TR radiator followed by a high-Z active layer made of proportional counters filled with a Xe-rich gas mixture. The atomic number considerations follow from the dominant photoelectric absorption cross section per atom going roughly as $Z^n/\omega^3$, where $n$ varies between 4 and 5 over the region of interest.<fnref n="1" /> To minimize self-absorption, materials such as polypropylene, Mylar, carbon, and (rarely) lithium in the form of foils, fibers or foams are used as radiators. The TR signal in the active regions is in most cases superimposed upon the particle ionization losses, which are proportional to Z. In most of the detectors used in particle physics the radiator parameters are chosen to provide $\gamma_{sat} \approx 3000$. Those detectors normally work as threshold devices, ensuring the best electron/pion separation in the momentum range $1 \text{ GeV}/c \lesssim p \lesssim 150 \text{ GeV}/c$.

One can distinguish two design concepts—“thick” and “thin” detectors. In “thick” detectors the radiator, optimized for a fixed total radiation length at maximum TR yield and maximum TR absorption in the detector, consists of few hundred foils (for instance 300 20 $\mu$m thick polypropylene foils). Most of the TR photons are absorbed in the radiator itself. To maximise the number of TR photons reaching the detector, part of the radiator far from the active layers is often made of thicker foils, which shifts the x-ray spectrum to higher energies. The detector thickness, about 2-4 cm for Xe-filled gas chambers, is optimized to absorb most of the incoming x-ray spectrum. A classical detector is composed of several similar modules which respond nearly independently. Such detectors were used in the UA2, NA34 and other experiments [180], are being used in the ALICE experiment [181, 182] and are built for the CBM experiment [183]. In another TRD concept a fine granular radiator/detector structure exploits the soft part of the TR spectrum more efficiently. This can be achieved, for instance, by distributing small-diameter straw-tube detectors uniformly or in thin layers throughout the radiator material. This approach allows to realise a TRD as an integral part of a tracking detector providing many points of measurements on the particle track. Even with a relatively thin radiator stack, radiation below 4 keV is mostly lost in the radiators themselves. However, for photon energies above this value, the absorption is reduced and the radiation can be registered by several consecutive detector layers, thus creating a strong TR build-up effect. Descriptions of detectors using this approach in both accelerator and space experiments can be found in [181, 184–187]. For example, in the ATLAS TR tracker (TRT), charged particles on average cross about 35 straw tube layers embedded in the radiator material [184]. The effective thickness of the Xe gas per straw is about 2.5 mm and the average number of foils per straw is about 40 with an effective foil thickness of about 18 $\mu$m. In this approach straw walls also act as radiator and make some contribution to the TR spectrum.

Although the values mentioned above are typical for most of the plastic radiators used with Xe-based detectors, they vary significantly depending on the detector requirements. Careful simulations are usually needed to build a detector optimized for a particular application. For TRD simulations the codes are based on well understood TR emission formulas (see for instance [179] for regular radiators and [188] for irregular radiators). They are realised as the stand-alone simulation programs [178, 189, 190] or GEANT4 based ones [191] and give both a good agreement of the TR energy spectra and of the angular distributions with data [178, 192, 193].

The discrimination between electrons and pions can be based on the charge deposition measured in each detection module, on the number of clusters – energy deposits observed above an optimal threshold (usually it is 5–7 keV), or on more sophisticated methods such as analyzing the pulse shape as a function of time. The total energy measurement technique is more suitable for thick gas volumes, which absorb most of the TR radiation and where the ionization loss fluctuations are relatively small. The cluster-counting method works better for detectors with thin gas layers, where the fluctuations of the ionization losses are bigger. Cluster-counting replaces the Landau-Vavilov distribution of background ionization energy losses with the Poisson statistics of

<footnote n="1">¹Photon absorption coefficients for the elements (via a NIST link), and $dE/dx$|min and plasma energies for many materials are given in https://pdg.lbl.gov/current/AtomicNuclearProperties.</footnote>
<figure><img src="image_214.png" /><figcaption>**Figure 35.17:** Two dimensional distributions of photon energy versus reconstructed production angle obtained with the polypropylene radiator with 20 GeV/c electron beam. Data - the left plot, MC - the right plot. Z-axis is a number of photons per particle [178]</figcaption></figure>

δ-electrons, responsible for the distribution tails. The latter distribution is narrower than the Landau-Vavilov distribution. In practice, most of the experiments use a likelihood method, which exploits detailed knowledge of the detector response for different particles and gives the best separation. The more parameters are considered, the better achievable separation power. The neural network method is the most powerful tool. When it used by the ALICE TRD (ALICE point in Fig. 35.18) it lead to an increase of the rejection power by another factor of 2–3 with respect to the likelihood method [181].

The major factor in the performance of any TRD is its overall length. This is illustrated in Fig. 35.18, which shows, for a variety of detectors, the pion efficiency at a fixed electron efficiency of 90% as a function of the overall detector length. As TRD performance depends on particle energy, the experimental data in this figure covering a range of particle energies from 1 GeV to 40 GeV, are rescaled to an energy of 10 GeV when possible. Phenomenologically, the rejection power against pions increases as $5 \cdot 10^{L/38}$, where the range of validity is $L \approx 20–100$ cm. Apart from the beam energy variations, the observed scattering of the points in the plot reflects how effectively the detector space is used and how well the exact response to different particles is taken into account in the analysis. For instance, the ATLAS TRT was built as a compromise between TR and tracking requirements; that is why the test-beam prototype result (lower point) is better than the real End-Cap TRT performance at the LHC shown in Fig. 35.18 for different regions in the detector (in agreement with MC).

