35. Particle Detectors at Accelerators

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35. Particle Detectors at Accelerators
Revised 2024. See the various sections for authors.

35.1
35.2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Photon detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.2.1 Vacuum photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.2.2 Gaseous photon detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.2.3 Solid-state photon detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.2.4 Superconducting photon detectors . . . . . . . . . . . . . . . . . . . . . . . .
35.3 Organic scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.3.1 Scintillation mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.3.2 Plastic scintillator practicalities . . . . . . . . . . . . . . . . . . . . . . . . . .
35.3.3 Organic glass scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.3.4 Liquid scintillator practicalities . . . . . . . . . . . . . . . . . . . . . . . . . .
35.4 Inorganic scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.5 Cherenkov detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.6 Gaseous detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.6.1 Energy loss and charge transport in gases . . . . . . . . . . . . . . . . . . . .
35.6.2 Multi-Wire Proportional and Drift Chambers . . . . . . . . . . . . . . . . . .
35.6.3 High Rate Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.6.4 Micro-Pattern Gas Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.6.5 Time-projection chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.6.6 Transition radiation detectors (TRD’s) . . . . . . . . . . . . . . . . . . . . . .
35.6.7 Resistive-plate chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.7 LAr Time Projection Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.7.2 A Mass of ultra-pure Liquid Argon . . . . . . . . . . . . . . . . . . . . . . . .
35.7.3 Charge and Light Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.7.4 LAr TPC topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.7.5 Data Acquisition and event reconstruction . . . . . . . . . . . . . . . . . . . .
35.7.6 Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.8 Semiconductor detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.8.1 Signal generation in semiconductors . . . . . . . . . . . . . . . . . . . . . . .
35.8.2 Junction detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.8.3 Detectors with structured electrodes . . . . . . . . . . . . . . . . . . . . . . .
35.8.4 Precise timing with silicon detectors . . . . . . . . . . . . . . . . . . . . . . .
35.8.5 Radiation damage in silicon detectors . . . . . . . . . . . . . . . . . . . . . .
35.9 Low-noise detector readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.9.1 Principal noise origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.9.2 Equivalent noise analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.9.3 Timing measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.9.4 Digital signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.9.5 What to use when? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.10 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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35.10.2 Electromagnetic calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
35.10.3 Hadronic calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
35.10.4 Free electron drift velocities in liquid ionization chambers . . . . . . . . . . . 95
35.11 Accelerator-based neutrino detectors . . . . . . . . . . . . . . . . . . . . . . . . . . 96
35.11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
35.11.2 Signals and Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
35.11.3 Instances of Neutrino Detector Technology . . . . . . . . . . . . . . . . . . . 98
35.11.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
35.12 Superconducting magnets for collider detectors . . . . . . . . . . . . . . . . . . . . 104
35.12.1 Solenoid Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
35.12.2 Properties of collider detector magnets . . . . . . . . . . . . . . . . . . . . . 106
35.12.3 Toroidal magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
35.13 Measurement of particle momenta in a uniform magnetic field . . . . . . . . . . . . 109

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 suchapplications 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 theirunderlying physics can be found in books by Kolanoski & Wermes [1], Ferbel [2], Kleinknecht [3],Knoll [4], Green [5], Leroy & Rancoita [6], and Grupen [7].
Table 35.1: Typical resolutions and deadtimes of common charged particle detectors. Revised September 2023.

Detector Type
Resistive plate chamber
Liquid argon TPC
Scintillation tracker
Bubble chamber
Wire chambers(proportional and drift chambers)
Micro-pattern gas detector
Silicon strips/pixels

Intrinsinc Spatial
Time
Dead
Resolution (rms) Resolution
Time
50 µm
50–1000 ps∗ 10 ns†
0.5–1 mm‡0.01-1 µs§—¶
k∼100 µm
100 ps/n
10 ns
10–150 µm
1 ms
50 ms∗∗
50–100 µm

5–10 ns†† 20–200 ns‡‡

30–40 µm

5–10 ns†† 20–200 ns‡‡

. 10 µm§§

few ns¶¶ ‡‡ . 50 ns‡‡∗

LHC: ∼2 mm gap, ∼1 ns. HL-LHC: ∼1 mm gap, ∼350 ps. Timing RPC: ∼50 ps
Limited by amplifier and discriminator bandwidth, usually around 100 MHz‡
Detector geometry dependent§
Using the scintillation signal¶
No deadtime for mediumkn = index of refraction.
∗∗
Multiple pulsing time.
††
For fast particles‡‡
Depending/limited by the amplifying electronics [8]§§Depending on electrode pitch, best values around 2–4 µm have been achieved¶¶
Resolutions < 100 ps are reached in dedicated pixel developments†

In Table 35.1 are given typical resolutions and deadtimes of common charged particle detectors.
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35. Particle Detectors at Accelerators

The quoted numbers are usually based on typical devices, and should be regarded only as roughapproximations 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.

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 ornear the visible range, 100 nm . λ . 1000 nm, or 1 eV . E . 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:
1. quantum efficiency (QE or Q ): the average number of primary photoelectrons generated per
incident photon (0 ≤ Q ≤ 1; in silicon more than one e-h pair per incident photon can begenerated for λ . 165 nm),
2. collection efficiency (CE or C ): the overall acceptance factor other than the generation ofphotoelectrons (0 ≤ C ≤ 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 Ne )and statistical fluctuations in the amplification process compound the Poisson distribution ofnγ photons from a given source:vuσ(I) u
=t

hIi

fN
+
nγ Q CNe
Gnγ Q C!2,(35.1)

where fN , 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.
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35. Particle Detectors at Accelerators

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Table 35.2: Representative characteristics of some photodetectors commonly used in particle physics.
Type
PMT †
MCP-PMT†
HPD†
HAPD†
GPD†
APD
SiPM
∗
†

λ
Q C
Gain Risetime Single photon
(nm)
(ns)
time resol. (ps)
115–1700 0.15–0.25 105 –107 0.7–10∼200
115–650 0.01–0.10 103 –107 0.15–0.3∼20
115–850
0.1–0.3 103 –104
O(1)
∼1000
115–850
0.1–0.3 104 –105
O(1)∼30
115–500 0.15–0.3 103 –106 O(0.1)∼100
300–1700∼0.7
10–108O(1)-‡
125–1000 0.15–0.4 105 –106
∼1
∼50

Area 1-p.e noise ∗(mm2 ) (Hz/mm2 )10–10510−2 –102
4
1–10
1–10
10–105
10–100
10–105
∼1
O(10)
∼1
1–103
O(107 ) §1–36
104 –105

HV(V)
500–3000
500–3500∼2 × 104∼1 × 104
300–2000
400–1400
30–60

Normalized to photocathode/sensor area; room temperature operation assumed.
These devices often come in multi-anode configurations. In such cases, the area is to be considered on a “per readout-channel" basis.

‡

No single photon detection possible.
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.
§

The QE is a strong function of the photon wavelength (λ), and is usually quoted at maximum,
together with a range of λ where the QE is comparable to its maximum. Spatial uniformity andlinearity 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 chemicalcomposition, 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 rangeof 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 bya vast majority of all particle physics experiments to date [9]. Both “transmission-" and “reflectiontype" PMTs are widely used. In the former, the photocathode material is deposited on the insideof a transparent window through which the photons enter, while in the latter, the photocathodematerial 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 andliberates an electron (the photoelectric effect), the latter is accelerated and guided by electric fields
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535. Particle Detectors at Accelerators

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 asufficient 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 ≈ 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 105 –107 ; time resolution is O(1ns) but
can be as good as ≈ 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 (Al2 O3 ) 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 inTable-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 micromachining 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 suchas 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 thesurrounding 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 (≥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 ≈ 10) placed close to the photocathode, and a mesh anode plane between the two, tohelp it cope with the strong magnetic field, which is not too unfavorably oriented with respect tothe 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 ∼1mm thick glass plates with densely packed O(10 µm)-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 ratioof 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 thesaturation 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 theatomic layer deposition (ALD) coatings on the MCP surfaces to increase the lifetime (>20 C/cm2 of
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635. Particle Detectors at Acceleratorscharge accumulated on the anode) and gain. The Large Area Picosecond 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 thephotocathode 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 ≈ eV/w, where e is theelectronic 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 Q 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 superiorrate 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 35.3: Properties of photocathode and window materials commonlyused in vacuum photodetectors. [10]λWindow
Peak Q(nm)
material(λ/nm)
115–200
MgF2
0.13 (130)
115–320
MgF2
0.17 (200)
300–650
Borosilicate
0.27 (390)160-650 Synthetic Silica
0.27 (390)"Ultra Bi-alkali" 300–650
Borosilicate
0.43 (350)
160-650 Synthetic Silica
0.43 (350)Multi-alkali
300–850
Borosilicate
0.20 (375)
160-850 Synthetic Silica
0.25 (380)
GaAsP(Cs)280-720
Borosilicate
0.40 (480-530)
Photocathodematerial
CsI
CsTe
Bi-alkali

35.2.2 Gaseous photon detectors
In a gaseous photon detector (GPD) a photoelectron in a suitable gas mixture initiates anavalanche 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 ingaseous 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.
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735. Particle Detectors at Accelerators

The devices can be divided into two types depending on the photosensitive material. One typeuses 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 tri-ethyl-amine (TEA),
which have smaller work functions (5.3 eV for TMAE and 7.5 eV for TEA), are suited for XUVphoton 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 m2 )), 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 O2 or H2 O 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 matchingor exceeding most performance criteria.
Silicon photodiodes (PD) are widely used in high-energy physics as particle detectors and ina 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 thetemperature) can create e-h pairs (the photoconductive effect), which are collected on the p and nsides, 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 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 inroom-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 Q C ≈ 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 108 in Geiger mode of operation. Stability
and close monitoring of the operating temperature are important for linear-mode operation, andsubstantial 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(103 )) of tiny APDs packed over a small area (O(1 mm2 )) and31st May, 2024

835. Particle Detectors at Accelerators

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 allcells 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 throughdecent separation of photoelectron peaks and offer gains of O(106 ) at a moderate bias voltage (∼30
V). However, the single-photoelectron noise of a SiPM, being the logical “or" of O(103 ) Geiger APDs,
is rather large: O(10-100 kHz/mm2 ) 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 coverageof 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] orsuitably designed meta-materials [29]. In this way, photons propagate from a larger entry window toa considerably smaller semiconductor sensor, resulting in an improved signal photon to dark-countratio. Intense R&D is expected to improve radiation hardness of these sensors. The fabricationof 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) toread 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 ≈ 5 × 104 ) yet sharp response to single photons with
Q ≈ 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 themicrowave 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 anddark 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 tocryogenic 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.

31st May, 2024

935. Particle Detectors at Accelerators

35.3 Organic scintillators
Revised August 2023 by S. C. Eno (U. Maryland) and M. 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 thisReview). 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 thephoton-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 usedin 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 canbe very low cost.
35.3.1 Scintillation mechanism
Plastic and liquid scintillators are based on an aromatic “matrix” such as benzene. The pelectrons 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 timescales (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 2,5diphenyloxazole, 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: thematrix (whether liquid or plastic) is where most of the radiation/matter interaction occurs. Afterradiation 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, canbe up to the solubility limit. Transfer via the Förster mechanism increases both speed and light
output 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” isalso 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 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 theternary 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
31st May, 2024

35. Particle Detectors at Accelerators

TripletexcitedstatesSingletexcitedstatesEnergy

10

s*
s3
T3

Internal
conversion

s2

T2

s1

s0

T1
Phosphorescence

Quenching

Delayed Fluo.

Fluorescence

Absorption

Intersystem crossing

Ground stateλ (nm)
Radiative relaxation
Non-radiative relaxation

Emission

Intensity

Absorption

Figure 35.1: Schematic of scintillation mechanism. Schematic of typical excitation and deexcitation of matrix modules.

Matrix260

310

360−370

420

Primary
Secondaryfluorophore fluorophore

Wavelength [nm]Figure 35.2: Schematic of scintillation mechanism. Typical emission and absorption spectra forthe matrix, the primary, and the secondary fluorophore.
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 thedensity of the excited molecules. Birks’ formula is
dL
dE/dx
= L0
,
dx
1 + kB dE/dx(35.2)

where L is the luminescence, L0 is the luminescence at low specific ionization density, and the
product kB is known as Birks’ constant, which must be determined for each scintillator by measurement. The value of kB for polystyrene is 0.126 mm/MeV, which is large enough to play an
31st May, 2024

1135. Particle Detectors at Accelerators

important role in compensation in scintillator-based calorimetry. The high hydrogen content ofplastic, which enhances the neutron interaction cross section, as well as the its large mass stopping
power, also contributes to calorimetry compensation. In the case of large dE/dx values (e.g. withalpha 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), thentriplet-triplet annihilation may occur following the Dexter process [42], leading to delayed fluorescence. This phenomenon is useful for α/β or neutron/γ discrimination and is more efficient inliquid 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 guidelight to photodetectors, and as the active element in the type of calorimeter pioneered by theRD52/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-yieldmeasurement showing damage due to aging [49].
Plastics are susceptible to radiation damage [50]. At high enough dose, the visible color of theplastic 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 andin 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 atmosphereat 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 doserate, can quickly bind to the radicals, reducing but not eliminating temporary damage at the priceof 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
31st May, 2024

1235. Particle Detectors at Acceleratorslarge 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 tensof 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 seenin single crystals. The maintenance of the amorphous state of these bulk optical materials wasachieved 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 withheavy 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 mobilityof 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 highlight 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 thecrystal lattice itself. However, other crystals require the addition of a dopant, typically fluorescentions such as thallium (Tl) 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 electronsor positrons which subsequently produce ionization. This energy is transferred to the luminescentcenters which then radiate scintillation photons. The light yield LY in terms of the number ofscintillation photons produced per MeV of energy deposit in the crystal can be expressed as [56]
LY = 106 S · Q/(β · Eg ),31st May, 2024

(35.3)

35. Particle Detectors at Accelerators

13

Table 35.4: Properties of several inorganic crystals. Most of the notation
is defined in Sec. 6 of this Review.
Parameter:ρ

MP X0 ∗ RM ∗ dE/dx∗

λI ∗Units:NaI(Tl)BGO
BaF2

g/cm3 ◦ C cm cm MeV/cm cm
3.67 651 2.59 4.13
4.8
42.9
7.13 1050 1.12 2.23
9.0
22.8
4.89 1280 2.03 3.10
6.5
30.7

CsI(Tl)CsI(Na)CsI(pure)

4.51 621 1.86 3.57
4.51 621 1.86 3.57
4.51 621 1.86 3.57

5.6
5.6
5.6

39.3
39.3
39.3

PbWO4

8.30 1123 0.89 2.00

10.1

20.7

9.6
9.4
8.42
6.90
6.65

20.9
21.0
23.2
30.4
31.5

LSO(Ce) 7.40 2050
PbF2
7.77 824
CeF3
6.16 1460
LaBr3 (Ce) 5.29 783
CeBr3
5.23 722

1.14
0.93
1.70
1.88
1.96

2.07
2.21
2.41
2.85
2.97

τdecay λmax
ns
245
300
650s
<0.6f
1220
690
30s
6f
30s
10f
40
30
20
17

nm
410
480
300s
220f
550
420
310

n†

Relativeyield‡

1.85
2.15
1.50

100
21
36s
4.1f
165
88
3.6s
1.1f
0.3s
0.077f85
Cherenkov
7.3
180
165

1.79
1.84
1.95

425s 2.20
420f
402 1.82
340 1.62
356 1.9371 1.9

Hygro- d(LY)/dT
scopic?
%/◦ C§
yes
−0.2
no
−0.9
no
−1.9s
0.1f
slight0.4
yes
0.4
slight
−1.4
no

−2.5

no
no
no
yes
yes

−0.2
0
0.2
−0.1

∗

Numerical values calculated using formulae in this review.
Refractive index at the wavelength of the emission maximum.
‡
Relative light yield measured for samples of 1.5 X0 cube with a Tyvek paper wrapping and a full end face coupled toa photodetector. The quantum efficiencies of the photodetector are taken out.
§
Variation of light yield with temperature evaluated at the room temperature.
f = fast component, s = slow component†

where β · Eg 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 thequantum efficiency of the luminescent center. The values of β, S and Q are crystal dependent andare the main factors in determining the intrinsic light yield of the scintillator. The decay time ofthe 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 (highplasticity 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 (Bi4 Ge3 O12 or BGO) has a high density, and consequently a shortradiation length X0 and Molière radius RM . Similar to CsI(Tl), BGO’s emission is well-matched tothe spectral sensitivity of silicon photodiodes, and it is easy to handle and not hygroscopic. Leadtungstate (PbWO4 or PWO) has a very high density, with a very short X0 and RM , but its intrinsic
light yield is rather low.
31st May, 2024

1435. Particle Detectors at Accelerators

Cerium doped lutetium oxyorthosilicate (Lu2 SiO5 :Ce, or LSO:Ce) [57] and cerium doped lutetiumyttrium oxyorthosilicate (Lu2(1−x) Y2x SiO5 , LYSO:Ce) [58] are dense crystal scintillators which havea 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 andCeF3 , 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 bialkali photocathode for 0.662 MeV γ-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 wherea 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 (Y3 Al5 O12 :Ce) and LuAG (Lu3 Al5 O12 :Ce) and their mixed compositions. These have beenshown 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 hadronicparts [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 fora clear discrimination between the Cherenkov and scintillation light. The preferred scintillation
light 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 andshowers, which may be used to mitigate pile-up effects and/or for particle identification since thetime 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 numberof 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 timeof 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 inachieving good time resolution with fast scintillating crystals.
Table-35.4 gives the light yield of other crystals relative to NaI(Tl) and their dependence tothe 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
31st May, 2024

1535. Particle Detectors at Acceleratorsof 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 numberof photoelectrons per MeV produced by a given photodetector. The relationship between thelight yield (LY ) in number of photons/MeV produced (Nphotons /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 · LCE · QE.