In most cases, recent TRDs combine particle identification with charged-track measurement in the same detector [181, 183, 186]. This is particularly important for collider experiments, where the available space for the inner detector is very limited. For a modest increase of the radiation length due to the radiator (~4% X0), a significant enhancement of the electron identification was obtained in the case of the ATLAS TRT. Here, the combination of the two detector functions provides a powerful tool for electron identification even at very high particle densities.

In addition to the enhancement of the electron identification during offline data analysis, TRD signatures are often used in the trigger algorithms at collider experiments. The ALICE experiment [182] is a good example for the use of the TRD in a First Level Trigger. In the ATLAS experiment, the TRT information is used in the High Level Trigger (HLT) algorithms. At increasing luminosities, the electron trigger output rate becomes so high, that a significant increase of the calorimeter energy threshold is required to keep it at an acceptable level. This may affect the trigger efficiency of very important physics channels (e.g. $W \to e\nu$ inclusive decay). Even a very soft TR cut at the HLT level, which preserves high electron efficiency (98%), allows to suppress a significant part of fake triggers and enhance the purity for physics events with electrons in a final state. The TRT also plays a crucial role in the studies where an electron suppression is required (e.g.

<figure><img src="image_215.png" /><figcaption>**Figure 35.18:** Pion efficiency measured (or predicted) for different TRDs as a function of the detector length for a fixed electron efficiency of 90%. The plot is based on the table given in [180]. Results from more recent detectors are added from [181, 185–187, 194].</figcaption></figure>

hadronic mode of τ-decays). TR information is a completely independent tool for electron identification and allows to study systematic uncertainties of other electron reconstruction methods.

Electron identification is not the only TRD application. Some TRDs for particle astrophysics are designed to directly measure the Lorentz factor of high-energy nuclei by using the quadratic dependence of the TR yield on nuclear charge; see, for instance, in [195]. The radiator configuration ($\ell_1, \ell_2$) is tuned to extend the TR yield rise up to $\gamma \approx 10^5$ using the more energetic part of the TR spectrum (up to 100 keV). High density radiator materials (such as Al) are the best for this purpose. Direct absorption of the TR-photons of these energies with thin detectors becomes problematic and TR detection methods based on Compton scattering have been proposed, see in [196].

The high granularity of the semiconductor pixel or microstrip detectors provides spatial separation of the TR photons and $dE/dx$ losses at relatively modest distances between radiator and detector. These detectors may be the basis for novel devices which combine precise tracking and PID properties [178, 190, 197]. Use of the TR production angle in addition to its energy can help to improve PID properties of the TRD. The presence of a magnetic field could enhance the separation between TR photons and $dE/dx$ losses [198]. New detector techniques for TRDs are also under consideration. GasPixel detectors allow to reconstruct a track segment with a space point accuracy of < 30 µm and ex-
ploit all details of the particle tracks to highlight individual TR clusters in the gas, see in [199]. Thin films of heavy scintillators might be a very attractive option for non-gas based TRD [200].

### 35.6.7 Resistive-plate chambers

Revised August 2023 by G. Aielli (Rome U. Tor Vergata).

The resistive-plate chamber (RPC) is a gaseous detector working at atmospheric pressure developed by R. Santonico and R. Cardarelli in the early 1980's [201]. A precursor of the RPC was the Pestov spark chamber [202] [203], which had a metallic plate cathode and a thick glass plate anode, designed to work at 12 bar to obtain an outstanding 0.1 ns time resolution. Although the original purpose of RPCs was to provide a competitive alternative to large scintillator counters, the RPC's potential for timing tracker systems was quickly recognized given its high detection efficiency (>95%), excellent temporal and spatial resolutions and ease of constructing large-format single frame detectors. The RPC, as sketched in Fig. 35.19, is a large planar capacitor with two parallel high bulk resistivity electrode plates (10⁹–10¹<fnref n="3" /> Ω·cm) separated by a set of insulating spacers. The spacers define a gap in the range from a few millimeters down to 0.1 mm with a precision of a few µm. The gap is filled with a suitable atmospheric-pressure gas mixture which serves as a target for ionizing radiation. The gas gap thickness practically determines the time resolution of the RPC. On the other hand, the limit for reaching full detection efficiency at atmospheric pressure is typically 1 mm (also influenced by the gas molecular weight). Since the primary ionization released in sub-millimeter gas gaps is limited, multiple gaps can be combined to effectively obtain a very high detection efficiency [204]. The electrodes are most commonly made of high pressure phenolic-melaminic laminate (HPL), commonly referred to as "bakelite", or soda-lime glass (glass from

<figure><img src="image_216.png" /><figcaption>**Figure 35.19:** Schematic cross section of a generic single gap RPC.</figcaption></figure>

now on), having a lower resistivity than borosilicate glass. An uniform electric field of several kV/mm is established on the gas gap, sufficient to promptly start an avalanche multiplication of the primary electrons. The electric field is typically applied through a moderately conductive (~10⁵ to 10⁸ Ω/□) graphite varnish, forming an ohmic contact with the external faces of the electrodes. Its conductivity is sufficiently low to be transparent to the fast avalanche signal transients, and high enough to suppress surface voltage gradients arising from the working current flowing in it. Due to the high electrode resistivity in RPCs, the time constant of the equivalent RC circuit ($τ = ρε_r$ being $ρ$ the electrode resistivity and $ε_r$ its dielectric constant) is much longer than the discharge processes duration. Therefore only the locally-stored electrostatic energy contributes to the discharge, preventing the formation of sparks and leaving the rest of the detector field unaffected. The gas-facing surface of HPL electrodes are commonly coated with a few µm-thick layer of polymerized linseed oil [205] with the function of smoothing the electrode surface, improving the electric field uniformity. Glass-based RPCs don't require such treatment. It also has the function of protecting the electrode from the being eventually etched by free radicals generated in the discharge e.g. in presence of fluorocarbons. In RPCs the gaseous target and the multiplication region coincide. In the early stage of the avalanche multiplication the uniform electric field exponentially amplifies each primary ionization cluster, as the avalanche progresses away from the location of the primary ionization. Since the ionization clusters generated by the incident MIP are randomly distributed along the ionizing particle track, for low gains

the observed RPC charge spectrum is broad and approximately exponentially distributed<fnref n="2" /> with the mode close to zero. Because of this, it is difficult to separate noise from signals using a discrimination threshold. This is not the case in gaseous detectors where ionization and amplification occur in separate regions.

For increasingly larger avalanches, the space-charge progressively saturates the avalanche growth from exponential to almost linear, producing a peaked charge spectrum, essential to efficiently separate the signal from the noise [207]. For large gains<fnref n="3" /> the avalanche, with increasing probability, onsets a transition to "streamer" [208], a plasma filament connecting the electrodes, depleting all the locally-available energy [209], and generating an almost fixed amplitude signal. This prevents any further evolution of the discharge. This streamer mode was the first ever used by RPCs, until the introduction of very electronegative gases and more sensitive front end electronics made it possible to detect the precursor avalanche independently on the streamer [210, 211] Any of this operating regimes can be used in RPC detectors, depending on the application.

As with other gaseous detectors, the gas mixture is optimized for each specific application. In general it needs to contain an UV photons quencher suppressing the photon-mediated feedback that can lead to self generated after-pulse discharges, and one or more electronegative components, to extend the avalanche growth, free from streamers, to as high as possible electric fields [212]. The addition of small fractions of electronegative molecules with a very high capture cross section for slow electrons, such as SF₆, was proven to inhibit the transition to streamer over a wide electric field range. Even though there is not yet an accepted and robust avalanche-to-streamer-transition model, this effect is commonly explained as a delay in the growth of the electron density of the avalanche front, which perturbates the electric field driving the transition to streamer. As a reference, the mixture for stable avalanche operation in ATLAS and CMS is C₂H₂F₄/i-C₄H₁₀/SF₆=94.5%/5%/0.3%.

The avalanche induces a fast electron signal on a set of metallic readout electrodes (e.g. pads or strips) commonly placed externally and insulated from the resistive electrodes. The signal is isotropically distributed with respect to the field direction and present with equal but opposite amplitude on both electrodes. Thanks to these features, performances of the readout electrodes on both RPC sides are equivalent. The induced charge density distribution can be ideally calculated for a simplified RPC model [213] [214] as: $σ(x) = A/cosh[(r)/δ]$ where A is a normalization constant, r is the distance from the center of the avalanche axis and $δ = (g+2d)/π$ depends on the gap and electrode width (g and d, respectively). Depending on the specific RPC layout and geometry, the interplay between conductive coating and pick-up electrodes typically broadens, by means of a diffusion-like process (see [214] [215]). This effect mostly preserves the information on the avalanche position, which can be obtained using the charge centroid method, with the drawback of increasing the signal space occupancy. Sensitivity to the high-frequency spectrum of electron avalanche signals over large RPC areas requires a correspondingly adequate Faraday cage and readout design. At the same time, to preserve the excellent timing features of the RPC signal, the front end electronics should have a short rise time (ideally ≪ than the signal rise time) and low noise, although these requirements could be in competition [216].

### 35.6.7.1 RPC types and applications

RPCs are generally classified in two categories depending on the gas gap structure: single gap RPCs (described above) and multiple gap RPCs [204] (typically referred as MRPCs). While they are both based on the same principle they have different construction techniques, performance and limitations, making them suitable for different applications. Due to its simplicity and robustness, the single gap RPC is ideal for covering very large surfaces. Typical detector systems can have sensitive surface areas

<footnote n="2">²An analytic treatment of the low gain avalanche process shows that the charge distribution is well described by the Γ function [206]</footnote>

<footnote n="3">³A multiplicity of the order of 10⁸ electrons is classically referred as Raether/Meek limit for on-setting a streamer</footnote>
up to ~$10^4$ m², with single module areas of a few m², and a space-time resolution down to ~0.4 ns × 100 µm [217] [218]. Representative examples are the muon systems of ATLAS [219] and CMS [220] or ground and underground based cosmic rays [221] and neutrino arrays [222]. It is interesting to note that CMS implemented a bi-gap structure, i.e. the pickup signal is sandwiched by 2 single gas gaps, both contributing to the signal induction, improving efficiency and time resolution with respect to the single gas gap. Relevant new trends for single gap RPC applications are represented by new Dark Matter search experiments such as CODEX-B [223] and ANUBIS [224], in both cases exploiting RPCs to enclose and instrument large detection volumes with a good space-time tracker. Single gap RPCs have also recently demonstrated good candidates for application in tracking calorimetry [225].