(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 internal 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 suchas 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 andshould 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 canbe 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 γrays 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 istherefore 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 ina 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 formationof color centers originated from the impurities or point defects in the crystal. This radiation
31st May, 2024

35. Particle Detectors at Accelerators

Hamamatsu PMT
R2059

0.4

Hamamatsu MPPC
s14160-3015ps, @43 V

⎯⎯

⎯⎯⎯

BGO: QE=8.0 ± 0.4%⎯⎯
LSO/LYSO: QE=13.6 ± 0.7%

BGO: PDE=31.1 ± 1.6%⎯⎯⎯
LSO/LYSO: PDE=27.5 ± 1.4%

CsI(Tl): QE=5.0 ± 0.2%

CsI(Tl): PDE=28.7 ± 1.4%

PMT QE, SiPM PDE⎯⎯

Emission Intensity (Arbitrary Unit)

16

⎯⎯⎯

LSO

0.3

LYSO

0.2

CsI(Tl)

0.1

BGO

0
300

400

500

600

700

800

Wavelength (nm)Figure 35.3: The quantum efficiency for a Hamamatsu R2059 PMT with bi-alkali cathode andquartz window and the particle detection efficiency (PDE) for a Hamamatsu S14160-3015ps multipixel photon counter (MPPC), which is also called silicon photomultiplier (SiPM), are shown as afunction 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.

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 longenough so that its light response uniformity, and thus its energy resolution, does not change.
31st May, 2024

17

35. Particle Detectors at Accelerators

While radiation damage induced by ionization dose is well understood [77], investigation is ongoing to understand radiation damage caused by hadrons, including both charged hadrons [78] andneutrons [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 (andit’s often difficult to separate them), neutrons can produce only the last two, and electrons andphotons only produce ionization damage. Studies on hadron induced radiation damage to leadtungstate [80] show a proton-specific damage component caused by fragments from fission inducedin 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-specfic 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 theirhigh 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 fromeach category include; (1) the BaBar luminosity detector [81] and the Quartic fast timing counterfor 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 basedon 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, lightcollection 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 thesequantities 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 thresholdfor radiation; and the dependence of the Cherenkov cone half-angle θc and the number of emitted
photons on the velocity of the particle vp and the refractive index n of the medium. The Cherenkov
angle can be calculated as1cos θc =,(35.5)n(E)β31st May, 2024

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35. Particle Detectors at Accelerators

where β = vp /c with c being the speed of light, and E the photon energy. The number of photoelectrons (Np.e. ) detected in a given device with radiator of length L is
α2 z 2
Np.e. = L
re me c2Z(E) sin2 θc (E)dE,(35.6)

where (E) is the efficiency for collecting the Cherenkov light and transducing it into photoelectrons,
and α2 /(re me c2 ) = 370 cm−1 eV−1 . The quantities  and θc are functions of the photon energy. As
the typical energy dependent variation of the index of refraction is modest, a quantity called theCherenkov detector quality factor N0 can be defined as
α2 z 2N0 =re me c2Z

 dE,

(35.7)

so that, taking the charge number z = 1 (the usual case in high-energy physics),
Np.e. ≈ LN0 hsin2 θc i.

(35.8)

This definition of the quality factor N0 is not universal, nor, indeed, very useful for those common
situations where  factorizes as  = coll det with the geometrical photon collection efficiency (coll )varying substantially for different tracks while the photon detector efficiency (det ) remains nearlytrack independent. In this case, it can be useful to explicitly remove (coll ) from the definition of N0 .
A typical value of N0 for a photomultiplier (PMT) detection system working in the visible and near
UV, and collecting most of the Cherenkov light, is about 100 cm−1 . Practical counters, utilizing avariety of different photodetectors, have values ranging between about 30 and 180 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 thatthe 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 investigatedas 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 (θc ) 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 ofimaging detectors can be extremely good as it scales approximately as √ 1 .
Np.e.

Threshold Cherenkov detectors [88], in their simplest form, make a yes/no decision based onwhether the particle is above or below the Cherenkov threshold velocity βt = 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 amomentum some 20% above the threshold momentum of the heavier particle in a typical case).
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35. Particle Detectors at Accelerators

Careful designs give hcoll i & 90%. For a photomultiplier with a typical bialkali cathode,det dE ≈ 0.27 eV, so that
Np.e. /L ≈ 90 cm−1 hsin2 θc i(i.e., N0 = 90 cm−1 ).

(35.9)

Suppose, for example, that n is chosen so that the threshold for species a is pt ; that is, at thismomentum species a has velocity βa = 1/n. A second, lighter, species b with the same momentum
has velocity βb , so cos θc = βa /βb , andNp.e. /L ≈ 90 cm−1

m2a − m2b.
p2t + m2a(35.10)For K/π separation at p = pt = 1(5) GeV/c, Np.e. /L ≈ 16(0.8) cm−1 for π’s and (by design) 0 for
K’s.
For limited path lengths Np.e. will usually be small. The overall efficiency of the device iscontrolled 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 (seethe 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 backgroundnoise, 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 becarefully 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 thering-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 misidentification 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]. Typicallythe 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 regionof 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) canbe performed in large water counters by combining the individual space position and time of eachphoton together with the constraint that Cherenkov photons are emitted from each track at thesame polar angle (Sec. 36.3.1of this Review).
In a simple model of an imaging PID counter, the fractional error on the particle velocity (δβ )is given byσβδβ == tan θc σ(θc ) ,(35.11)β
wherehσ(θi )iσ(θc ) = p⊕ C,(35.12)
Np.e.
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35. Particle Detectors at Acceleratorsand hσ(θi )i 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 thephoton 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 β ≈ 1 particle of momentum (p) well above threshold entering a radiator with index ofrefraction (n), the number of σ separation (Nσ ) between particles of mass m1 and m2 is approximately|m21 − m22 |√Nσ ≈.
(35.13)2p2 σ(θc ) n2 − 1
In practical counters, the angular resolution term σ(θc ) varies between about 0.1 and 5 mraddepending on the size, radiator, and photodetector type of the particular counter. The range ofmomenta 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 σ(θc ) =2 mrad, a fused silica radiator (n = 1.474), ora fluorocarbon gas radiator (C5 F12 , n = 1.0017), would separate π/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 3σ.
Many different imaging counters have been built during the last several decades [87]. Amongthe 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 opticalfocusing and/or geometrical masking to select particles having velocities in a specified region. With
careful design, a velocity resolution of σβ /β ≈ 10−4 –10−5 can be obtained [88].
Practical multi-track Ring-Imaging Cherenkov detectors (generically called RICH counters) area more recent development. RICH counters are sometimes further classified by ‘generations’ thatdiffer 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 (C6 F14 , n =1.276) and gas (C5 F12 , n = 1.0017) radiators, the former being proximity imaged with the latter using mirrors. The phototransducers are a TPC/wire-chamber combination. They are madesensitive 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 interactingwith materials in the system. In spite of their unforgiving operational characteristics, these counters attained good e/π/K/p 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
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35. Particle Detectors at Accelerators

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 arraymade 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 neongas as radiator and spherical mirrors to focus the photons on two arrays of 2 000 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, aremirror-focused on arrays of multi-anode PMTs (MaPMTs) with a total of about 55,000 pixels, toidentify 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 C4 F10 (originally in combination withaerogel, which was removed in 2015) while the second volume contains CF4 . Photons are mirrorfocused onto arrays of photon detectors to cover a π/K separation momentum range between 1
and 150 GeV/c. Additional upgrades, including the replacement of the HPDs by MaPMTs andimproved 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(C6 F14 radiators and solid CsI photocathodes (similar photodectors 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 CF4 radiator to a photodetector based onelectron 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 π/K
separation up to 8 GeV/c. The forward endcap Aerogel RICH (ARICH) for the Belle II upgrade at
KEKB, designed to provide clean π/K separation for momenta up to 3.5 GeV/c, is an example ofthe 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 oflight from the radiator by collecting and imaging the total internally reflected light rather than thetransmitted 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 duringtransport 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 ∼ 1.47 for fused silica), themomentum range with good π/K separation goes up to 4–5 GeV/c. It is plausible, but difficult, to
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35. Particle Detectors at Accelerators

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 Υ (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 andlight guide. The photons were imaged via a “pin-hole” through an expansion region filled with6 000 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 π/K separation of 2.5 standard deviations or more up to 4 GeV/c momentum. Fora 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 measurementof 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 π/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 decommissioned
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 π/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 π/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 thecenter 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 toachieve good particle identification. In the truncated mean method for calculating hdE/dxi, theionization 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].
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 describedby 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 unitcharge minimum-ionizing particles (MIPs) [97] [98]. When an ionizing particle passes through thegas it creates electron-ion pairs; often the ejected electrons have sufficient energy to further ionize
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35. Particle Detectors at Accelerators

23

Table 35.5: Properties of noble and molecular gases at normal temperature and pressure (NTP: 20◦ C, one atm). EX , EI : first excitation,
ionization energy; WI : average energy for creation of ion pair; dE/dx|min ,NP , NT : 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.
Gas
H2
He
Ne
Ar
Xe
CH4
C 2 H6iC4 H10CO2
CF4

Density,
mg cm−3
0.084
0.179
0.839
1.66
5.495
0.667
1.26
2.49
1.84
3.78

Ex
eV
10.8
19.8
16.7
11.6
8.4
8.8
8.2
6.5
7.0
10.0

EI
WI dE/dx|min NP
NT
−1
−1
eV
eV
keV cmcm
cm−1
13.6 37
0.34
5.2
9.2
24.6 41.3
0.32
3.5
8
21.6 371.45
13
40
15.7 262.53
25
97
12.1 226.87
41
312
12.6 30
1.61
28
54
11.5 26
2.91
48
112
10.6 265.67
90
220
13.8 343.35
35100
16.0 35-52
6.38
52-63
120

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 theprimary electrons, form clusters of one, several, or sometimes many, electron-ion pairs. As shown in
Table 35.5, the total number of pairs (NT ) is a few times larger than the number of primaries (NP ).
For different conditions and for mixtures, and neglecting energy transfer processes (e.g. Penningeffect), one can scale the density, NP , and NT with temperature and pressure assuming a perfectgas 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 βγ [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 µm and this can contribute to the error in the coordinate determination.
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 ionsdrift in opposite directions and diffuse towards the electrodes. The electron-molecule collision crosssections 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
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35. Particle Detectors at Accelerators

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].

inelasticity implies that high fields are required to raise the electron energy. For noble gases, theinelastic cross section is zero until the electrons reach the first excitation and ionization energies
O(10 eV ); on the contrary, for molecular gases, like CH4 , inelastic channels, involving rotationaland vibrational levels, open up at energies above ∼ 0.1 eV. Large drift velocities are achieved byadding polyatomic gases (usually hydrocarbons Cx Hy , CO2 , CF4 ) having large inelastic component
at moderate energies of a few eV; this results in the electron ”cooling” into the energy range of theRamsauer-Townsend minimum (at ∼ 0.5 eV) of the elastic (”momentum-transfer”) cross-section inAr [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 dependenceof the drift velocity (vd ) on E/P and temperature; this has a particularly strong effect for noble
gases, as illustrated in Fig. 35.5 for Ar. Carbon tetrafluoride (CF4 ) has the largest drift velocity
and the lowest electron diffusion among known gases due to the sizeable Ramsauer-Townsend dip inthe elastic cross-section which coincides with a very large vibrational modes. Another principal roleof the polyatomic gas is to absorb the ultraviolet photons emitted by the excited noble gas atoms.
Addition of molecular gases (hydrocarbons or CO2 are widely used in the proportional counters
as a quencher) to noble gas allows to dissipate a good fraction of energy through rotational andvibrational radiationless transitions without the creation of photons or ions. On the contrary, CF4
has a small quenching cross-section of excited Ar states and light emission in CF4 (from the far
UV to the visible light) is a complex process, involving the creation of CF3+ 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
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35. Particle Detectors at Accelerators[108]. Fig. 35.5 and Fig. 35.6 show drift velocity and transverse diffusion for some commonlyused gases at NTP, computed with the Magboltz program [102, 103]. For different conditions, thehorizontal axis must be scaled inversely with the gas density. Standard deviations for longitudinal(σL ) and transverse diffusion (σT ) are given for one cm of drift, and scale with the the square rootof the drift distance.
In a simple approximation, gas kinetic theory provides the drift velocity vd as a function of
the mean collision time τ and the electric field E: vd = eEτ /me (Townsend’s expression). In thepresence 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 anapproximate expression for the vector drift velocity v as a function of electric and magnetic field
vectors E and B, of the Larmor frequency ω = eB/me , and of the mean collision time τ (moreprecise calculation is available in Magboltz, which computes drift velocity by tracing electrons at
the microscopic level through numerous collisions with gas molecules):
e
τ
ωτ
ω2τ 2
v=
E
+
(E
×
B)
+
(E · B)Bme 1 + ω 2 τ 2
B
B2




(35.14)To a good approximation, and for moderate fields, one can assume that the energy of theelectrons is not affected by B, and use for τ 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√2
vector is tan θB = ωτ and v = (E/B)(ωτ / 1 + ω τ 2 ). For parallel electric and magnetic fields, drift
velocity and longitudinal diffusion√ are not affected, while the transverse diffusion can be strongly
reduced: σT (B) = σT (B = 0)/ 1 + ω 2 τ 2 . As an example, the dotted line in Fig. 35.6 represents σTfor the classic Ar/CH4 (90:10) mixture at 4 T. Large values of ωτ ∼ 20 at 5 T are consistent withthe measurement of diffusion coefficient in Ar/CF4 /iC4 H10 (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).
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 thesame additive in different mixtures. As an example, at moderate fields (up to 1 kV/cm) the additionof 0.1% of oxygen to an Ar/CO2 mixture results in an electron capture probability about twenty
times larger than in Ar/CH4 . Among common molecules, the largest electron affinities are found
for the halogenides, O2 and H2 O. The attachment probability in O2 or H2 O is large at low fields
and electron energies close to thermal, but decreases at increasing fields. On the contrary, CF4 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 mixtureand 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, λi ,decreases exponentially with the field; its inverse, α = 1/λi , is named the first Townsend coefficient.
In wire chambers, most of the increase of avalanche particle density occurs very close to the anodewires, and a simple electrostatic consideration shows that the largest fraction of the detectedsignal 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 shapeof 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, N0 initial electrons multiply over a length
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35. Particle Detectors at Accelerators

Figure 35.5: Computed electron drift velocity as a function of electric field in several gases at
NTP and B = 0 [102, 103].

x forming an electron avalanche of size N = N0 eαx ; N/N0 is the gain of the detector. Fig. 35.7 shows
examples of Townsend coefficients for several gas mixtures, computed with Magboltz [102, 103].
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 thefits 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 efficiencyof 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 ionizationby 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 atmopheric 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-C2 H2 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
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35. Particle Detectors at Accelerators

Figure 35.6: Electron longitudinal diffusion (σL ) (dashed lines) and transverse diffusion (σT )(full lines) for 1 cm of drift at NTP and B = 0. The dotted line shows σT for the P10 mixture at
4 T [102, 103].