The MRPC [226], as sketched in Fig. 35.20, segments the gaseous target by means of a stack of floating glass electrodes separated by a monofilament (i.e. fishing line) sandwiched between two external electrodes providing the high-voltage bias. Since the current flowing in between the gas gaps must be in average equal, the difference of potential between each couple of adjacent floating electrodes will tend to be the same. An extensive description can be found in [227]. It has been observed that higher time resolution is inversely correlated to the gas gap size, so this configuration allows for smaller gas thicknesses while maintaining a sufficient total gas thickness. This tends to separate primary clusters avalanches in different gas gaps, treating them independently, and determines a shorter avalanche growth time, increasing time resolution by one order of magnitude with respect to the classic RPCs [228]. The mechanical fragility of sub-mm-gap structures makes this technique less suitable for very large detector areas. Moreover the only material nowadays practically suitable for building such structures is soda-lime glass with resistivity above $10^{12}$ Ω·cm, limiting the rate capability to about 500 Hz/cm² [229].

MRPCs have been largely used in Time Of Flight systems such as ALICE [230], HADES [231], FOPI [232] and BESSIII [233], and in applications such as timing PET [234]. In perspective MRPC will be used for upgraded and new nuclear physics experiments such as CBM@FAIR [235] and SoLID [236].

<figure><img src="image_217.png" /><figcaption>Figure 35.20: Schematic cross section of a generic multi gap RPC.</figcaption></figure>

### 35.6.7.2 Time and space resolution

Space-time uncertainties in RPCs are determined by the statistical fluctuations of the primary and secondary ionization, the avalanche multiplication rate, which is a function of the electric field, and on the Signal/Noise ratio of the front end electronics. The intrinsic signal latency is commonly in a few ns range (avalanche growth time to produce a detectable signal), making the RPC suitable for applications where a low latency is essential.

The gas gap size is a crucial feature for the RPC timing performance: producing the same total charge (for a detectable signal) in a smaller gas gap implies the necessity of increasing the first Townsend coefficient by increasing the electric field, reducing at the same time the total signal duration and the related time fluctuations; moreover the chance of having multiple clusters in the

same gas gap decreases with the gap size, suppressing the charge collection fluctuations [237], due to the unknown distance in between the clusters. This chance becomes necessarily higher along with the intrinsic efficiency of the single gas gap. Typical timing performances range from around 1 ns with a 2 mm gas gap, down to 20 ps for a stack of several 0.1 mm gaps [238].

The intrinsic position sensitivity of an RPC is in the range of tens of µm depending on the lateral spread of the avalanche induced charge distribution, influenced also by the gap size. In typical RPC applications the pick up electrodes pitch L (~1 cm) is much broader than the intrinsic resolution, and being readout via a discriminator, the spatial resolution is geometrically limited in the range of L/√12. A much better result is obtained by using a finer electrodes granularity and measuring the charge in each strip collecting the avalanche charge, so to reconstruct the charge centroid. It has been demonstrated, through charge centroid techniques, that the RPC avalanche space-time localization can be as good as ~50 ps × 40 µm [239] [240].

### 35.6.7.3 Rate capability and ageing

RPC rate capability is limited by the voltage drop on resistive electrodes, $\Delta V = V_a - V_{gas} = I \cdot R$ [241]. Here $V_a$ is the applied voltage, $V_{gas}$ is the effective voltage on the gas, $R = \rho \cdot d/S$ is the total electrode resistance, $\rho$ being the resistivity and d,S the sample thickness and surface respectively, and I is the working current. Assuming uniform irradiation we can express $I = \phi \cdot S \cdot \langle Q \rangle$ where $\phi$ is the particle fluence and $\langle Q \rangle$ is average charge per avalanche. So we obtain a state equation for the RPC rate capability:

$$ \Delta V / \phi = \rho \cdot d \cdot \langle Q \rangle $$

A large I not only limits the rate capability but also affects the long term performance of the detector since the working current, associated to discharges, depletes the conductive properties of HPL electrodes [242]. In presence of fluorocarbons and water, discharges generate hydrofluoric acid (HF) and other fluorinated compounds, which damage internal detector surfaces, especially if made of glass, known to be not resistant to HF [243]. The practical way to suppress HF formation in glass RPCs is preventing water vapor contamination. Conversely, HPL electrodes, coated with linseed oil, are relatively resistant to HF, but the presence of water can not be avoided since it mediates the HPL conduction. In this case the HF damage is mitigated by removing it with a forced flow of gas through the gas gap.

Operating in the streamer regime places low requirements on the front end electronics sensitivity, but generally limits the counting rate capability to ~100 Hz/cm². Higher-rate operation can be achieved by reducing gas gain in favor of electronic amplification, operating the detector in avalanche mode. Increasing concentrations of electronegative gases, such as $C_2H_2F_4$ and $SF_6$ [212], shifts the streamer transition to higher gains, thus the avalanche signal can access a higher dynamic range, which puts further stress on the performance request on the front end electronics. By further lowering the avalanche mode gas gain compatibly with the front end performance, efficient and stable performance at high rates (e.g. 10 kHz/cm²) has been achieved for large area single gap RPCs [216]. Two complementary strategies rely either on the natural redundancy and higher signal yield of multiple micro gap structures [244] or on electrodes made with lower resistivity materials [245]. Lowering the electrode resistivity in presence of high uniform field is increasingly difficult, since high resistivity limits the appearance of larger discharge events and increase of spurious counts, favoured by the effect of local electrode defects on the field gradient. In this case, to safely lower the electrode resistivity, a safety margin would be given by operating with a lower electric field, and a correspondingly lower average charge per count.

### 35.6.7.4 Alternative gas mixtures

The standard gas mixture mentioned above is based on Hydrofluorocarbon (HFC), specifically the R134A, extensively used in the refrigeration industry. R134A features matches very well the RPCs performance requirements. It has high density that results in high primary ionization. It is electronegative, which limits secondary discharge phenomena. It is not flammable, and it has a
limited degradation if exposed to UV photons due to the absence of saturated bonds. This last feature permits high rate operation, limiting the ageing effects due to the byproducts of the avalanche discharges. However, this gas has a Global Warming Potential (GWP) of 1450 thus it is not considered anymore a viable option for future industrial applications. Therefore, since a few years the RPC community is researching alternative gases [246,247] to replace R134A, focusing on the Hydro-Fluoro-Olefins, a category of gases recently proposed for industrial applications. HFOs exhibit important limitations with respect to HFCs, if used in high concentrations. In particular its much higher electronegativity implies an impractically high applied electric field for the existing RPC systems, and a much higher charge per count due to a large fraction of negative ions produced by electron capture, which do not contribute to the prompt signal. A further side effect is a larger production of fluoride ions by UV decomposition of the gas. To contrast the ageing acceleration drive represented by the phenomena stated above, the proposed strategy was to largely dilute HFO with a neutral gas, such as CO₂, compatibly with keeping an enough dense gaseous target, and whenever possible, operate at a lower gain by using very performing front end electronics. A representative example of the several variants tested [248] is CO₂/C₃H₂F₄/i-C₄H₁₀/SF₆=59%/35%/5%/1%. This mixture with a large fraction of CO₂ is suitable for thicker (2mm) gas gap. The presence of CO₂ in 1 mm gas gaps lower the amount of primary electrons thus practically limiting its fraction to no more than 30%. Thus for a safe operation a reduction of the charge per count by an order of magnitude is necessary to compensate the stronger ageing phenomena. It has to be noted that the research in this field is recent and very intensive [249, 250], so relevant updates are expected in future.

### 35.6.7.5 A new detector: the Resistive Cylindrical Counter

<figure><img src="image_218.png" /><figcaption>Figure 35.21: Schematic drawing of an RCC.</figcaption></figure>

The RCC, illustrated in fig. 35.20, has been recently proposed as an evolution of the RPC [251] and is essentially an RPC warped to a cylindrical shape. The idea is to combine the advantages of parallel plate geometry and high pressure drift tubes in a single detector. The electric field $E(r)$, which is uniform in RPCs, here depends instead on the distance from the axis $r$, according to $E(r) = -\frac{V}{r\ln(R_1/R_2)}$. By choosing appropriate values for $R_1, R_2$, $V$ and its polarization (the innermost cylinder is the cathode), it is possible to virtually segment the cylindrical gap in an innermost sensitive layer, where the field is sufficiently high to start the avalanche multiplication, and an outermost layer where the drift happens, increasing the induced signal with lower or no multiplication at all. This effect is called geometrical quenching and limits the avalanche growth without the necessity of electronegative gases. Moreover a geometrically quenched avalanche would have a much better prompt to total charge ratio, lowering the total operative current, hence increasing the rate capability. The cylindrical structure has a further major advantage with respect to the planar one, it can be easily pressurized overcoming the RPC limitation of working at atmospheric pressure only. Pressurization on one side increases the gaseous target density, thus increasing the efficiency of narrow gaps, on the other, it could largely improve RPC time resolution since the Townsend coef-

ficient $\alpha = A p \exp(-Bp/E)$ (where $p$ is the pressure, $E$ the electric field and A,B are constants), as we learn from the RPC precursor, the Pestov spark chamber [203]. The performance of the RCC concept in terms of time resolution and counting rates are yet to be demonstrated. On the other side, being insensitive to the environmental pressure, potentially extends its range to space and under water applications.

## 35.7 LAr Time Projection Chamber

Written in October 2021 by F. Pietropaolo (CERN; INFN, Padova) and S. Pordes (FNAL). Revised in August 2023 by A. Fava (FNAL) and F. Pietropaolo (CERN; INFN, Padova).

### 35.7.1 Introduction

Liquid argon is an attractive material for particle detection. Some properties of argon are given in table 35.8; for many more see [252]. Energy deposition in the argon produces scintillation light

<table><caption>Table 35.8: Some physical properties of liquid argon from [253].</caption><thead><tr><td>Property</td><td>Unit</td><td>Value</td></tr></thead><tbody><tr><td>Boiling Point (BP) at 1013 hPa</td><td>K</td><td>87.3</td></tr><tr><td>Density (ρ) at 1013 hPa</td><td>kg m<sup>-3</sup></td><td>1395</td></tr><tr><td>d(BP)/dP</td><td>K hPa<sup>-1</sup></td><td>9 × 10<sup>-3</sup></td></tr><tr><td>dρ/dT</td><td>kg m<sup>-3</sup> K<sup>-1</sup></td><td>-6.2</td></tr><tr><td>Latent Heat of Evaporation</td><td>kJ kg<sup>-1</sup></td><td>161</td></tr><tr><td>Freezing Point (1013 hPa)</td><td>K</td><td>83.8</td></tr></tbody></table>

and ionization electrons; in the presence of a moderate electric field, a significant fraction of the electrons escape recombination, making them available for detection as a charge signal. Typical values for a minimum ionizing particle are ~ 40,000 photons/MeV at zero field (lower at finite fields) and ~ 30,000 electrons/MeV at a field of 500 V/cm. That the liquid has a relative density of 1.4, that the free electrons can be drifted many meters with minimal dispersion and that it is abundant in the atmosphere and commercially available as a by-product in the distillation of air to produce nitrogen and oxygen, makes it particularly attractive for use in massive time-projection chambers (TPC) to study rare processes, as realized in [254] and [255]. Since that time, the liquid argon TPC (LAr TPC) has been developed into a detector that combines mm³ resolution with particle identification, calorimetry, and 100% live time. Detectors with masses up to 600 tons have been built and operated and detectors of 10's of kilotons are being planned.