µ, the ratio of drift velocity to electric field, is constant for a given ion type up to very highfields. Values of ions mobility at NTP are given in Table 35.6 [111]. For different temperaturesand 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 thedrift 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 thelowest 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 CO+
2 ·(CO2)n+cluster ions, and not CO2 or noble gas ions [112]. Since the cluster ions are slower than the initialions, 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 matterssearches [113].
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, followedby charge multiplication and collection around a thin (typically 20 – 50 µm diameter) wire, havebeen 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] intro31st May, 2024

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35. Particle Detectors at Accelerators

Figure 35.7: Computed first Townsend coefficient α as a function of electric field in several gases
at NTP [102, 103].
Table 35.6: Mobility of ions in gases and mixtures at NTP [111].
Gas
He
Ne
Ar
Ar/CH4
Ar/CO2CH4
CO2Mobility µ(cm2 V−1 s−1 )
10.4
4.7
1.54
1.87
1.72
2.26
1.09

duced 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 ED , and the capacitance C per unit length of anode wire are approximately given
by
CV0 1
CV0
2π0
E(r) =
ED =C=,(35.15)2π0 r20 s
π(`/s) − ln(2πa/s)
where r is the distance from the center of the anode, s the wire spacing, ` and V0 the distance and31st May, 2024

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35. Particle Detectors at Accelerators

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 themechanical tension of the wire, up to a maximum unsupported stable length, LM [118], above which
the wire displaces:s pLM =4π0 TM(35.16)
CV0
The maximum tension TM depends on the wire diameter and modulus of elasticity. Table 35.7
gives approximate values for tungsten and the corresponding maximum stable wire length underreasonable assumptions for the operating voltage (V0 = 5 kV) [119]. Internal supports and spacers
can be used in the construction of longer detectors to overcome limits on the wire length imposedby Eq. (35.16).
Table 35.7: Maximum tension TM and stable unsupported length LM
for tungsten wires with spacing s, operated at V0 = 5 kV. No safety factor
is included.
Wire diameter ( µm) TM (newton) s (mm) LM (cm)
10
0.16
1
25
20
0.65
2
85
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 withthe 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 eachwire 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 areoften 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 degradesto ∼ 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 ofinteraction is known [122]. The distance between anode wires (e.g. Au-plated W) is usually several
cm, allowing coverage of large areas at reduced cost. In the original design, a thicker wire (thefield wire, often from Cu-Be or Al) at the proper voltage, placed between the anode wires, removes
the low-field region at the mid-point 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
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35. Particle Detectors at Accelerators

30

0.15

y-axis [cm]0.10(a) Multiwire proportional chamber

0.05
0.00
−0.05
−0.10

y-axis [cm]0.10(b) Drift chamber

0.05
0.00
−0.05
−0.10
−0.15
−0.3

−0.2

−0.1

0.0

0.1

0.2

0.3

x-axis [cm]Figure 35.8: Electric field lines and equipotentials in (a) a multiwire proportional chamber and(b) a drift chamber.

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 recordingof charge sharing from the two ends of the anode wires provides the coordinates of segments oftracks. 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 dNcl /dx techniques. In allcases, a good knowledge of electron drift velocity and diffusion properties is required. This has tobe combined with the knowledge of the electric fields in the structures [103]. Accumulation of ions
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35. Particle Detectors at Acceleratorsin the gas volume may induce gain reduction and field distortions, especially for long drift distancesin TPC (see Sec. 35.6.5). An important major innovation is related to the replacement of MWPCwith 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 × 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 (∼ 106 ). This gas mixture wasused 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 theprecursors 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 beachieved 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 alight 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 theentire 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 ofultrasonic 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 resultin 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 109 electrons per second andmm of wire, independently of the avalanche size. For a proportional gain of 104 and 100 electrons
per track, this corresponds to a particle flux of 103 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.
Although almost any gas can be used to operate wire chambers, CF4 -based mixtures have been
preferred due to their properties. Their main advantage for the use in large volume detectors arehigh drift velocity, low diffusion, non-flammability and low sensitivity to neutrons; also they do notform polymers in avalanches.
However, the problem of greenhouse gases, such as CF4 , 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 havebeen initiated, together with a better understanding of their long-term ageing effects [135] (see alsoSec. 35.6.4).
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35. Particle Detectors at Accelerators

Figure 35.9: Charge rate dependence of normalized gas gain G/G0 (relative to zero countingrate) in proportional thin-wire detectors [134]. Q is the total charge in single avalanche; N is theparticle rate per wire length.
Ageing phenomena (formation of polymer deposits on the electrodes) constitute one of the mostcomplex 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 ofwater in many (but not all) cases has been shown to extend the lifetime of the detectors. Additionof fluorinated gases (e.g., CF4 ) 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 104 , to a total particle
flux of ∼ 1014 MIPs/cm2 .
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 MicroPattern Gaseous Detectors (MPGD) [138–140]. Since the very beginning, the goal was the develop31st May, 2024

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35. Particle Detectors at Accelerators

ment of novel devices with high rate capability (up to 106 Hz/mm2 ) 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 broadfamily of MPGD technologies are being developed and optimized for numerous applications, suchas [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).

50 µm

140 µmFigure 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 anddiffuse transversally.
The MSGC concept, invented in 1988, was the first of the micro-structure 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
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35. Particle Detectors at Acceleratorsand simple photolithography process, the anode strips can be made very narrow (∼ 10 µm) with atypical pitch (distance between strips) of ∼ 100 µm. When appropriate potentials are applied tothe electrodes, electrons released in the drift volume move toward the strips and multiply in thehigh-field region. Owing to the small anode-to-cathode distance, the fast removal of positive ionsby nearby cathode strips reduces space charge build-up, and improves siginicantly 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 andtime-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 (substratematerial, 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 processes: GEM, Micromegas andothers, 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 typicallybetween 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 athickness 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 proportionalcounter. 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 withcascaded multi-GEM structures confirm that the gains and charge transfer processes are predictablefrom electrostatic considerations and avalanche development models; an overall gas gain well above
104 can be reached in the presence of highly ionizing particles, while strongly reducing the riskof 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 thestructures [146]. This effect is known as “charging-up” effect; its time constant and amplitudedepend 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 readout 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 homogeneousin both the drift (electric field ∼ 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 the electric field, resulting
in a more uniform gain. The transverse size of the electron avalanche due to diffusion is of theorder 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
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35. Particle Detectors at Accelerators

35

100 µm

HV1

Drift gap

50-70 kV/cm

e−Micromesh

Amplification
gap
Anode plane

HV2

E2
Particle

Figure 35.11: Schematic drawing of the Micromegas detector.
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 morethan two orders of magnitude compared to MWPC (see Fig.35.12) [149] [150]. Even larger ratecapability has been reported for Micromegas [151].
The fine granularity and high-rate capability of GEM and Micromegas can be fully exploitedby using high-density pixel readout with a size corresponding to the intrinsic width of the detectedavalanche 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 connectedto the amplification and digitization circuits, integrated in the underlying CMOS layers. A thininsulating 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 byan 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 endplatewith a 160 GridPix ASICs, each 2 cm2 , corresponding to 10.5 million pixels, demonstrating forthe 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].
Gaseous detectors represent the most cost-effective solution to cover very large areas with pho31st May, 2024

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35. Particle Detectors at Accelerators

Figure 35.12: Normalized gas gain as a function of particle rate for MWPC [149] and GEM [150].

tosensitive 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 electricalinstability. 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 holespacing 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 underirradiation, while large rims permit to attain larger maximum gain and to reduce discharges, at thecost 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 detectionin the COMPASS RICH where a hybrid architecture formed by two THGEM layers (one coveredby 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 havebeen 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 beachieved 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
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35. Particle Detectors at Accelerators

Figure 35.13: Photo of the Micromegas (’GridPix”) detector. The grid holes can be accuratelyaligned with readout pixels of Timepix CMOS chip. The insulating pillars are centered between
the grid holes, thus avoiding dead regions.

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 DiamongLike Carbon (DLC) layer, and grounding by edges (2D charge evacuation for low-rates O(kHz/cm2 ))and a more sophisticated scheme using double-resistive layer with a through-vias between themand the grounding done by means of the readout electrodes (3D charge evacuation for high-rate
O(MHz/cm2 ) applications) [160]. The µ-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 electricfield 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 andsignificantly reduce detector assembly time) [163]. Scaling up of MPGDs to very large single unit
detectors of O(m2 ), has facilitated their use in the High Luminosity LHC upgrades: Micromegas
will instrument an area of O(1000 m2 ) in the New Small Wheel of the ATLAS Muon endcaps,
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while GEMs be used in the CMS Muon system and for the ALICE TPC readout. Exploiting theMicromegas, GEM, and µ-RWELL ability to measure both position and arrival time of the charge
released in the drift gap, a novel µ-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 µ-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 flourishingof novel ones, often specific to well-defined applications. Modern technologies have been also
derived from Micromegas and GEM concepts, hybrid approaches combining different elements ina 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 foraddressing future experimental challenges such as high granularity and picosecond-precision timing(e.g. PICOSEC-Micromegas concept [166]). A clear direction for future developments is thatof 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 that drift in a uniform electricfield 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 fastinteraction 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 basicallyadjacent, which facilitates the track finding enormously. This advantage is often exploited forpattern 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
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35. Particle Detectors at Accelerators

Figure 35.14: Schematic view of the ALICE TPC [170, 171]. The drift volume with 5 m diameteris divided into two halves, each providing 2.5 m drift length. The amplification stage has recently
been upgraded from wire planes to GEMs.

Outer wallE, B
directions

Inner wall and field cage

Beam
direction

Central cathode

Front end
cards

Central cathode HV

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.

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35. Particle Detectors at Accelerators

Energy deposit per unit length (keV/cm)

40

Momentum (GeV/c)
Figure 35.16: Energy deposit versus momentum measured in the ALICE TPC.

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 measurementsin the plane transverse to the magnetic field are most important. The specific energy deposit isestimated from many charge measurements along the particle trajectory (e.g. one measurement peranode 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 mostprobable value of the corrected signal amplitudes for a given track provides the best estimator forthe 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 isillustrated 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 empiricalformula [173]:
σdE/dx = 0.41 N −0.43 (t P )−0.32 .

(35.17)

Typical values at nominal pressure are σdE/dx = 4.5 to 7.5%, with t = 0.4 to 1.5 cm and N = 40
up to more than 300. The 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
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35. Particle Detectors at Acceleratorsof ions in the drift volume. The electron drift in a TPC in the presence of a magnetic field isdefined by Eq. (35.14). The E × B term of Eq. (35.14) vanishes for perfectly aligned electric andmagnetic fields, which can however be difficult to achieve in practice. Furthermore, the electron
drift depends on the ωτ factor, which is defined by the gas mixture and the magnetic field strength.
The electrons will tend to follow the magnetic field lines for ωτ > 1, or the electric field lines forωτ < 1. The former mode of operation makes the TPC less sensitive to non-uniformities of theelectric 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 islimited to around√
σD L
σx = √,
n(35.18)where σD 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, σD,B=0 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 ωτ can significantly reduce diffusion:
σD,B>01.
=√
σD,B=01 + ω2τ 2(35.19)This factor can reach values of up to 10. In practice, the final resolution limit due to diffusion
typically lies around σx = 100 µm.
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
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 ofωτ .
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 electricfields used in TPCs (up to a few 100 V/cm). As a consequence, it is quite sensitive to the ambientconditions. Freon admixtures like CF4 can be an attractive option for a TPC as well, since theresulting 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 andthe 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, theincoming ionisation electrons are displaced in the direction of the wires (“wire E ×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
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35. Particle Detectors at Accelerators

particular, E ×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 siliconsensors 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 canlead 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 (see35.6).
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) toallow 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 inacceptable data loss. The employed readout
schemes are based on MPGDs, as these can be optimised in order to drastically reduce the ion backflow. 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 (γ & 103 )crosses a refractive index interface, as discussed in Sec. 34.7. Since the TR yield is about a few % perboundary crossing, radiation from multiple surface crossings (e.g., a stack of foils) is used in practicaldetectors. 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 γ, but, for√multiple boundary crossings, interference leads
to saturation above a Lorentz factor γ sat = 0.6 ω1 `1 `2 /c [177], where ω1 is the radiator material
plasma frequency, `1 is its thickness, and `2 the spacing between material elements. The probability
density function of TR is a fairly complex function of γ, radiator parameters, photon energy (ω)
and its emission angle (θ). For well defined radiator parameters a measured two-dimensional
distribution of photon energy vs its reconstructed emission angle is in very good agreement withthe theory predictions [178].
Integration over the angle yields the TR spectrum, which typically features many maxima (seeSec. 34.7). Most of the TR energy is emitted near the last maximum of the spectra determinedby radiator material parameters at ωmax = `1 ω12 /2πc. The effective TR photon emission starts at
about γthr = `1 ω1 /c. By varying radiator parameters one may optimize the particle separation
for a given range of the γ-factor. The angular distribution of TR photons has a few maxima
and extends up to θmax = (1/γ 2 + ω12 /ω 2 )1/2 [179]. For a single foil the largest part of the TR
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43

10−3

30
25
20

10−4

35

25
20
10−4
15

10

10

0.5

1

1.5

2

2.5

3

3.5

4

10−5

θ (mrad)

10−3

30

15

5
0

MC

40

5
0

0.5

1

1.5

2

2.5

3

3.5

4

Number of TR photons

35

Photon energy (keV)

Data

40

Number of TR photons

Photon energy (keV)energy is emitted around the most probable angle θ = (1/γ 2 + ω22 /ω 2 )1/2 , where ω2 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 expressionforq the angle which corresponds to the last interference maximum of the energy spectra is θ ≈1.4π 2 /γ 2sat − 1/γ 2 [178]. The higher is the gamma-factor, the larger is the angle of the firstinterference maximum. It reaches almost its asymptotic limit at γ = γsat . This effect is illustrated
in Fig. 35.17 [178] which shows two-dimensional distribution of the TR photon energy versus thereconstructed production angle obtained in 20 GeV electron beam with the radiator containing
a stack of foils of 15.5 µm thickness spaced by 210 µm (the left plot) using a Si-pixel detector.
TR produced by 20 GeV electrons is emitted mostly around θ ∼ 0.9 mrad. All features of this
distribution are well reproduced with MC simulations (the right plot).

10−5

θ (mrad)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]

The simplified numerical expressions√can be used for practical estimation of the √main TR
production parameters [178]: θ ∼ 1.2/ω1 l1 l2 , γthr ∼ 3 × 103 ω1 `1 , γ sat ∼ 3 × 103 ω1 `1 `2 andωmax = 0.65 `1 ω12 , where θ in mrad, ω1 in eV, ωmax in keV and l1 and l2 in mm.
In the simplest concept, a detector module might consist of a low-Z TR radiator followed bya 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 /ω 3 , where n varies between 4 and 5 over the region of interest.1 To minimize
self-absorption, materials such as polypropylene, Mylar, carbon, and (rarely) lithium in the formof foils, fibers or foams are used as radiators. The TR signal in the active regions is in mostcases 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 γ sat ≈ 3000.
Those detectors normally work as threshold devices, ensuring the best electron/pion separation in
the momentum range 1 GeV/c . p . 150 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 µm thick polypropylene
foils). Most of the TR photons are absorbed in the radiator itself. To maximise the number ofTR photons reaching the detector, part of the radiator far from the active layers is often made1

Photon 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.

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35. Particle Detectors at Acceleratorsof 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. Suchdetectors 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 finegranular 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 anintegral 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 radiatorsthemselves. However, for photon energies above this value, the absorption is reduced and theradiation can be registered by several consecutive detector layers, thus creating a strong TR buildup 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 isabout 40 with an effective foil thickness of about 18 µm. In this approach straw walls also act asradiator and make some contribution to the TR spectrum.
Although the values mentioned above are typical for most of the plastic radiators used with Xebased 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 regularradiators 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 depositions 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 thickgas 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 LandauVavilov distribution of background ionization energy losses with the Poisson statistics of 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 moreparameters 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 anincrease 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 inFig. 35.18, which shows, for a variety of detectors, the pion efficiency at a fixed electron efficiencyof 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 · 10L/38 , where the range of validity is L ≈ 20–100 cm. Apartfrom 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
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45

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).

NOMAD
KEK
UA2
H.Butt et al.
D0
M.Holder et al.
H.Weidkamp..
H.Grassler et al.

Pion efficiency

0.1

ATLAS
AMS
ALICE
PAMELA
NA34 (HELIOS)
C.Fabjan et al.
R 806..
A. Bungener et al.
ZEUS

0.01

0.001

10

20

50
100
Total detector length (cm)200

Figure 35.18: Pion efficiency measured (or predicted) for different TRDs as a function of thedetector 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].
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 theavailable 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 obtainedin 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 → eν inclusive decay). Even a very soft TR cut at the HLTlevel, which preserves high electron efficiency (98%), allows to suppress a significant part of fake31st May, 2024

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35. Particle Detectors at Accelerators

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. hadronic mode ofτ –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(`1 , `2 ) is tuned to extend the TR yield rise up to γ ≈ 105 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 anddetector. 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 toimprove 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 underconsideration. GasPixel detectors allow to reconstruct a track segment with a space point accuracyof < 30 µm and exploit all details of the particle tracks to highlight individual TR clusters in thegas, 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 wasthe 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 theoriginal 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 twoparallel high bulk resistivity electrode plates (109 –1013 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 precisionof a few µm. The gap is filled with a suitable atmospheric-pressure gas mixture which serves as atarget 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 obtaina 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 (glassfrom 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 multiplicationof the primary electrons. The electric field is typically applied through a moderately conductive(∼ 105 to108 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
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47

Induced positive
signal on X strip

Low density filler 3 mm
Graphite layer

HV

Frame

Resistive electrode 2 mm
spacer

Gas 2 mm

HV contact
Insulating foil

Induced negative
signal on Y strip

Copper ground plane

Figure 35.19: Schematic cross section of a generic single gap RPC.
(τ = ρr being ρ the electrode resistivity and r its dielectric constant) is much longer than the
discharge processes duration. Therefore only the locally-stored electrostatic energy contributes tothe 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 layerof polymerized linseed oil [205] with the function of smoothing the electrode surface, improving theelectric field uniformity. Glass-based RPCs don’t require such treatment. It also has the functionof 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 isbroad and approximately exponentially distributed2 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 casein gaseous detectors where ionization and amplification occur in separate regions.
For increasingly larger avalanches, the space-charge progressively saturates the avalanche growthfrom exponential to almost linear, producing a peaked charge spectrum, essential to efficiently
separate the signal from the noise [207]. For large gains3 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 a UV photons quencher suppressing the photon-mediated feedback thatcan lead to self generated after-pulse discharges, and one or more electronegative components, toextend 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 forslow 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 mix2
An analytic treatment of the low gain avalanche process shows that the charge distribution is well described bythe Γ function [206]3
A multiplicity of the order of 108 electrons is classically referred as Raether/Meek limit for on-setting a streamer

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35. Particle Detectors at Accelerators

ture for stable avalanche operation in ATLAS and CMS is C2 H2 F4 /i-C4 H1 0/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 isisotropically 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 onboth RPC sides are equivalent. The induced charge density distribution can be ideally calculated fora 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 adiffusion-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 theserequirements 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 andlimitations, 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 havesensitive surface areas up to ∼104 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 systemsof 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 CODEXB [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 goodcandidates for application in tracking calorimetry [225].
The MRPC [226], as sketched in Fig. 35.20, segments the gaseous target by means of a stackof 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, anddetermines a shorter avalanche growth time, increasing time resolution by one order of magnitudewith 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 1012 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],
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35. Particle Detectors at Accelerators

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].
Induced positive signal

Cathode pick-up

Graphite layer

HV

Floating
electrodes

Gas gap 0.2 mm

Electrode thickness 0.2 mm

HV contact

Anode pick-up
Insulating foil

Induced negative signal Copper ground plane

Figure 35.20: Schematic cross section of a generic multi gap RPC.
35.6.7.2 Time and space resolution
Space-time uncertainties in RPCs are determined by the statistical fluctuations of the primaryand 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 thefirst 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 thesame 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 alongwith the intrinsic efficiency of the single gas gap. Typical timing performances range from around1 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 thelateral 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 andmeasuring 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, ∆V = Va −Vgas = I ·R
[241]. Here Va is the applied voltage, Vgas is the effective voltage on the gas, R = ρ · d/S is the total
electrode resistance, ρ 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 = φ · S · hQi where φis the particle fluence and hQi is average charge per avalanche. So we obtain a state equation for
the RPC rate capability:∆V /φ = ρ · d · hQi
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35. Particle Detectors at Accelerators

A large I not only limits the rate capability but also affects the long term performance of thedetector 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 madeof 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 linseedoil, 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 ofgas 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 beachieved by reducing gas gain in favor of electronic amplification, operating the detector in avalanche
mode. Increasing concentrations of electronegative gases, such as C2 H2 F4 and SF6 [212], shifts thestreamer transition to higher gains, thus the avalanche signal can access an 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 andstable 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), specificallythe 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 theavalanche 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 forthe existing RPC systems, and a much higher charge per count due to a large fraction of negativeions 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 theageing acceleration drive represented by the phenomena stated above, the proposed strategy wasto largely dilute HFO whih 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 /C3 H2 F4 /iC4 H10 /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
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35. Particle Detectors at Acceleratorsof 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 35.21: Schematic drawing of an RCC.
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 advantagesof 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) = − r ln(RV1 /R2 ) . By choosing appropriate values for R1 , R2 , V and its polarization (theinnermost cylinder is the cathode), it is possible to virtually segment the cylindrical gap in a innermost sensitive layer, where the field is sufficiently high to start the avalanche multiplication, andan 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 amuch better prompt to total charge ratio, lowering the total operative current, hence increasing therate capability. The cylindrical structure has a further major advantage with respect to the planarone, 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 efficiencyof narrow gaps, on the other, it could largely improve RPC time resolution since the Townsend
coefficient α = 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 performanceof 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 tospace and under water applications.

35.7 LAr Time Projection Chamber
Written in October 2021 by F. Pietropaolo (CERN; INFN, Padova) and S. Pordes (FNAL). Revisedin 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
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35. Particle Detectors at Accelerators
Table 35.8: Some physical properties of liquid argon from [253].
Property
Unit
Value
Boiling Point (BP) at 1013 hPa
K
87.3
Density (ρ) at 1013 hPa
kg m−31395
d(BP)/dP
K hPa−1
9 × 10−3dρ/dT
kg m−3 K−1−6.2
Latent Heat of Evaporation
kJ kg−1
161
Freezing Point (1013 hPa)K
83.8

and ionization electrons; in the presence of a moderate electric field, a significant fraction of theelectrons escape recombination, making them available for detection as a charge signal. Typicalvalues 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 densityof 1.4, that the free electrons can be drifted many meters with minimal dispersion and that it isabundant 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 liquidargon TPC (LAr TPC) has been developed into a detector that combines mm3 resolution withparticle identification, calorimetry, and 100% live time. Detectors with masses up to 600 tons havebeen 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 toescape 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 [256] [257]and in detailed descriptions of detectors which have operated in experiments [258–264]. 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 andsubject of intense activity, are also introduced [265–267]. References are also given for a number ofancillary devices - cameras that can operate in the liquid argon [264], monitors to provide a rapid
measurement of the purity of the argon [268, 269], ionization lasers to measure distortions of thedrift field due to space charge or electrical problems [270] - 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 toproduce 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 andpressure. Evacuable double-walled vacuum cryostats are practical for detectors with a mass ofO(100) t. Based on the demonstration that ultra-clean argon can be achieved without initial
evacuation [269], current and proposed larger detectors are hosted in foam-insulated non-evacuable
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35. Particle Detectors at Accelerators

cryostats based on a technology used in liquefied natural gas transport [264]. A convenient featureof 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 thecase of vacuum degradation.
The absence of electronegative contaminants, mainly environmental oxygen and water, fromthe 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’, τ , is the parameter describing the purity level ofargon. 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 [271, 272],
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 [273], 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 waterlevels. Molecular sieve and activated copper on alumina [274] are commonly used to remove waterand oxygen, respectively. This purification is performed in the liquid phase and the discovery
that purification with standard materials is effective at cryogenic temperatures [275] allowed foran 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 orresidual leaks. To avoid the build-up of contaminants, both the boil-off gas and the liquid arecontinuously recirculated through the purification system. Schematics of experiment cryogenics
systems are shown in [259, 261, 264]. 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 [264].
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 [276] and transmission [277]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 ‘Wel ’ = 23.6 eV [278], the energy deposit that generates one ion-electron
pair, the dE/dx of the particle, and ‘R’ the (unfortunately labeled) fraction of electrons that escaperecombination - see figure 35.22 (left). Measurements of electron yield have been made at various
electric fields and at different ionization densities [279–283] and show good consistency. Of themodels proposed to predict recombination [284, 285], none is fully successful; the so-called ‘box
model’ [286] which considers the situation of mobile electrons and stationary ions makes more
realistic assumptions than other models and it is commonly used [287]. The data from [282] which
0.8
are some of the most comprehensive are described by the form R = (1+0.049(dE/dx)/E)
where dE/dx
is in MeV/cm and E in kV/cm. At a drift field of 500 V/cm, The recombination factor R for aminimum ionizing particle is 70%. A comprehensive summary and analysis of charge yield is given
in [288].
The movement of the free electron charge towards the charge sensors is characterized by thedrift velocity, the charge loss due to impurities, and the diffusion. The drift velocity depends on thestrength of the electric field and slightly on the argon temperature (see table 35.9); a measurementof drift velocity vs electric field from [289] with a fit from [290] is shown in 35.22 (right). At an
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35. Particle Detectors at Accelerators

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 thesense electrodes is e−t/τ where τ is the electron lifetime. Values of τ exceeding tens of ms havebeen achieved [291–293]. 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
2 = 2Dt. Several measurements of the longitudinalsensor from diffusion after a drift of time, t, via σD
diffusion component, DL , have been made with a typical value around 0.4 mm2 /ms [281, 294–296].
For a 3 ms drift, this gives a contribution of (0.4 · 6)1/2 mm, ∼ 1.5 mm, to the spread of the charge.
Table 35.9: Some Detector Relevant Properties of liquid argon.
Property
Unit
Value
Stopping Power (m.i.p.)
MeV g−1 cm2
1.51−2
Radiation Length
g cm
19.6
Nuclear Interaction / Collision Lengthg cm−2120 / 76
Wel , Energy to form one electron-ion paireV
23.6 (±0.3) [278, 297]
Ion mobility
cm2 V−1 s−1
1.6 ×10−3 [298]−1Temperature dependence of drift velocity%K-1.7 [290]2−1Longitudinal diffusion coefficient, DL
mm ms
0.4 (see text)
Wph , Energy to produce one scint. photoneV
25 [299, 300]
Scintillation photon wavelength (vacuum)nm
128 ±8 (FWHM) [301]
Scintillation light inverse velocity
ns m−1
7.46 (±0.08) [302]Rayleigh scattering length (predicted)m
0.9 (±0.2) [302–304]
Scintillation Decay times fast/slow
ns
6 (±1)/1500 (±100) [276, 305, 306]
Dielectric strengthkV cm−1>40 [307, 308]
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 [301]. The relative populations of the two states
depends on the ionization density; typically 1:3 (singlet:triplet) for minimum ionizing and 3:1 forhighly ionizing nuclear fragments [305]. The long lifetime of the triplet state makes it sensitive toquenching impurities such as nitrogen or oxygen to which the excitation energy of the dimer canbe transferred without the subsequent emission of a visible photon [276, 311].
The propagation of the scintillation is affected by two processes: absorption and Rayleighscattering. 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 [277] level lead to lightabsorption. Rayleigh scattering increases the effective travel distance of photons between theirproduction point and their detection and for detectors where the distance between origin anddetection covers a range of many meters, the short Rayleigh scattering length for argon scintillation
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 excitationenergy 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].
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35. Particle Detectors at Accelerators

Figure 35.22: (left) the form of the light yield and the charge yield vs electric field redrawn
from [309]; (right) electron drift velocity vs electric field redrawn from [289].

35.7.4 LAr TPC topologies
Currently operating LAr-TPC detectors come in a range of sizes but the basic form of a cathodeand 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 theactive 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 fordetectors at surface, the slow-moving positive ions generated by the flux of cosmic rays distort thefield, particularly for TPCs with long drift [288, 293, 317–319]. Particular challenges in the drift
field system are the feed-through [259, 320] that brings the voltage from the HV supply outside thecryostat to the cathode (the cathode can sit at negative voltages up to 300 kV), avoiding damage tothe electronics from a potential cathode discharge [264], and ensuring the integrity of the field-cageresistor 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 perpendicular 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 areuseful in the 3D reconstruction procedures to remove ambiguities in the hit associations and incase 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. (Thecondition for transparency across one plane is derived in [322].) The drift electrons follow the fieldlines, inducing bi-polar current pulses on the first two planes, and terminate on the last one, thecollection plane, producing a unipolar signal [323].
The raw signal rise and fall times are a few µs as determined by the electron drift velocity andthe plane spacing, and any geometric effects from the track angles. The signals from each wire arerecorded 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
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35. Particle Detectors at Accelerators

56

Induced current

E2

t=0
FADC

Induction
1

FADC

Induction
2

FADC

Charge-> AreaCollection

E2

E1

>

E1

EdriftEdrift

p
V-t
view
d

Drift time

>

Y-t
view

U-t
view
d

Collection Induction Induction
12electronpaths
m.i.p. ionization~6200 e-/mm

Y

X
Z

Drift Time
Scintillation light yield~5000 γ/mm @ 128 nm

Drift direction

Edrift ~ 500 V/cm

Figure 35.23: Schematic of an event in the ICARUS 3 t LAr TPC; Top (from right to left): fieldlines from drift region to collection wires, electron flow & arrangement of wire-planes, signal shapeson the wires, and wave-forms from the continuous readout and digitization; Bottom: the passage
of a muon. The gray scale on the track indicates the ionization density.

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 electrical challenge in that long (>few m) cables from the sense electrodes to the first-stage amplifier will introduce an unacceptableamount of noise through their capacitance, and attempts to avoid such cables leads to impracticalconstraints on the charge sensor geometry; both of these are emphasized in [323]. To address thisproblem, 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, andsuccessfully deployed [324, 325]. The subsequent problem that individual feed-throughs for eachsignal in a detector with hundreds of thousands of channels complicate the cryostat structure
and raise the specter of leaks has been resolved by the development of flash-ADC and signal
multiplexers [326] that also operate in the liquid. These implementations have resulted in equivalentnoise charge levels of a few hundred electrons [293, 327] to be compared with a charge yield for am.i.p of 30000 e/MeV or, equivalently, 60000 e/cm. With such low noise, energy depositions 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 primary scintillation light. These
provide an event time for drift time measurement [328], a trigger [329, 330], calorimetry that canbe independent of and complementary to the charge [293], and event position information [265].
Given the VUV nature of the scintillation, a wavelength shifter is typically used to move the lightinto the visible [310]. Photo-multiplier tubes that operate in liquid argon were developed underthe 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 [264, 332, 333].
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35. Particle Detectors at Accelerators

35.7.5 Data Acquisition and event reconstruction
For the operation of large mass LAr-TPCs, the recording and storage of large volumes ofdata from the digitised charge waveforms and scintillation light channels is a critical issue. For
instance, 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 fromphoton detectors or from external sources (for instance a neutrino beam), to trigger the readoutof the TPC over a limited, predefined time window. The trigger rate is tuned to match thethroughput capabilities of the Data AcQuisition (DAQ). Recent advances in communication andcomputing technologies have reshaped the approach to DAQ for LAr-TPCs. It is now possible
to readout the complete digitised data and process them online [336], [337], allowing to identify
space-time Regions 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 andphoton detectors become truly complementary and their information can be combined online forhigh 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.
Generally, this proceeds in subsequent stages. (1) Signal Processing: the waveforms providing ameasure of the charge deposited in the TPC as a function of time are conditioned to mitigate
detector 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 readout LArTPCs produce 2D images in drift
time and coordinate transverse to the wire direction with, generally, 3 planes allowing for stereo
imaging for 3D reconstruction. Pattern Recognition (PR) approaches are distinguished between
those acting of the 2D images with matching of objects to build the 3D picture and those working inthe 3D space directly. The common goal is to find and reconstruct tracks and showers, their common
vertices and identify the event topology. An example of 2D to 3D PR is the Pandora package [341].
An example of a pure 3D approach is the WireCell package [342]. Recent efforts in PR aim at
employing sophisticated machine learning (ML) techniques. In the 2D-to-3D approach convolution
neural networks (CNNs) are applied on 2D images to identify objects which can be matched acrossplanes [343] [344]. In the 3D approach CNNs, graph neural networks (GNNs), etc., are used inseveral steps to de-ghost the original 3D image and perform full event reconstruction including
calorimetry, particle ID, etc. [345]. (3) The reconstructed tracks and showers are then passed tothe calorimetry and particle ID modules. These modules utilize the charge deposition per unit
length, after calibrations, to compute track and/or shower energy and particle identification [346].
35.7.6 Developments
The successful operation [347] of the ICARUS T600 TPC served as clear demonstration of thefeasibility of the liquid argon TPC technology on a massive scale. Since this milestone, the liquid argon TPC community has expanded and the technology has continued to evolve. Notabledevelopments include in-liquid electronics, the adoption of Silicon Photo-Multipliers and new lightcollection technologies, the use of dopants in the argon to improve the light performance, improved
techniques for wavelength shifting, the adoption of a cryostat technology which permits detector masses of tens of kilotons and, in a major change to the standard single-phase topology, theimplementation of pixelated readout to replace projective geometry in busy environments [348].
Technical R&D is continuing; as examples, the vertical-drift single-phase design for the second
DUNE far-detector that uses strips on perforated printed circuit boards as charge sensors [349],
a dual-phase TPC readout [350] using fast cameras to read out the scintillation light produced in
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35. Particle Detectors at Accelerators

58

the gas region in place of a charge readout; a light detection system powered and readout using
optical fiber allowing the readout to operate at any potential and therefore anywhere in the TPC,
and efforts to build up the HV directly in the liquid argon with a voltage multiplier (Greinacher
design) [351].
An abundance of data from recent experiments is encouraging insights into the liquid argon
medium as in [288,352] and revealing new phenomena. For a taste, see [353]. The ground is fertile,busy, and full of opportunity.