The operation of a liquid argon time projection chamber requires

1. a cryostat and cryogenic system to maintain ultra-pure liquid argon clean and stable,

2. an electric field that permeates the liquid argon volume and allows ionization electrons to escape recombination, and drifts them to the charge sensors,

3. an array of charge sensors and associated electronics to amplify and digitize the charge signals,

4. sensors to detect the scintillation light and associated electronics,

5. a data-acquisition system to read out and record the data,

6. software to reconstruct and interpret the data.

Surveys of previous, present and proposed detectors are described in the literature [271] [272] and in detailed descriptions of detectors which have operated in experiments [273–279]. This article provides a description of the challenges in achieving items 1 to 4 with some of the solutions presently adopted. Topics 5 and 6, crucial to the successful exploitation of the LAr TPC technology and subject of intense activity, are also introduced [280–282]. References are also given for a number of ancillary devices - cameras that can operate in the liquid argon [279], monitors to provide a rapid measurement of the purity of the argon [283,284], ionization lasers to measure distortions of the drift field due to space charge
<table><caption>**Table 35.9:** Some Detector Relevant Properties of liquid argon.</caption><thead><tr><th>Property</th><th>Unit</th><th>Value</th></tr></thead><tbody><tr><td>Stopping Power (m.i.p.)</td><td>MeV g<sup>-1</sup> cm<sup>2</sup></td><td>1.51</td></tr><tr><td>Radiation Length</td><td>g cm<sup>-2</sup></td><td>19.6</td></tr><tr><td>Nuclear Interaction / Collision Length</td><td>g cm<sup>-2</sup></td><td>120 / 76</td></tr><tr><td>W<sub>el</sub>, Energy to form one electron-ion pair</td><td>eV</td><td>23.6 (±0.3) [256, 257]</td></tr><tr><td>Ion mobility</td><td>cm<sup>2</sup> V<sup>-1</sup> s<sup>-1</sup></td><td>1.6 × 10<sup>-3</sup> [258]</td></tr><tr><td>Temperature dependence of drift velocity</td><td>% K<sup>-1</sup></td><td>-1.7 [259]</td></tr><tr><td>Longitudinal diffusion coefficient, D<sub>L</sub></td><td>mm<sup>2</sup> ms<sup>-1</sup></td><td>0.4 (see text)</td></tr><tr><td>W<sub>ph</sub>, Energy to produce one scint. photon</td><td>eV</td><td>25 [260, 261]</td></tr><tr><td>Scintillation photon wavelength (vacuum)</td><td>nm</td><td>128 ±8 (FWHM) [262]</td></tr><tr><td>Scintillation light inverse velocity</td><td>ns m<sup>-1</sup></td><td>7.46 (±0.08) [263]</td></tr><tr><td>Rayleigh scattering length (predicted)</td><td>m</td><td>0.9 (±0.2) [263–265]</td></tr><tr><td>Scintillation Decay times fast/slow</td><td>ns</td><td>6 (±1)/1500 (±100) [266–268]</td></tr><tr><td>Dielectric strength</td><td>kV cm<sup>-1</sup></td><td>>40 [269, 270]</td></tr></tbody></table>

or electrical problems [285] - that have been developed to improve performance. A list of experiments with their masses is also given in 35.14.

### 35.7.2 A Mass of ultra-pure Liquid Argon

Argon is commercially available in large quantities as a by-product in the distillation of air to produce liquid nitrogen and oxygen. Critical to any LAr TPC are the cryostat and the cryogenic and purification system to maintain the argon liquid, ultra-clean and stable in temperature and pressure. Evacuable double-walled vacuum cryostats are practical for detectors with a mass of O(100) t. Based on the demonstration that ultra-clean argon can be achieved without initial evacuation [284], current and proposed larger detectors are hosted in foam-insulated non-evacuable cryostats based on a technology used in liquefied natural gas transport [279]. A convenient feature of these cryostats is that their components (inner walls, insulation, outer structures) are modular and of a size suited to assembly in underground environment. In addition, passive insulation is intrinsically safer than vacuum insulation because the heat input cannot rapidly increase as in the case of vacuum degradation.

The absence of electronegative contaminants, mainly environmental oxygen and water, from the liquid argon is crucial to ensure the ionization electrons drift from their point of production to the charge sensors without being captured (the drift motion of the produced negative ions is too slow to be detectable). The 'electron lifetime', $\tau$, is the parameter describing the purity level of argon. To set a scale, the electron capture time in liquid argon with a concentration of oxygen of 0.1 ppb (part per billion by volume - all concentrations here are by volume) is ~ 3 ms [286, 287], largely independent of electric field in our range of interest. For detectors with electron drift times in the milliseconds, the oxygen level must be well below 0.1 ppb to avoid losing most of the signal. In order to achieve this goal, first the air is removed from the cryostat volume mostly by controlled purging with argon [288], allowing to reach ppm purity levels; a purification system is then required during filling, to purify the commercial argon delivered from its typical ppm oxygen and water levels. Molecular sieve and activated copper on alumina [289] are commonly used to remove water and oxygen, respectively. This purification is performed in the liquid phase and the discovery that purification with standard materials is effective at cryogenic temperatures [290] allowed for an enormous gain in throughput compared to purification in the gas phase. The purification system delivers essentially pure argon - which then mixes with contaminants from outgassing or residual leaks. To avoid the build-up of contaminants, both the boil-off gas and the liquid are continuously recirculated through the purification system. Schematics of experiment cryogenics systems are shown in [274, 276, 279]. While reconstructed tracks eventually determine the argon quality, so-called 'purity monitors', double-gridded ionization chambers, are often installed to give rapid feedback on the purity of the liquid [279].