35.8 Semiconductor detectors
Revised August 2023 by N. Wermes (Bonn U.).
Semiconductor detectors provide outstanding detection opportunities in terms of position, energy and also time resolution, often in combination. In accelerator experiments, they are mostwidely used as position-sensing devices, e.g. in tracking detectors, or as photodetectors (Sec. 35.2),
for example in calorimeters (Sec. 35.10) or in imaging Cherenkov detectors (Sec. 35.5). In recent
years also precise time measurement (O(10–30 ps)) with silicon detectors has come into the focus
of development. When comparing semiconductor detectors particularly with gaseous detectors, themain features are high density and low ionisation threshold, providing in high resistivity substrates
comparatively large signals even without intrinsic amplification. Silicon detectors with active layers
only 100–300 µm thick provide adequately large and fast signals on a typical time scale4 of 10–50 ns.
Challenges are the purity of the semiconductor material, characterised by its mobility-lifetime (µτ )product, and its radiation resistance. The development of modern semiconductor detectors isstrongly interconnected with integrated circuit technology. Micro-processing and micro-electronics
technologies enable fabrication of high-density micron-scale electrodes on large wafers (6–8 in ≈ 15–
20 cm diameter for sensor wafers) and allow for high-density amplification and readout circuits
connected to them (chip wafer sizes are up to 12 in ≈ 30 cm with typical reticles of 26×33 mm2 ).
Some important material properties of common semiconductors used as detectors are summarised in Tab. 35.10. While for particle tracking the excellent position resolution is the main (butnot the only) interest, high stopping power and high energy resolution are key parameters in X-ray,
gamma-ray, and β spectroscopy, for example in neutrinoless double-beta decay searches. Due toits small bandgap, germanium excels in energy resolution but needs to be operated at very low
temperatures (liq. N2 ) to reduce thermally generated reverse bias current. Besides Ge, also GaAs,
CdTe and CdZnTe (CZT) feature high atomic numbers and hence much higher stopping power andshorter absorption length which is important, especially for X-ray detection. Diamond, fabricatedby chemical vapour deposition (CVD) and strictly speaking classified as an insulator with a large
bandgap (Tab. 35.10), features low Z and large radiation length X0 . Thanks to its radiation hardness (Sec. 35.8.5) it is used for particle detection in dedicated applications, especially in zones withhigh particle flux (see e.g. [354] and references therein).
Materials R&D for radiation sensors extends to other bulk semiconductors as well, for example,
ZnS, SiC, GaN or InP, and also to new material structures and metamaterials. Examples are semiconductor Quantum Dots, realised by nanometer-sized semiconductor “particles” embedded in asemiconductor bulk, or graphene, which – as a zero bandgap 2D material – features extraordinarily
high conductivity (electrical and thermal) as well as outstanding photonic properties. A bandgap
can be introduced by employing doped bi- or multi-layer graphene structures, thus rendering transistor and sensor realisations possible. The interested reader is referred to references [355] or [356],
for example.
Operating usually without intrinsic amplification, semiconductor detectors crucially depend on
4

Characterised here by the peaking time of the signal pulse.

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35. Particle Detectors at Accelerators

59

low-noise electronics (see Sec. 35.9), so the detection sensitivity is determined largely by signal
charge and input capacitance. Reviews of semiconductor detectors and electronics can be foundfor example in Refs. [1, 8, 357–359]
Table 35.10: Properties of some detector-relevant semiconductors; temperature-dependent quantities given at 300 K (from [1] and references therein).
Property

Si

Ge

GaAs

CdTe (CZT∗ ) Diamondatomic number (Z)
14
32
31/33
48/(30)/52
3
density ρ (g/cm )
2.328
5.327
5.32
5.85
dielectric constant 
11.9
16.0
13.1
10.2
semiconductor typeindirectindirectdirectdirectbandgap EG (eV)
1.12
0.66
1.424 1.44(1.44–2.2)−3
10
13
intr. carrier density (cm ) 1.09×10
2.4×102.1×106
107
radiation length X0 (cm)
9.36
2.30
2.29
1.52
average energy wi
3.65
2.96
4.35
4.43
for (e/h) creation (eV)mobility (cm2 /Vs)
electrons µn
1450
3900
8500
1050
holes µh
500
1800
400
90
lifetimeelectrons τe>100 µs∼ms
1–10 ns
0.1–2 µs
holes τh>100 µs∼ms
20 ns
0.1–1 µs
∗
†

6
3.51
5.7
indirect
5.5
≈0
12.15
13.1
≈1800†≈2300†≈100 ns≈ 50 ns

CZT = CdZnTe with the bandgap depending on the Cd to Zn ratio.
Approximate averages. Values quoted in the literature for the mobility in diamond vary strongly.

35.8.1 Signal generation in semiconductors
35.8.1.1 Creation of charges
Semiconductor detectors are solid-state ionisation chambers. Absorbed energy forms electronhole (e-h) pairs, i.e. negative and positive charge carriers which—when moving in an applied electricfield—generate a signal current on the electrodes by electrostatic induction (see Sec. 35.8.1.2). For
the signal charge carriers to (freely) drift in the electric field and to become detectable, semiconductors must feature small intrinsic charge-carrier densities (as existing for example in diamondand to some extent also in GaAs and CZT) or they must be depleted by reverse-bias junction
configurations (as for Si, Ge or CdTe). In addition, they should feature low intrinsic density ofdefects which can act as trapping or generation/recombination centers (see Sec. 35.8.5).
The minimum energy required to form an e-h pair is the bandgap energy (1.12 eV in Si, 0.66 eV
in Ge, 5.5 eV in diamond). However, impinging radiation or particles also release energy to lattice
vibrations (phonons) such that the average energy for e-h pair creation is higher. In an “indirect”
semiconductor like Si, the valence-band maximum is not at the same position in k-space (crystalmomentum space) as the conduction-band minimum and additional momentum transfer is required
for a band transition to occur. Since the “direct” bandgap energy without k-transfer in Si is 3.4 eV,
fewer-eV photons must receive momentum from lattice phonons. Because phonons are Bose-Einstein
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35. Particle Detectors at Accelerators

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distributed the needed momentum kick causes a steep rise in photon absorption probability between
1.12 eV and about 3.4 eV. For larger energy deposits the average energy wi needed to produce an e-hpair assumes a constant value of 3.65 eV at room temperature. For other semiconductors consult
Tab. 35.10.
For minimum-ionising particles, the most probable charge deposition in a 300 µm thick silicondetector is about 3.7 fC (∼23 000 electrons). In tracking detectors, a particle’s energy loss andscattering in the detector material should be minimal (large X0 ), whereas, for energy spectroscopy,
e.g. of X-ray photons, the stopping power should be maximised by choosing high-Z semiconductors5 .
A smaller bandgap (in fact a smaller wi ) leads to a larger signal per deposited energy and improves
the energy resolution, but also (exponentially) increases thermally excited carrier generation. To
cope with excessive leakage currents at room temperature, Ge diodes are typically operated at
liquid nitrogen temperature (77 K). In pure Si at 300 K, the intrinsic carrier concentration is ni '1010 cm−3 (Tab. 35.10), corresponding to a resistivity in the order of ρ ' (eµn)−1 ≈ 400 kΩ cm.
In reality, crystal imperfections and minute impurity concentrations limit Si carrier concentrations
to about 1011 cm−3 at 300 K (ρ ≈ 40 kΩ cm). In practice, wafer resistivities up to 20 kΩ cm areavailable, with mass production ranging from 1 to 10 kΩ cm.
The energy released in a semiconductor is absorbed by electronic excitations (e/h) and lattice
excitations (phonons) in an anti-correlated way. Therefore, for a fixed released energy E (forexample of an X-ray photon), the variance in the number of charge carriers N = E/wi follows
binomial statistics. Due to the energy constraint, this variance is√reduced by the Fano factor F
relative to Poisson
statistics (F ≈ 0.1 in Si and Ge). Thus, σN = F N and the energy resolutionpis σE /E = F wi /E. However, for semiconductors the measured fluctuations of a detected energy
signal are usually dominated by electronic noise rather than by signal fluctuations. The electronicnoise contribution depends much on the detector leakage current and the electrode capacitance aswell as on pulse shaping (i.e. the shaping time) in the signal processing electronics (see Sec. 35.9).
For X-ray detection, a major effort is made to find high-Z materials with a bandgap that is sufficiently large to allow for room-temperature operation while still providing good energy resolution.
Compound semiconductors, e.g. CZT, can allow this but typically suffer from charge collection
problems, which are characterised by the product µτ of mobility and carrier lifetime; this is thedepth per field strength that generated carriers can drift before being trapped, i.e. in this context
the distance over which photon absorption can still be detected.
In Si and Ge µτ is orders of magnitude larger than in compound semiconductors for bothelectrons and holes (see Tab. 35.10). Since for holes µτ is typically much smaller than for electrons, detector configurations where the electron contribution to the charge signal near the readout
electrode dominates—e.g. strip or pixel structures with electron collection—usually provide better
performance (see also next section).
35.8.1.2 Signal formation~ x),
The signal and its pulse shape depend on the instantaneous carrier velocity ~v (~x) = µE(~
µ = mobility, and the electrode configuration and its geometry which determine the distribution of
induced current according to the Shockley-Ramo theorem~ w (~x) ~v (~x(t)) ,iS (t) = N e E(35.20)~ w (~x) is the “weighting
where N e represents a drifting charge cloud of N elementary charges, E
field”, which accounts for the coupling of the charge to a specific electrode and depends on the~ andelectrode configuration; ~v is the drift velocity. Note the difference between the electric field E~
the weighting field Ew and take account of the fact that the mobility is, in general, field-dependent,
5

The cross section for photo effect scales as Z 5 .

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35. Particle Detectors at Accelerators

61µ = µ(E), with v ≈ const at high fields (velocity saturation, for electrons in Si approaching 107 cm/s
at E > 104 V/cm). Both, electron and hole movements contribute to an electrode’s signal. Hence,
if the carrier mobility is very different for electrons and holes, like e.g. in CdTe where µh  µe(Tab. 35.10), a photon signal, for example, becomes absorption-point dependent.
Integration of the induced current signal on an electrode yields the “collected charge”. The
average time to collect the created charge decreases with increasing bias voltage (i.e. field strength)
until velocity saturation occurs at field strengths of about 104 V/cm in Si.
For a simple parallel-plate geometry with two electrodes the weighting field is constant, whereas
for structured electrode geometries, like for example strips or pixels, Ew is position dependent which
for small electrodes (compared to the sensor dimensions) strongly enhances the contribution of the
movement close to the electrode (“small-pixel effect”). More details and practical accounts of the
Shockley-Ramo theorem and its usage can be found in [1, 8] and references therein.
Position resolution is ultimately limited by transverse diffusion of the moving charge cloud(typically 3–5 µm for 200–300 µm thickness) and by the emission of δ electrons. The performancethen depends on optimal usage of charge sharing between neighbouring electrodes and on noise. In
magnetic fields, Lorentz drift deflects the electron and hole trajectories thus increasing the spatial
spreading. The total spreading and hence charge sharing between electrodes can be tuned (increased
or decreased) by tilting the detector relative to the incoming (average) particle direction. Overall
spatial resolutions of 2–4 µm (rms) have been obtained.
35.8.2 Junction detectors
Si and Ge detector substrates must be—others like CdTe, GaAs should be and CZT can be—
depleted from free charge carriers by operating them as reverse-bias junctions (p-n or Schottky)
to be sensitive to the charge created by impinging particles. A typical cross-section of a junction
detector is shown in Fig. 35.24, here with structured electrodes at the top. A p-n junction—even
without external voltage—forms a sensitive space-charge region across itself depleted of mobile
charges, hence also called “depletion region”. The space charge establishes an electric field corresponding to a “built-in” voltage Vbi . Additional reverse-bias voltage V applied externally increases
the space-charge region such that injected charge liberated by radiation is swept to the electrodesby the existing field. Detectors typically use an asymmetric structure, for example, a thin andhighly doped p+ electrode6 region and a lightly doped n− substrate region – or vice versa, so thatthe depletion region extends predominantly into the more lightly doped bulk volume.
In such planar Si (or Ge) devices, the thickness of the depleted region isd=q2 (V + Vbi )/N e =

0.5
×
µm

s

0.3
≈
×
µm

s

≈

q

2ρµ (V + Vbi )ρVΩ cm · V

for n-type Si bulk

ρV
Ω cm · V

for p-type Si bulk

with (values for Si)
V = external bias voltage
Vbi = “built-in” voltage (≈ 0.5 V for typ. used resistivities)
N = doping concentratione = elementary charge
 = dielectric constant = 11.9 0 ≈ 1 pF/cm
6n+/++ , p+/++ as well as n− , p− qualitatively denote relative doping-concentration levels.

31st May, 2024

(35.21)

35. Particle Detectors at Accelerators62ρ = resistivity (typically 1–10 kΩ cm)µ = charge carrier mobility(∼ 1450 cm2 /Vs (electrons), ∼ 500 cm2 /Vs (holes) [360])
The conductive p and n regions together with the depleted volume form a capacitor with capacitance
per unit area
1 pF/cm
C0 = ≈
in Si.
(35.22)dd
The depletion depth d becomes as large as the sensor’s thickness at the “full depletion voltage”
V = Vf d for which the sensor capacitance reaches a minimum (about 35 pF/cm2 for d = 300 µm). In
strip and pixel detectors (see next section) the capacitance is dominated by the fringing capacitanceto neighbouring electrodes as the electrode pitch is typically much smaller than the sensor thickness.
For example, the strip-to-strip Si fringing capacitance is about 1–1.5 pF per cm of strip length ata strip pitch of 25–50 µm.

particle
track

metal
oxide
p+ implant
_
_
+
+ _

n substrate+ _depleted bulk+

undepleted

n+ implant+VbiasFigure 35.24: Reverse-biased junction detector with planar readout electrodes at the top in astandard sensor configuration (p+ -in-n): lightly doped n-type substrate with p+ implants forming
the diode junction at the top side. Electrons move to the bottom electrode and holes to the top.
Both movements contribute to the (induced) signal at the top electrodes with amounts as specified
by the weighting field (see Sec. 35.8.1.2). The n+ implant at the bottom side forms an ohmic
contact between bulk and metal.
The electric field strength and shape inside the semiconductor bulk are important for efficientsignal charge collection. Governed not only by the applied external voltage but also by the spacecharge inside the semiconductor bulk, leads (for constant space charge) to a linear field-strength
decrease from its maximum at the junction’s boundary into the depleted semiconductor bulk. Space
charge can also occur from ionised lattice defects which either naturally exist for example in GaAs
or can be created by irradiation in any semiconductor material. This can lead to low-field regions
as well as to changes in the field’s shape (deviating from linear), both of which usually deteriorate
the charge collection properties of a detector.
In partial depletion (i.e. V < Vf d ) the field decreases to zero at the end of the depletion zone.
Overbias (V > Vf d ) adds a constant electric field component which avoids a vanishing field region
and also provides faster charge collection as long as the carrier drift velocity has not yet saturated.
At an average field of E = 104 V/cm, the onset of velocity saturation, where µe ≈ 7×103 cm2 /Vs,µh ≈ 3.5×103 cm2 /Vs, the collection times for Si are about 15 ps/µm for electrons and 30 ps/µm
31st May, 2024

35. Particle Detectors at Accelerators

63

columns

activeedge~100 µm~50 µm

n
h

e

h

e

50−300 µm

p~50 µmFigure 35.25: Junction detector with vertical electrodes, n (red) and p (blue), and “active” edges
called 3D-Si. Dimensions given are typical. This electrode configuration provides short drift paths
for moving charges while keeping a large sensing thickness. An active edge minimises dead areasat the sensor boundaries. This geometry has also been employed in CVD diamond substrates.
for holes. In typical fully-depleted detectors, 100–300 µm thick, electrons are collected within lessthan about 5 ns, and holes within less than about 10 ns.
Large volume (∼ 102 − 103 cm3 ) germanium detectors, especially for γ-ray detection, are commonly configured in cylindrical or hexagonal rod shapes, for example, a 10 cm long cylindricaln-type crystal with 5–10 cm diameter with an inner 5–10 mm diameter n+ electrode and an outerp+ layer forming the diode junction. Germanium can be grown with fairly low impurity levels, 109 –
1010 cm−3 (HPGe, high-purity germanium), so these large volumes can be depleted with several
kilovolts.
Diamond, featuring free charge carrier densities close to zero, needs no further depletion and isoperated as a parallel plate capacitor with an insulator dielectric inside. Still, a substantial bias
voltage is required to overcome charge trapping.
35.8.3 Detectors with structured electrodes
35.8.3.1 Microstrip-, Si-drift- and hybrid-pixel detectors
In HEP experiments semiconductor detectors usually aim at good position resolution achieved
with electrodes patterned in “strips” or “pixels” with typical dimension scales (electrode pitch) of
50–100 µm, or in “pads” (mm2 –cm2 ) if coarser granularity is affordable for the benefit of fewer
channels.
Electrodes are usually placed “planar”, i.e., at the surface of the sensing Si bulk (Fig. 35.24).
In an alternative, but more elaborate way, electrodes can be shaped as columns or trenches running orthogonally to the surface and hence parallel to the average direction of impinging particles(Fig. 35.25) [361]. This geometry (termed “3D-Si”, but is also exercised with diamond) enhances
the radiation tolerance due to shorter drift distances of charges at the same thickness (see alsoSec. 35.8.5).
In strip detectors, the strip ends are connected to dedicated readout ICs where the signals
are amplified and processed. Two-dimensonal readout is realised either by angled double-layers of
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35. Particle Detectors at Accelerators

strip detectors or by “double-sided” strip sensors structured by readout strips on either side (seee.g. [1, 358] and references therein). For the latter, one electrode surface features n+ n or p+ p strip
junctions (rather than pn), respectively, which require dedicated measures, e.g. intermediate strips
or special doping profiles to break the electron accumulation layer that occurs at an n+ n interface.
For p+ p, intermediate n strips or similar are not necessary, thanks to positive oxide charges residing
at the Si/SiO2 interface.
As for gaseous driftchambers, silicon driftchambers provide the position of a hit orthogonal to a
strip’s coordinate from a measurement of the charge cloud’s drift time, drifting over centimeter-longpaths inside the silicon bulk. For this to work the bulk is “sidewards depleted” by using junction
strip implants of the same polarity on both sides of the sensor (p in n or n in p, respectively),
different to standard double-sided strip detectors (see e.g. [1]). This way a quadratic potential
minimum for electrons is created, confining them amid the sensor bulk, on which a linear electric
potential in drift direction is superimposed; holes, instead, drift to the sides. In comparison to
strip detectors, much fewer electrodes are necessary for the same active area coverage. Low ratecapability is a drawback caused by the long drift path of created charges. Arranged with only one
small electrode with low capacitance in the center of a cylindrical disk, so-called silicon-drift diodes(SDD) are low-noise single-channel devices with large area coverage, used for example in X-ray
fluorescence analysis and electron microscopy.
Very small pixel structures for particle detection were first realised with CCDs [362]. Most
current applications, particularly those for high-rate applications such as at the LHC, employ the“hybrid-pixel” concept in which both, the sensing diode structure as well as the readout IC, haveequal electrode structures and patterns (pixels). The connection is made by two-dimensional arraysof solder or indium bumps that mate the two parts by employing flip-chip technology (Fig. 35.26,
usually chip-to-chip or chip-to-sensor; more details e.g. in [358, 363]). Further advancements inbonding techniques especially address chip-to-wafer or even wafer-to-wafer placements, such as
SLID (Solid Liquid Interface Diffusion) employing a very thin liquid metal layer (Sn) in between
metals with higher melting points (e.g. Cu). Also, Cu–Cu, Cu–Sn, or oxide–oxide (SiO2 ) diffusion
bonding without solder is feasible.
The hybrid approach excels in optimally utilising chip and sensor technologies for radiation
hardness and rate capability (see e.g. [364]). It is, therefore, the technology of choice for pixel
trackers in high-rate, high-radiation environments optimised for the purpose by employing very thinmodules (O(300 µm) total). A disadvantage is the complex and cost-intensive module assembly.
35.8.3.2 Monolithic pixels
Partially or fully monolithic pixel detectors directly connect the generated signal charge with
an embedded active electronics device (i.e. one or several transistors). An example of a partiallymonolithic device is the DEPFET (depleted p-channel FET) pixel sensor (see e.g. [365]), employed,for example, in the pixel tracker of the Belle-II detector. A single transistor (pMOSFET) is implemented in every pixel (Fig. 35.27 (a)). The sensor substrate is “sidewards depleted”, as similarly
done in Si driftchambers (Sec. 35.8.3.1), by means of the backside p-contact and several p regions
near the transistor. Depletion is provided by the n+ clear contact (see below) plus a bulk n-implantoutside the matrix. In addition, the structure features a deep n-implant located a few micrometers
underneath the transistor channel on floating potential. This implant becomes the most positive
point of the structure, hence being an electron accumulation point, which acts as an “internal gate”
of the transistor. The gate voltage changes by an amount αqS /C, with qS = signal charge, gateoxide capacitance C = Cox W L with W ×L = gate area, and α . 1 accounting for stray capacitance.
The gate voltage changes due to an accumulated signal charge qS and leads to a detectable change
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65

35. Particle Detectors at Accelerators

particle
track
readout chipbump bondsensore

CMOSelectronicsnEhp substrate-VbiasFigure 35.26: Cross-sectional view of a hybrid-pixel detector cell (one pixel) consisting of sensor(bottom) and readout chip (top) with CMOS circuitry illustrated by three transistors (red and blue
implant areas plus metal lines). The sensor is a depleted diode structure (here p substrate with nelectrode). Both parts are mated by a microbond (bump bond), typically solder or indium.
in drain current (in saturation):
W
α qS
ID =
µCox VG +
− Vth
2L
C


2

.

(35.23)

Other elements in Fig. 35.27 (a) like the external FET gate and the clear implant provide control
and reset of the structure. The device gain gq = dID /dqS ≈ αgm /C, with transconductance−
gm = µCox W
L (VG − Vth ), is of order 500 pA/e . The small capacitance of the internal gate (few fF)
enables very low noise operation (. 2e− ) when operating with long shaping times (see Sec. 35.9).
Fully monolithic pixels combine the sensing task and the complete readout circuitry, i.e. thetwo separated parts of hybrid pixels, in one chip. Both functions must be properly shielded against
each other, which is achieved by exploiting multi-well IC technology. Realised as MAPS (monolithic
active pixel sensors) standard CMOS wafers can be used for pixel detector fabrication. CMOS
wafers often feature a Si epitaxial layer where the transistors are implanted. It is possible to use this
epi-layer as a sensitive detection volume for particle detection. However, in such detectors, only theimmediate regions near the collection nodes (see Fig. 35.27(b)) are depleted. Outside these confined
regions there is no or little electric field and charge collection is dominantly governed by slow andnon-directional charge diffusion, a problem for high-rate applications. Depleted MAPS (DMAPS)
exploit non-standard high resistivity wafers or high-ohmic epi-layers, typically with resistivities>1 kΩ cm, as well as high bias voltage (up to & 300 V) resulting in charge collection by directed drift
motion. Charge collecting electrodes are deep wells (n-wells in Fig. 35.27(b)), either formed as large(typ. 50×100µm2 ) structures to fully contain the CMOS circuitry (Fig. 35.27(b), top) or as small
31st May, 2024

66

35. Particle Detectors at Acceleratorschargesignalp+

CMOSelectronics
nw
pw
deep n wellp substrate-chargesignaln+pw-(a) DEPFET pixel structure.

p+

CMOS
electronics

nw
deep p welln+p substrate(b) DMAPS pixel structures.

Figure 35.27: Partially (a) and fully (b) monolithic pixels: (a) DEPFET pixel structure with anembedded pMOSFET transistor; source and drain are p implants (red), gate metal (black), oxide(grey), deep-n internal gate (light green), other metal (blue), clear contact (green), and deep p-well(brown). (b) Depleted MAPS with joint sensing and electronics volumes: (top) charge collection
by a large-electrode which houses the electronics in a deep-n well; (bottom) charge collection by asmall electrode set aside from the electronics area.

nodes, set aside the electronics (Fig. 35.27(b), bottom), with obvious pros and cons resulting fromshorter average drift distance (large electrode) versus much smaller capacitance (small electrode).
The former benefits radiation tolerance, whereas the latter allows for smaller pixels and benefits
from small sensor capacitance in noise and rise time. However, in both approaches radiation
tolerance levels of & 1015 neq /cm2 (fluence) and 1 MGy (ion. dose) have been demonstrated.
A variant of the monolithic approach are SOI (silicon on insulator) pixels providing high spatial
resolution, but less radiation tolerance: A high-resistivity supporting wafer, employed for particle
sensing, connects through an embedded insulator (a buried oxide layer, BOX) to the CMOS readout
circuitry. The BOX separates the sensing volume from the electronics layer and provides shielding.
Because the area between BOX and the transistor layer acts as a “back-gate”, transistor operation
can be affected requiring dedicated cures (see e.g. [366]).
35.8.4 Precise timing with silicon detectors
Typical time scales for silicon detector output signals are several tens of nanoseconds (e.g.
rise times, shaping times, etc.) accompanied by a typical time mark precision in the order ofnanoseconds. Essential for achieving precision timing (< 100 ps) are steep signal rise and low
noise according to eq. (35.38) in Sec. 35.9. This, in turn, requires fast charge collection, e.g. inthin planar or 3D-Si detectors with high E-fields, as well as fast and strong amplification, both
together yielding large slew rates (dS/dt, with S=“signal”, e.g. an induced current or a voltage).
Important parameters that influence timing precision are the detector capacitance (including stray
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35. Particle Detectors at Accelerators

67

contributions) and the amplification gain.
Detectors that have achieved precise time measurement are so-called LGADs (low gain avalanche diodes, Fig. 35.28). They have planar electrode geometry that includes an implanted lowgain (g = 10–50) amplification structure on either the top or bottom electrode side to maximise theslew rate. Electrons created from ionising traversing particles are accelerated towards a very highfield created by an amplification layer near the (here) top electrode, where impact ionisation createsa multitude of e-h pairs. They induce a very fast and large signal rise, mainly governed by theholes’ movement away from the amplification layer. Sufficiently low amplification gain minimises
excess noise contributions and avoids the creation of hole-induced avalanches moving in the opposite
direction to electron avalanches.

300 kV/cm

n++ electrodep++ electrodeJTE

p+ multiplication layer
high res. p-substrate

20 kV/cm

50 - 300 µm

typ. 1–5 mm

|E|

Vbias

x

Figure 35.28: LGAD amplification structure for precision timing. Amplification (typ. × 20–50)
occurs at the structure boundary in a highly doped p-n junction near the (here: top) surface (JTE
= Junction Termination Extension, deep n-well).
The achievable time resolution has several contributions:
σt2 ≈

σSthr
dS/dt

!2



+

σn
dS/dt

2

2
2
2
+ σarrival+ σdist+ σTDC.

(35.24)

The first term represents “time walk” coming from Landau fluctuations, defined as originatingfrom number and energy-transfer fluctuations in the energy-loss process with σSthr being the signalheight variations at discriminator threshold. This term can be kept minimal, e.g., by employing
constant fraction discrimination or by applying corrections using amplitude information. The
second term is the contribution of noise to the time jitter, which can be approximated by (tr /SNR)2
with tr = rise time, SNR = signal-to-noise ratio. Both first terms are kept small by large signal
slew rates. An irreducible contribution comes from fluctuations in non-uniform depositions ofcharge along the particle path (including fluctuations in the amplification process) which causes
an intrinsic jitter in the arrival time (third term)7 . The thinner the detector the less disturbing is
this effect. The fourth contribution is signal distortion due to non-uniform weighting field regions
and variations in (non-saturated) drift velocities. “Junction Termination Extensions” (JTE, seeFig. 35.28) serve to lower this term. The final term denotes time fluctuations due to uncertainties
in digitization, which can, however, be made negligible with GHz TDCs. Timing precision oforder 30 ps has been reached. Structural and operational variants to improve charge collection andposition resolution are “resistive AC-coupled LGADs”, “deep junction LGADs”, “trench-isolated
LGADs” and others. More details on LGADs are given in [367] and [368].
Columnar electrode geometries such as shown in Fig. 35.25 with small diameter and small pitch
are by design a very suitable choice for precision timing due to short collection paths and strong
7

In LGAD literature these fluctuations are sometimes also referred to as “Landau fluctuations”.

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35. Particle Detectors at Accelerators

fields. Employing an optimised trench-like column shape field- and weighting-field distortions areminimised and time resolutions in the order of 10 ps have been achieved in prototypes [369].
High precision timing can also be approached by exploiting the benefits of SiGe BiCMOS
technology: strain mismatch of Si-Ge alloy layers results in a smaller bandgap as well as higher
mobility and hence larger transconductance. This benefits the speed in hetero-junction bipolartransistors (HBTs) which also feature less 1/f noise than MOS transistors. Resolutions of order
20 ps have been reached in a monolithic pixel matrix using this technology [370]. More elaborate
discussions on timing in silicon detectors can be found e.g. in [371].
35.8.5 Radiation damage in silicon detectors
High channel density and response times in the nanosecond range render micro-patterned semiconductor detectors particularly suited for high particle rates. This is usually accompanied by highradiation causing damage of sensors and front-end electronics. We restrict ourselves here to damage
in Si detectors and their electronics. Radiation damage occurs in semiconductor detectors throughtwo basic mechanisms:
1. Bulk damage due to displacement of atoms from their lattice sites resulting in defect energy
levels inside the band gap. This leads to increased leakage current, carrier trapping, andbuild-up of space charge that changes the required operating voltage. Displacement damage
results from non-ionizing energy loss (NIEL). The energy imparted to the recoil atoms caninitiate a chain of subsequent displacements including “damage clusters”. For a description, it
is critical to consider both, particle type and energy. Conventionally, for silicon, the received
NIEL is normalised to the damage level caused by 1 MeV neutrons and specified in units ofneutron-equivalent fluence Φeq with units neq /cm2 .
2. Surface damage due to charge build-up in surface layers and formation of interface traps at e.g.
Si–SiO2 boundaries. These influence transistor currents and thresholds or cause thin charge
carrier layers at a silicon surface, leading to increased surface leakage currents in sensors or
circuits and affecting electrodes’ isolation and/or transistor characteristics. The effects ofcharge build-up are strongly dependent on the device structure and on fabrication details.
The damage is dominantly due to ionising energy loss (IEL) and hence proportional to theabsorbed total ionisation dose (TID) measured in Gy (or rad), independent of the particle
type.
The increase in reverse bias generation current (leakage current) due to bulk damage is ∆IL= αΦeq V , where V is the volume under an electrode and α ' 4 × 10−17 A/cm, a universal constantwhen normalised to temperature (conventionally 20◦ C), and measured after annealing for 80 min at
60 ◦ C. Note that for devices with intrinsic amplification, generation current is amplified accordingly.
Reverse bias leakage current depends strongly on temperatureIL (T ) ∝ T 2 exp −

Ea
2kT



,

(35.25)where Ea ≈ 1.2 eV (activation energy), so rather modest cooling can reduce the current substantially(∼6-fold reduction in cooling from room temperature to 0 ◦ C).
For bulk damage in silicon, the NIEL hypothesis is a good first-order description of the observed
damage (especially regarding IL ). It states that all lattice radiation damage in silicon linearly scaleswith NIEL and can be traced back to the abundance of primary defects (point defects and clusters),
irrespective of their initial distribution over energy and space, that is, regardless of the damage’s
topology and origin. Under the NIEL hypothesis, the observed differences in damage caused byneutrons, protons, pions and electrons are hence usually scaled to each other.
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35. Particle Detectors at Accelerators

conduction band
donor (+)

acceptor (–)

valence band(a) charged defect(b) generation –(c) trapping
recombination center
centerFigure 35.29: Characteristic locations of energy levels caused by bulk radiation damage and theirmain action effects.
Three main bulk displacement damage effects are sketched in Fig. 35.29: (a) defects acting as
charged donors/acceptors, (b) deep defects (near the middle of the bandgap) causing increased
leakage current, and (c) carrier trapping centers. Damage effects are not constant with time; forexample in n-type bulk, radiation-induced negative space charge anneals at first, reaching a stabledamage minimum (beneficial annealing), but later electrically active defects (negative space charge
from acceptor-type damage) build up over the time scale of months (reverse annealing).
Acceptor- (usually dominant) or donor-like (deep) defect states, when ionised, build up spacecharge (dominantly negative), which in turn normally requires an increase in the applied voltage
to sweep signal charge through the detector thickness. For n-type bulk starting material, however,donor (e.g. phosphorous) removal by forming electrically inactive vacancy-phosphor (V-P) complexes induced by the incipient radiation, leads to a faster decrease in depletion voltage (fasterthan only by the compensation of donors through generated deep acceptors) until positive and negative space charges effectively balance; only little bias voltage then is required for operation (pointof effective space charge inversion, also called “type inversion” (Fig. 35.30)). At larger fluences thenegative space charge dominates, and the required operating voltage increases proportional to theincreasing effective space charge density Neff , also called effective doping concentration. Also thespace-charge distribution can no longer be regarded as constant and homogeneous over the detector
volume, thus destroying the linear slope of the electric field from the junction to the backside as
was introduced in Sec. 35.8.2; instead “double-junction”-like field distributions typically occur.
Today, p-type silicon with n+ electrode-implants is the preferred choice for sensors operating in
high-radiation environments for reasons of cost-effectiveness in production as well as high radiation
hardness due to fast (high mobility) electron collection in high electric- and high weighting-fieldregions at small segmented n+ electrodes. Space charge inversion is usually not observed since theinitial space charge is negative already (Fig. 35.30).
Removal of acceptors (i.e. substitution of electrically active boron at its lattice site) in p material is found to be dominantly caused by interstitial silicon replacing boron on its lattice position.
The highly active interstitial boron then can cause the formation of other defects such as interstitial oxygen-boron complexes (Bi Oi , subscript i for “interstitial”) which absorb boron atoms into
electrically active defects, dominantly as donors, that means that space charge is changed twice.
Various techniques have been explored to neutralise radiation damage effects by defect engineer31st May, 2024

35. Particle Detectors at Accelerators

70

3

10

2

10

1

100

10

0

10

-1

10 -1
10

5000

p-Si (FZ)

1000

type inversion
n-type10“p-type”
0

10

1

10

2

10

3

(d ≈ 300 µm)

10Vdep (V)|Neff | (1011 cm-3)

ing. For n-type material, oxygen enrichment with a larger abundance than phosphorus, introduced
during the Si growth, successfully reduces the formation of multi-vacancy, acceptor-like complexes
which are dominantly produced by charged hadrons, because it enhances instead the formationof electrically neutral V-O complexes. Carbon enrichment, on the other hand, reduces acceptor
removal in p-type Si by building stable Ci -Si complexes, thus trapping the Si interstitials which
could else remove boron as described above.