Another potential contaminant is environmental nitrogen. This does not affect the free electron lifetime at levels up to many ppm but it does affect light production [267] and transmission [291] at

the few ppm level.

### 35.7.3 Charge and Light Signals

Figure 35.22 (left) shows how the electron and scintillation yields for a minimum ionizing particle (m.i.p.) change with electric field. The free electron yield from the passage of a charged particle can be calculated from 'W<sub>el</sub>' = 23.6 eV [256], the energy deposit that generates one ion-electron pair, the $dE/dx$ of the particle, and 'R' the (unfortunately labeled) fraction of electrons that escape recombination - see figure 35.22 (left). Measurements of electron yield have been made at various electric fields and at different ionization densities [292–296] and show good consistency. Of the models proposed to predict recombination [297, 298], none is fully successful; the so-called 'box model' [299] which considers the situation of mobile electrons and stationary ions makes more realistic assumptions than other models and it is commonly used [300]. The data from [295] which are some of the most comprehensive are described by the form $R = \frac{0.8}{(1+0.049(dE/dx)/\epsilon)}$ where $dE/dx$ is in MeV/cm and $\epsilon$ in kV/cm. At a drift field of 500 V/cm, The recombination factor R for a minimum ionizing particle is 70%. A comprehensive summary and analysis of charge yield is given in [301].

The movement of the free electron charge towards the charge sensors is characterized by the drift velocity, the charge loss due to impurities, and the diffusion. The drift velocity depends on the strength of the electric field and slightly on the argon temperature (see table 35.9); a measurement of drift velocity vs electric field from [302] with a fit from [259] is shown in 35.22 (right). At an electric field of 500 V/cm, the drift velocity is 1.55 m/ms at 89 K. The charge loss depends on the purity of the liquid. For a drift of duration, $t$, the fraction of charge that survives to the sense electrodes is $e^{-t/\tau}$ where $\tau$ is the electron lifetime. Values of $\tau$ exceeding tens of ms have been achieved [303–305]. Diffusion broadens the charge distribution as it travels to the sensor. The diffusion coefficient, D, defines the contribution to the spatial distribution of the charge at the sensor from diffusion after a drift of time, $t$, via $\sigma_D^2 = 2Dt$. Several measurements of the longitudinal diffusion component, $D_L$, have been made with a typical value around 0.4 mm$^2$/ms [294, 306–308]. For a 3 ms drift, this gives a contribution of $(0.4 \cdot 6)^{1/2}$ mm, ~ 1.5 mm, to the spread of the charge.

The scintillation light comes from the decay of excited argon dimers, $Ar_2^*$, (excimers) produced through direct excitation and through recombination of ionized argon ions and electrons [309]. The contribution of the latter process is reduced in the presence of an electric field as shown in figure 35.22, (left). The excimer is produced either in a singlet ('allowed' decay) or in a triplet spin state ('forbidden' (spin-flip) decay), with lifetimes of 6 ns and 1.5 µs respectively. The states are almost degenerate and photons are emitted, somewhat inconveniently [310], in the VUV with a spectrum peaked at 128 nm with a ±8 nm (FWHM) spread [262]. The relative populations of the two states depends on the ionization density; typically 1:3 (singlet:triplet) for minimum ionizing and 3:1 for highly ionizing nuclear fragments [266]. The long life-
time of the triplet state makes it sensitive to quenching impurities such as nitrogen or oxygen to which the excitation energy of the dimer can be transferred without the subsequent emission of a visible photon [267,311].

The propagation of the scintillation is affected by two pro-
cesses: absorption and Rayleigh scattering. While the large Stokes
shift [312] makes pure LAr transparent to its own scintillation
light, methane at the few ppb level [313] and nitrogen at the
few ppm [291] level lead to light absorption. Rayleigh scattering
increases the effective travel distance of photons between their
production point and their detection and for detectors where the
distance between origin and detection covers a range of many
meters, the short Rayleigh scattering length for argon scintilla-
tion has a serious effect on the uniformity of detection. In this
situation, the long lifetime of the triplet state can be exploited
by the use of dopants to which the argon dimers can transfer
their excitation energy with subsequent photon emission. Xenon,
where almost complete transfer of the long-lived state energy is
achieved at a concentration of 10's of ppm (mass), is a leading
candidate. [314,315].

**35.7.4 LAr TPC topologies**

Currently operating LAr-TPC detectors come in a range of sizes but the basic form of a cathode and field cage generating a field which drives the ionization electrons to planes of charge sensors at ground potential is universal. A standard criterion is to make the TPC drift as long as considered possible to maximize the detector mass for a given channel count; this can result in a single drift volume; two drift volumes with a common cathode, or multiple drift volumes with multiple common cathodes. An exception is the DUNE near detector TPC; it is segmented into many small TPCs to help resolve the large interaction rate [316].

The drift field is produced by a planar cathode at -HV, a graded field-cage surrounding the active volume, and the sensing electrodes at a potential near ground which form the anode. The field cage is designed to produce a uniform electric field throughout the drift region although for detectors at surface, the slow-moving positive ions generated by the flux of cosmic rays distort the field, particularly for TPCs with long drift [301, 305, 317–319]. Particular challenges in the drift field system are the feed-through [274, 320] that brings the voltage from the HV supply outside the cryostat to the cathode (the cathode can sit at negative voltages up to 300 kV), avoiding damage to the electronics from a potential cathode discharge [279], and ensuring the integrity of the field-cage resistor chain [321]. Avoiding discharge and current draw in a medium chosen because it allows electron flow is possibly the hardest challenge in the technology.