1Φeq (1012 cm-2)
Figure 35.30: Effective space charge concentration Neff (left axis) and required voltage for full
depletion Vdep (right axis) of approximately 300 µm thick Si sensors as a function of neutronequivalent radiation fluence for typical n-type (blue) and p-type (black) silicon float zone (FZ)
material before annealing. While initial n-type Si inverts to effectively p-type Si, this is not observedfor initial p-type silicon. Bias voltage supply for large systems is usually limited to less than 600–
1000 V. Figure adapted using [372, 373] and [374].
Dopant removal plays a particularly important role in more complex sensor structures such as,
for example, DMAPS or LGADs. In particular, the high p-doping concentration in LGAD’s gain
layer is vulnerable to acceptor removal causing a drastic gain decrease with increasing fluence.
Deep level defects (Fig. 35.29(b)) typically are the origin of leakage current increase, whereas
trapping centers (Fig. 35.29(c)) dominate carrier lifetime and signal loss at high fluences beyond
1015 neq /cm2 . The safe limit on the operating voltage ultimately limits the detector lifetime. Stripand pixel detectors, specifically designed for high voltages, have been extensively operated at bias
voltages of 500–600 V. Sensors with columnar electrodes normal to the surface (3D-Si, Fig. 35.25)
need significantly lower voltages for full depletion and are prime contenders for radiation-hard
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35. Particle Detectors at Accelerators

sensors.
Synthetic CVD diamond has proven strong against radiation damage due to its large bandgap(see Tab. 35.10) and strong lattice binding with a roughly twice higher threshold (∼ 40 eV) for adisplacement of lattice atoms than silicon (see e.g. [354]). Even for polycrystalline material, chargecollection distances (CCD = sum of the mean free paths µτ E of e and h over which charges reachthe electrodes) of 300–400 µm have been achieved. Diamond wafer cost, however, is comparatively
very high. Smaller scale trackers acting e.g. as beam monitors have been built.
GaAs has received interest as a potentially radiation-hard material in the 1990ies. For particle
detection it must still be depleted from charge carriers despite comparatively small intrinsic carrier
densities (see Tab. 35.10). It suffers from a strong loss in charge collection efficiency when irradiated,dominantly because of electron trapping. Other semiconductor materials such as SiC or GaN featurewider bandgaps (3.26 eV and 3.39 eV, respectively) than Si (but smaller than diamond) and possessother suitable properties relevant to high-fluence operation, such as density, e-h ionisation energy,
and displacement energies. They have regained attention after the material quality has improved
much due to an industrial push coming from power devices and LEDs. So far, charge collection
degrades faster with radiation fluence than for Si and diamond, however.
Strip and pixel detectors have remained functional in large detectors even at particle fluences
well beyond 1015 neq /cm2 where charge loss due to recombination and trapping becomes significant.
Thin planar (∼100 µm) and 3D silicon detectors have been successfully operated at fluences of 2
and 3 × 1016 neq /cm2 , respectively, and measurements indicate that operation above 1017 neq /cm2
does not seem impossible. The large SNR obtainable with low capacitance pixel structures extends
the detector lifetime. The higher mobility of electrons makes them less sensitive to carrier lifetime
than holes, so detector configurations that emphasize the electron contribution to the charge signal
are advantageous, i.e. n+ strips or pixels on p- or n-substrates. The occupancy of the defect charge
states is strongly temperature dependent; competing processes can increase or decrease space charge
and the required operating voltage. It is critical to choose the operating temperature judiciously(−30 ◦ C to 0 ◦ C in typical collider detectors) and to limit warm-up periods during maintenance.
Detailed discussions of radiation damage and its effects on semiconductor detectors can be founde.g. in [373, 375]; an introduction to the subject can be found in [1].
Tolerance against surface damage, especially in SiO2 layers as in gates and in oxide trenchesof CMOS transistor structures, largely depends on the feature size of a technology and on appropriately designed circuitry. Deep submicron technology nodes of 130 nm and 65 nm sustain total
ionisation doses of up to 5 MGy (500 Mrad), corresponding to fluences of up to 5 × 1015 cm−2 ofminimum ionising pions or protons.

35.9 Low-noise detector readout
Revised November 2021 by N. Wermes (Bonn U.), revised November 2013 by H. Spieler (LBNL).
Many detectors rely critically on low-noise readout electronics, for best energy resolution or
to allow low thresholds for high detection efficiencies. A typical detector front-end is shown in
Fig. 35.31.
In a model relevant to most readout applications, the detector, represented by a capacitance
Cd , delivers a delta-function-shaped current signal, represented by a current source in parallel. Bias
voltage is applied through resistor Rb and the signal is (often) coupled to the amplifier througha blocking capacitor Cc . The series resistance Rs represents the sum of all resistances present in
the input signal path, e.g. the electrode resistance, any input protection network, and parasitic
resistances in the input transistor. The amplification stage contains the preamplifier providing
gain and a pulse shaper (characterized by a shaping time τ ), which tailors the overall frequency
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35. Particle Detectors at Accelerators

72

DETECTOR BIAS
BIAS
RESISTORPREAMPLIFIER

Cf

Rb

P
DETECTOR Cd

is(t)

Cc

Rs

PULSE SHAPER

OUTPUT

Figure 35.31: Typical detector front-end. The dashed circuit part is a charge-sensitive amplifier(CSA) realization.

response to optimize the signal-to-noise ratio (SNR) while limiting the duration of the signal pulse
to accommodate the signal-pulse rate. For a given input signal, purely random noise leads to agaussianly smeared signal distribution behind the shaper. Even if not explicitly stated, all amplifiers
provide some form of pulse shaping due to their limited frequency response.
It is useful to distinguish between noise inherent to a detector’s signal amplification and processing circuitry (per channel) on the one hand, depending on the detector specifics and the experimental environment (e.g. the data rate), and — on the other hand — external noise sources
introduced e.g. by systems external to a specific readout circuit often resulting in “common-mode”
noise, i.e. common to all channels. External noise can be introduced from power supplies, digital
signal switching, RF pick-up, or from effects due to “common grounding” allowing noise to couple
to the current loop connecting the detector to the preamplifier. These noise sources differ fromsetup to setup and must be dealt with – and should at best be eliminated – individually. In thefollowing, therefore, only the noise inherent to typical detector signal processing is discussed.
35.9.1 Principal noise origins
As principal noise origins in circuit elements we mainly distinguish thermal noise resulting fromvelocity fluctuations of charge carriers (Brownian motion), as well as shot noise and 1/f noise,both resulting from charge carrier number fluctuations. Shot noise is due to emission statistics
of electrons crossing a barrier, 1/f noise is often — especially in MOSFETs — due to charge
trapping–detrapping processes leading to a spectral behaviour as 1/f α with α = 0.5 . . . 2. Further
noise nomenclature, like for example RTS (random telegraph signal) noise, also called “burst noise’or “popcorn noise”, is in its origin usually related to trapping/detrapping processes, like 1/f noise.
The popping-up nature of individual RTS bursts eventually leads to the 1/f noise spectral density
when the noise of several traps with (very) different trapping times are superimposed. RTS noise
is omitted in the following for simplicity reasons.
35.9.2 Equivalent noise analysis
The equivalent circuit for noise analysis (Fig. 35.32) shows contributions of the mentioned noise
sources at several circuit points. Originating from fluctuations, noise is expressed as the variance
hi2 i or hv 2 i of a noise current or voltage distribution. Shot noise, such as that produced in asemiconductor detector by leakage current fluctuations, is represented by a current noise generator
in parallel with the detector and the amplifier input. The statistical fluctuations in a charge
measurement will scale with the square root of the total number of recorded charges, so this noise
contribution increases with the measurement (shaping) time. Thermal noise in resistors produces a
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35. Particle Detectors at Accelerators73

white noise, i.e. a noise power density independent of frequency. Hence limiting the bandwidth by ashaper, i.e. increasing the shaping time, will decrease the noise at the expense of slowing down thedetector response. Usually, resistors shunting the input act as noise current sources and resistors
in series with the amplifier input act as noise voltage sources, so that they are often referred toas “parallel” and “series” noise. Thermal fluctuations in the bias resistor result in fluctuations of
the voltage at point P in Fig. 35.31 and its noise current source hi2b i has the same effect as theshot noise current hi2d i from the detector. Conversely, the series resistor Rs acts as a voltage noise
generator hvs2 i for the amplifier input.
Shot noise and thermal noise have a “white” frequency distribution, i.e. the (power) spectral
densities (f = frequency) dhi2 i/df and dhv 2 i/df are constant with magnitudes
dhi2d i = 2eId df ,4kT
dhi2b i =df ,Rb
dhvs2 i = 4kT Rs df ,(35.26)

where e is the elementary charge, Id the detector leakage current, and k,T Boltzmann constantand temperature. Hence, in ap
1 kΩ resistor at roomfor example,√ temperature,√ one finds a currentp22
independent thermal noise of dhi i/df = 4 pA/ Hz or dhv i/df = 4 nV/ Hz, respectively. For
1/f noise, by contrast, the spectral power density is proportional to 1/f α (α = 0.5–2) with a device
specific proportionality constant. In what follows, we will assume α = 1 for simplicity reasons,noting though that more complex models exist.

BIAS
RESISTOR

DETECTORSERIESRESISTOR

vs2

Rs

Cd

Rb

id2

AMPLIFIER +PULSE SHAPER

va2

ib2

input
transistor

2
ich

vsh2

Figure 35.32: Equivalent circuit diagram for noise analysis.
An important noise source is the preamplifier input stage, very often dominated by the first
amplification transistor. In what follows we assume a MOSFET at this point, as the large majorityof amplification circuits is based on MOS transistors. Noise sources in bipolar amplification isshortly mentioned at the end of this section. A MOS transistor’s channel features thermal noisewith “resistance” 1/gm , where gm = ∂I/∂V is the transconductance. Correction factor(s) forparametrization depend on the transistor operation point. Conventionally, a factor γ is applied
varying between 0.5 and 1 when temperature dependence is implicit, but is commonly taken asγ ≈ 2/3 for operation in strong inversion and 0.5 in weak inversion.
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35. Particle Detectors at Accelerators

74

In addition, especially in MOSFETs, there is 1/f noise originating from trapping/detrapping
processes of charge carriers at the channel’s Si–SiO2 interface. The channel’s current noise isequivalent to a voltage noise at the transistor input (the gate) via
hi2ch i = h(gm va )2 i

(35.27)

leading to respective noise power spectral densities of
dhva2 i1
1
1
+ Kf 0= 4kT γ,df
gm
Cox W L f

(35.28)where the individual (uncorrelated) noise contributions add in quadrature. The “1/f noise constant” Kf has magnitude in the order of 10−24 – 10−26 J depending on the device type and the
0 is the oxide capacitance per unit area, and W, L are width and length of the gate.
technology8 . Cox
Particle and radiation detectors typically convert the deposited energy into charge (usually eion or e-h pairs) which can be measured by integrating the current induced on an electrode by
the drifting charge pairs (see e.g. Sec. 35.8) employing a “charge-sensitive (pre)amplifier” (CSA),
realized by feeding back the preamp’s output to the input through capacitor Cf (dashed circuit
part of Fig. 35.31). The feedback capacitance must be discharged for the next pulse to appear,
for example by a resistor, a (constant) current source or a switch. Noise contributions from suchcomponents can usually be kept small in comparison.
2 i relates to the input (current or
For a CSA the noise output voltage after the preamplifier hvpa
voltage) noise sources via the transimpedance 1/ωCf as
D

2
vpa

E

=

D

i2in

E

!2

1
ωCf

or

D

2
vpa

E

=

D

2
vin

E

ωCD
ωCf

!2

(35.29)with ω = 2πf . The capacitance CD includes the detector capacitance Cd plus all capacitances
shunting the input. Considering only the (usually) dominant noise sources, being the detector shotnoise as well as the transistor channel noise, and neglecting the resistor parallel and serial noise
sources of (35.26) by choosing Rb large and keeping Rs small, one obtains
D

2
d vpa

E

=

dω
with
c−2 =

1
e
Id 2 ,
π Cf

c−1 = Kf

0X

ck ω k

(35.30)

k=−2
2
1
CD
,
0 W L C2
Cox
f

c0 =

2
2γ
1 CD
kT
,
π
gm Cf2(35.31)

which correspond to the discussed main noise components, c−2 : shot noise, c−1 : 1/f noise, c0 : thermal noise, respectively.
The filtering effect of the shaper limits the bandwidth of the system and is generally described
2 i integrated over the full bandwidth
by a transfer function H(ω) for hvpa
D

E

2
vsh
=

Z ∞
0

2 i
dhvpa
|H(ω)|2 dωdω

(35.32)2 i being the shaper output voltage noise. H(ω) depends on the filter circuit, i.e. the shapewith hvsh
of the pulse formed by the shaper, and is characterized by a characteristic time τ , the shaping time,
8

Other 1/f noise parametrizations also exist with correspondingly different numerical values for Kf .

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35. Particle Detectors at Accelerators

75

which can, for example, be the peaking time of a semi-gaussian pulse or the sampling interval ina correlated double-sampler (see e.g. [8]). The peaking time is an important quantity for readout
systems since for peaking times large compared to the duration of the input signal the amplitude
at peaking time corresponds to the total input charge.
For a simple time-invariant CR–RC filter, consisting of a high-pass followed by a low-pass filter
with equal time constants, the transfer function is|H(ω)|2 = A2ωτ
1 + ω2τ 2

2(35.33)and (35.30) becomes
D

2
vsh

E

π
= A2
4



2
1
c−2 τ + c−1 + c0πτ(35.34)

with A being an overall gain factor.
The system noise for a charge measurement is conveniently expressed as an equivalent noise
charge (ENC) referring the noise to the equivalent signal of one electron at the input:
ENC2 =

2 i
hvsh
.
2
vsignal (1e− )(35.35)

While being dimensionless by definition, ENC is commonly expressed as an equivalent number ofelectrons (e− ) at the input or alternatively as equivalent Coulombs (C) when multiplying by theelementary charge or as equivalent deposited energy (eV), where 1e− equivalent charge corresponds
to 3.65 eV of equivalent deposited energy in Si (see Tab. 35.10 in Sec. 35.8).
A charge of one electron at the input yields a voltage signal (peak) behind the shaper ofA evsignal =. Hence with (35.35) and (35.34) one obtains:
2.71 Cf
2

ENC (e−2(2.71)2)=4e2

2eId τ + 2CD
Kf

21
2kT CD
+
γ
0 WL
Cox
gm τ

2
= ashot τ + a1/f CD+ atherm

2
CD
,
τ

!

(35.36)

where 2.71 is Euler’s number resulting from the amplitude peak value behind the (CR–RC) shaper(for t = τ ), while e is the elementary charge and (e− ) explicitly denotes the equivalent number ofelectrons at the input.
Equation (35.36) accentuates the main noise dependencies of the system. The contribution
from parallel current shot noise (i.e. detector leakage) increases with shaping time, i.e. with pulse
duration, whereas thermal noise (here serial voltage noise at the gate, originating from transistor
channel noise) decreases with increasing shaping time, i.e. with reduced bandwidth. Noise witha 1/f spectrum depends only on the ratio of upper to lower cutoff frequencies (low pass to highpass time constants) and is hence independent of τ for a given shaper topology. Furthermore, thecontribution of serial noise voltage (1/f and thermal noise) to ENC increases with input (detector)
capacitance CD . Pulse shapers can be designed to optimize the noise performance of a systemor to mitigate operation variations with time (e.g. due to radiation damage) deteriorating theperformance, at the expense of loss of simplicity. For example, a shaper with one high-pass filter
followed by four cascaded low-pass filters, increases the pulse symmetry and tends to decrease thecurrent noise, but increases the voltage noise contributions for the circuit of Fig. 35.32, if the same
peaking time is assured by adjusting the individual time constants of the filter stages. If instead
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35. Particle Detectors at Accelerators76

the low-pass filters cause the peaking time of the pulse to increase, the opposite can be true. Moredetails about shaping filters can be found e.g. in [8, 376–378].
Figure 35.33 shows a typical example of eq. (35.36) displaying ENC as a function of shaping timeτ for a system. At short shaping times, thermal noise dominates, whereas for longer shaping times
the shot noise contribution takes over. The total noise has a minimum at a shaping time where
shot and thermal noise contributions are equal. The minimum is flattened by the presence of 1/fnoise. Increasing the detector capacitance increases the thermal and 1/f contributions and shifts
the noise minimum to larger shaping times. One can hence exploit the shaping time dependence ofthe total noise to determine the individual noise contributions of a system.