The schematics in figure 35.23 shows the sensor arrangement using vertical planes of wires as sense electrodes and a horizontal electric field.

The sense planes are perpendic-
ular to the drift direction and can be arranged in a stack with
the wires in each plane oriented at a different angle. While the
schematic shows three planes, in principle only two are needed;
however three views are useful in the 3D reconstruction proce-
dures to remove ambiguities in the hit associations and in case
of dead or noisy channels. The wire-pitch, *p*, is a few mm and
the plane spacing is similar. As indicated in figure 35.23, the
planes are biased such that all field lines from the drift region
pass through the intermediate planes and terminate on the final
plane as shown in 35.23. (The condition for transparency across
one plane is derived in [322].) The drift electrons follow the field
lines, inducing bi-polar current pulses on the first two planes, and
terminate on the last one, the collection plane, producing a unipo-
lar signal [323].

The raw signal rise and fall times are a few µs as determined
by the electron drift velocity and the plane spacing, and any ge-
ometric effects from the track angles. The signals from each wire
are recorded as wave-forms spanning the maximum drift time at
typically 2 or 2.5 MHz sampling rate. The intersection of wires
on different planes which record signals at the same time, and the
drift time converted to a distance knowing the drift velocity give
the position of the charge source.

The design of large (> kiloton) detectors faces an intrinsic elec-
trical challenge in that long (> few m) cables from the sense elec-

trodes to the first-stage amplifier will introduce an unacceptable
amount of noise through their capacitance, and attempts to avoid
such cables leads to impractical constraints on the charge sensor
geometry; both of these are emphasized in [323]. To address this
problem, CMOS based ASIC amplifiers that operate in the cold
and can be placed next to the charge sensor (wire or strip or pixel)
have been developed, their design rules and robustness validated,
and successfully deployed [324,325]. The subsequent problem that
individual feed-throughs for each signal in a detector with hun-
dreds of thousands of channels complicate the cryostat structure
and raise the specter of leaks has been resolved by the develop-
ment of flash-ADC and signal multiplexers [326] that also operate
in the liquid. These implementations have resulted in equiva-
lent noise charge levels of a few hundred electrons [305, 327] to
be compared with a charge yield for a m.i.p of 30000 e/MeV or,
equivalently, 60000 e/cm. With such low noise, energy deposi-
tions well below 1 MeV on wires/pixels with 0.5 cm pitch or less
are quite accessible.

Large LAr detectors usually contain a system to detect the pri-
mary scintillation light. These provide an event time for drift
time measurement [328], a trigger [329,330], calorimetry that can
be independent of and complementary to the charge [305], and
event position information [280]. Given the VUV nature of the
scintillation, a wavelength shifter is typically used to move the
light into the visible [310]. Photo-multiplier tubes that operate
in liquid argon were developed under the ICARUS program [331],
while some recent systems are based on Silicon Photo-Multipliers.
This latter approach separates the light collection from the light-
to-electrical signal transducer, and many designs for the first task
are being pursued [279,332,333].

**35.7.5 Data Acquisition and event reconstruction**

For the operation of large mass LAr-TPCs, the recording and
storage of large volumes of data from the digitised charge wave-
forms and scintillation light channels is a critical issue. For in-
stance, in the DUNE experiment, the throughput will amount
to 1.5 TB/s per detector module (10 kt fiducial mass). To cope
with, data reduction strategies are typically applied [334], [335]:
(1) channel by channel zero suppression applied to the digitised
wave forms, (2) fast signals from photon detectors or from external
sources (for instance a neutrino beam), to trigger the readout of
the TPC over a limited, predefined time window. The trigger rate
is tuned to match the throughput capabilities of the Data AcQui-
sition (DAQ). Recent advances in communication and computing
technologies have reshaped the approach to DAQ for LAr-TPCs.
It is now possible to readout the complete digitised data and pro-
cess them online [336], [337], allowing to identify space-time Re-
gions of Interest (RoI) where charge or light activity is detected.
For the DUNE experiment, the data reduction could be in the
order of 10⁵. With this architecture, charge and photon detec-
tors become truly complementary and their information can be
combined online for high efficiency data filtering even for energy
depositions at a few MeV scale.

The goals of LArTPC event reconstruction are to provide the
building blocks necessary to perform physics analyses: reconstruct
the event topology, particle identification and calorimetry. Gen-
erally, this proceeds in subsequent stages. (1) Signal Processing:
the waveforms providing a measure of the charge deposited in
the TPC as a function of time are conditioned to mitigate de-
tector issues, suppress noise, deconvolve the detector/electronic
response; this allows to produce hit objects - measurements of
the drift time and charge deposited by tracks in the LAr active
volume on any readout channel [338] [339] [340]. (2) Wire read-
out LArTPCs produce 2D images in drift time and coordinate
transverse to the wire direction with, generally, 3 planes allow-
ing for stereo imaging for 3D reconstruction. Pattern Recogni-
tion (PR) approaches are distinguished between those acting of
the 2D images with matching of objects to build the 3D picture
and those working in the 3D space directly. The common goal
is to find and reconstruct tracks and showers, their common ver-
tices and identify the event topology. An example of 2D to 3D
PR is the Pandora package [341]. An example of a pure 3D ap-
proach is the WireCell package [342]. Recent efforts in PR aim
at employing sophisticated machine learning (ML) techniques. In