Equivalent noise charge (e- )

10000
5000

Increasing Cd

2000

Total

1000
500

1/f noise

200
100
0.01

Total

0.1

rm

o
tn

o

sh

the

ise

1

Shaping time (μs)

al

no

ise

10

100

Figure 35.33: Equivalent noise charge vs shaping time. Changing the detector capacitance CD
affects thermal and 1/f noise contributions and moves the noise minimum as indicated by the dottedand dash-dotted lines. The 1/f noise contribution is small for the chosen parameters (CD = 20 pF,
Id = 10 nA, gm = 1 mS) in this example.
For quick estimates (35.36) is cast into a useful equation for a typical CSA-shaper system [1]:2

ENC2 (e− ) = 11

2
2 /(100 fF)2
Id τ
1
CD
1
CD
+ 740
+
4000
,
nA ns
W L/(µm2 ) (100 fF)2
gm /mSτ /ns(35.37)

0 = 6 fF/µm2 has been used, the latter being typical forwhere γ = 2/3, Kf = 33 × 10−25 J, and Cox
CMOS technologies as employed for example for the detector readout chips of the LHC experiments
and their upgrades. Generally, noise performance is improved by reducing the detector capacitanceand the leakage current, judiciously selecting all resistances in the input circuit, and by choosing
the optimum shaping time constant τ . Another noise contribution to consider is the fact that noise
can cross-couple from the neighbouring front-ends in detectors with structured electrodes throughthe inter-electrode capacitance.
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35. Particle Detectors at Accelerators

As mentioned, the noise parameters of the amplifier depend primarily on the input device (input
transistor(s)). In field-effect transistors, the input noise current contribution of the transistor itself
is very small. Hence, if the experiment’s time structure permits, reducing the detector leakage
current and increasing the bias resistance will allow long shaping times with correspondingly lower
noise. For amplifiers employing bipolar transistors, shot noise sources originate from both, baseemitter and collector-base, junctions and from the series resistance at the base which is especially
important for small structures optimized for radiation hardness. For the shot-noise contribution,
the input base current IB sets a lower bound on the noise current, such that these devices are bestat short shaping times.
35.9.2.0.1 Examples Using (35.37) one finds for a typical pixel detector (before heavy irradiation) with CD = 200 fF, Id = 1 nA, τ = 50 ns, W = 20 µm, L = 0.5 µm, gm = 0.5 mS:
ENC2 ≈ (24 e− )2shot+ (17 e− )2

1/f+ (25 e− )2therm≈ (40 e− )2 .

For a typical silicon microstrip detector after radiation damage (fluence & 1014 neq /cm2 , assuming no degradation of the front-end electronics due to radiation) one obtains for CD = 20 pF, Id =1 µA, τ = 50 ns, W = 2000 µm, L = 0.4 µm, gm = 5 mS:
ENC2 ≈ (750 e− )2shot+ (200 e− )2

1/f+ (800 e− )2≈ (1100 e− )2 .

therm

Apart from the larger leakage current, the larger capacitance of strips compared to pixels leads toa much worse noise performance which can only be partially compensated by allowing more powerin the amplification transistor, i.e. by increasing gm .
A liquid argon calorimeter cell is a suitable example of a detector with a large electrode capacitance with typical parameters (similar to the ATLAS central electromagnetic calorimeter, seeSec. 35.10). Using CD = 1.5 nF, Id = < 2 µA, τ = 50 ns, W = 3000 µm, L = 0.25 µm, gm = 100 mS,
one obtains:
ENC2 ≈ (1000 e− )2shot+ (15000 e− )2

1/f+ (13500 e− )2therm≈ (20200 e− )2 .

Here only a small (negligible) parallel shot noise (leakage current) contribution is assumed, which
is typical for liquid argon calorimeters.
Practical noise levels range from ∼1e− for CCD’s at long shaping times to ∼104 e− in highcapacitance liquid argon calorimeters. Gaseous micropattern detectors like GEMs or MicroMegas(see Sec. 35.6.4) typically feature noise levels between 1000 e− and 1500 e− , depending on the ability
to correct for common-mode noise. Silicon strip detectors typically operate at levels of ∼103 e− ,whereas pixel detectors with fast readout typically have noise levels below about 100 electrons.
35.9.3 Timing measurements
In timing measurements, the slope-to-noise ratio must be optimized, rather than the signalto-noise ratio alone, so the rise time tr of the pulse is important. The “jitter” σt of the timing
distribution is
σn
tr
σt =
≈
,
(35.38)(dS/dt)trig
SN R
where σn is the rms noise, SNR the signal-to-noise ratio and the “slew rate” dS/dt, i.e. the derivativeof the signal, is evaluated at the trigger level. The rise-time of a CSA again depends on the detector
and feedback capacitances and on the amplifier transconductance
tr ∝

CD
.
Cf · gm

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35. Particle Detectors at Accelerators

To increase dS/dt without incurring excessive noise, the amplifier bandwidth should match therise time of the detector signal. The 10% to 90% rise time of an amplifier with bandwidth fU is
0.35/fU . For example, an oscilloscope with 350 MHz bandwidth has a 1 ns rise time. For cascaded
amplifiers, the individual rise times add in quadrature to first order.
As increasing SNR also improves the time resolution, minimizing the total input capacitance isextremely important for timing measurements (see also Sec. 35.8). At high signal-to-noise ratios,
the time jitter can be much smaller than the rise time. The time-mark distribution of pulses may
shift with the signal level (“time walk”), but this can be corrected by various means, either in
hardware or in software.
For applications aiming at extreme time resolution charge-sensitive (integrating) amplification
can be less optimal. Transimpedance or voltage amplifiers converting current/voltage to voltage
are usually preferred. Also, when aiming for picosecond timing using voltage amplifiers, e.g., withLGAD detectors having CD of O(pF) (see Sec. 35.8), not only the preamplifier rise time tr but also
the signal pulse duration td at the preamplifier input is important, i.e., the preamplifier must reactdraining the charge from CD before the input voltage vin = QS /CD (QS = signal charge) reaches
its peak. Both times must reasonably match, tr ≈ td , resulting in a time jitter of [379]σt2 ≈2 dhv 2 iCDntd ,Q2S df(35.40)where dhvn2 i/df is the voltage noise spectral density.
35.9.4 Digital signal processing
The filtering principles apply to both analog and digital signal processing. In digital signal
processing the pulse shaper shown in Fig. 35.31 is replaced by an analog to digital converter (ADC)
followed by a digital processor that determines the pulse shape. Digital signal processing allows
great flexibility in implementing filtering functions. The software can be changed readily to adapt
to a wide variety of operating conditions and it is possible to implement filters that are impracticalor even impossible using analog circuitry. However, this comes at the expense of increased circuit
complexity and increased demands on the ADC compared to analog shaping.
If the sampling rate of the ADC is too low, high frequency components will be transferred tolower frequencies (“aliasing”). The sampling rate of the ADC must be high enough to capture themaximum frequency component of the input signal. Apart from missing information on the fastcomponents of the pulse, undersampling introduces spurious artifacts. If the frequency range ofthe input signal is much larger than the sampling rate, the noise at the higher frequencies will betransferred to lower frequencies and will increase the noise level in the frequency range of pulses
formed in the subsequent digital shaper. The Nyquist criterion states that the sampling frequency
must be at least twice the maximum relevant input frequency. This requires that the bandwithof the circuitry preceding the ADC must be limited. The most reliable technique is to insert alow-pass filter.
The digitization process also introduces inherent noise, since the voltage range ∆V corresponding to a minimum bit step introduces quasi-random fluctuations relative to the exact amplitude∆V
σn = √ .
12(35.41)

When the Nyquist condition is fulfilled the noise bandwidth ∆fn is spread nearly uniformly andextends to 1/2 the sampling frequency fS , so the spectral noise density is
σ
∆V
1
∆V
√ n =√ ·p
=√
.
∆fn
6fS
fS /2
12
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35. Particle Detectors at Accelerators

Sampling at a higher frequency spreads the total noise over a larger frequency range, so oversampling
can be used to increase the effective resolution. In practice, this quantization noise is increasedby the ADC’s differential non-linearity (DNL). Furthermore, the equivalent input noise of ADCs
is often rather high, so the overall gain of the stages preceding the ADC must be sufficiently large
for the preamplifier to override the ADC input noise.
35.9.5 What to use when?
When implemented properly, digital signal processing provides significant advantages in systems
where the shape of detector signal pulses changes greatly, for example in large semiconductor
detectors for gamma rays or in gaseous detectors (e.g. TPCs) where the duration of the current
pulse varies with drift time, which can range over orders of magnitude. Analog signal processing isbest or most efficient in systems that require fast time response, but the high power requirementsof high-speed ADCs are prohibitive. Systems that are not sensitive to pulse shape can use fixedshaping time constants and rather simple filters (like CR–RC), which can be either continuous or
sampled. In high-density systems that require small circuit area and low power (e.g., in strip andpixel detectors), analog filtering often yields the required response and tends to be most efficient.
As stressed already in the introduction, it is important to consider that additional noise is often
introduced externally. Recognizing additional noise sources and minimizing cross-coupling to thedetector current loop is often essential to obtain the best overall noise performance. Understanding
basic physics and its practical effects is important in forming a broad view of the detector system
and recognizing potential problems (e.g. modified data), rather than merely following standard
recipes.
More comprehensive treatments of low noise detector readout and signal processing can befound, for example, in [8, 376, 378] and in [1, 363].

35.10 Calorimeters35.10.1 Introduction
Revised August 2023 by F. Sefkow (DESY, Hamburg) and F. Simon (KIT).
A calorimeter measures the energy and direction of particles by absorption in the detector material and registration of the energy deposited in an (ideally) contained electromagnetic (EM) or
hadronic shower. Calorimeters are central components of modern high energy physics experiments,
due to their ability to measure not only the energy of charged particles (with the exception ofmuons), but also of photons and neutral hadrons, thus enabling the reconstruction of π 0 and η
decays and of exclusive final states involving long-lived neutral kaons, or neutrons. They are indispensable for the measurement of particle jets and for the reconstruction of total event properties,
which, via the measurement of missing energy (or missing transverse energy in hadron colliders).
enable the detection of the presence of "invisible" particles such as neutrinos and hypothetical particles such as dark-matter candidates. Calorimeters are also important for the identification ofparticle species, using information on the longitudinal and transverse shape of the energy deposition to separate electrons, photons, hadrons and muons. While the performance of calorimeters istypically assessed by the quality of their energy measurements, position resolution, both for EM
and hadronic showers, is also highly relevant, for example for the reconstruction of effective jetmasses. The capability to measure high-level observables that serve to classify events, such as particle and jet energies, missing energy and isolated leptons, makes calorimeters central componentsof the trigger systems in high-energy physics experiments.
In collider experiments, the importance of calorimeters tends to increase with increasing collisionenergies since the relative energy resolution improves with increasing particle energy while the depth
required for full containment of the showers shows only logarithmic growth with energy. This
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80

is in contrast to the precision of track-based measurements, which is decreasing with increasing
momentum. With recent advances in timing capabilities calorimeters are also contributing to therejection of pile-up from multiple interactions within the same bunch crossings at colliders.
50

5

40

4

Fe Cu

Ru Pd

W Au PbU30

X0 /ρ (cm)λ I /ρ (cm)

3

λI

20

2

X0

10

0
20

30

40

50

60

Z

1

70

80

90

100

0

Figure 35.34: Nuclear interaction length λI /ρ (circles) and radiation length X0 /ρ (+’s) in cm forthe chemical elements with Z > 20 and λI < 50 cm.
The characteristic length scale for EM showers is the radiation length X0 , which ranges from
1.8 cm (13.8 g cm−2 ) in iron to 3.2 mm (6.0 g cm−2 ) in uranium for materials used to generate
showers in calorimeters.9 Similarly, the characteristic nuclear interaction length λI varies from
16.8 cm (132.1 g cm−2 ) (Fe) to 11.0 cm (209 g cm−2 ) (U).10 There is a premium on small λI /ρ
and X0 /ρ (both with units of length). These quantities are shown for elements with Z > 20 inFig. 35.34. The minima for both X0 and λI correspond to elements between W and Au. Some ofthese elements are very difficult to work with (e.g. W) or expensive (e.g. Au), so, depending on
the application (size of the required calorimeter) other materials, such as Fe, Cu, Pb, and different
alloys like brass and CuW are often chosen. For EM calorimeters high Z is preferred; here Pb is a
popular choice, while W provides even higher density and is generally affordable due to the limited
volume of EM systems.
Most existing calorimeters are subdivided into a front EM section (ECAL) and a hadronicpart (HCAL) behind; electrons and photons are measured in the ECAL, while hadrons and jets
are measured in the combined ECAL and HCAL system. The detailed design depends on energy
range and performance requirements as well as on size and cost constraints for the entire system.
EM calorimeters tend to be 15–30 X0 deep, while hadronic calorimeters are usually optimised forcost and performance at 5–8 λI . The depth of the ECAL typically corresponds to approximately
X0 = 120 g cm−2 Z −2/3 to better than 5% for Z > 23.
λI = 37.8 g cm−2 A0.312 to within 0.8% for Z > 15.
See https://pdg.lbl.gov/current/AtomicNuclearProperties for actual values.
9

10

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35. Particle Detectors at Accelerators

1 λI , with the exact value depending on the material. This means that approximately 70% of
all hadronic showers will already begin in the electromagnetic calorimeter, making its response toa hadronic cascade highly relevant for the overall performance of the system. The choice of thecalorimeter technology for the ECAL is thus a result of simultaneous optimisation for EM andhadronic performance of the overall system.
Sampling calorimeters consist of a high-density, normally metallic absorber sandwiched (orthreaded) with an active material which generates a signal in response to shower particles. The
active medium may be a scintillator, a noble liquid, a gas, silicon, or a Cherenkov radiator. These
active media all have a relatively low Z, a significantly lower density, and larger X0 and λI values
than typical absorber materials. The average radiation and interaction lengths in the full detector
are thus larger than those of the absorber alone.
There are also homogeneous calorimeters, in which the entire volume contributes to the signal. Homogeneous calorimeters may be built with inorganic heavy scintillating crystals or nonscintillating Cherenkov radiators such as lead glass and lead fluoride. Nuclear interaction lengths
in inorganic crystals range from 17.8 cm (LuAlO3 ) to 42.2 cm (NaI). Materials with low X0 usedin large systems are for example BGO with λI = 22.3 cm and X0 = 1.12 cm, and PbWO4 (20.3 cm
and 0.89 cm). Properties of these and other commonly used inorganic crystal scintillators can befound in Table 35.4. Cryogenic noble liquids, where scintillation light and/or inonization can bedetected, are also suitable materials for homogeneous detectors.
Homogeneous calorimeters at colliders are usually only used for the EM section. For the useof homogeneous calorimeters for hadron energy measurement, the large differences in the response
to EM and hadronic parts of the shower are a significant challenge, as is the three-dimensional
segmentation. This is still requiring substantial R&D, including the search for affordable materials.
In non-accelerator physics experiments or at neutrino beams, homogeneous calorimeters, where thesensitive medium can be water or ice, scintillator, a noble liquid or the atmosphere itself, are used
to detect both EM and hadronic showers.
Comprehensive tables of particle-physics calorimeters are given as Appendix C in Ref. [380].
35.10.1.1 Energy Resolution and System Performance
The energy resolution of calorimeters is a complex observable, due to the variety of contributing
processes with different energy dependencies, and response functions often not perfectly Gaussian.
Nevertheless, a simplified picture is useful in practice, and in particular for EM calorimeters also
numerically accurate. For hadronic calorimeters additional complications must be taken into account. In such a simplified picture, due to the stochastic
nature of shower evolution, the intrinsic√
calorimeter energy resolution, σ, is proportional to E, as the number of charged particles, or the
total ionising track length in a shower are on average proportional
to the incident particle energy√
E. The relative resolution σ/E therefore improves with A/ E, where A denotes the so-calledstochastic term. The readout system of the active medium will contribute noise to the resolution,
σN = B, which in general is not energy-dependent. Effects that are proportional to the total
deposited energy result in a constant term, σC = C · E. Different sources contribute to this term,
depending on the type of calorimeter. For both EM and hadronic calorimeters, imperfections of thedetector, inhomogeneities such as density variations or those introduced by the detector mechanics,
instabilities in time, imperfections of the readout or incorrect calibration of channels contribute.
Shower leakage, which depends on particle energy, also contributes to the resolution with approximately linear dependence on energy. In non-compensating hadronic calorimeters, fluctuations of
the EM fraction fem from shower to shower, together with the energy dependence of the averagefem value, can lead to a significant constant term that often dominates over the instrumental effects. Adding up all contributions in quadrature yields the standard parameterisation of the relative
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35. Particle Detectors at Accelerators

energy resolution of a calorimeter:AσB= √ ⊕ ⊕C.
(35.43)E
E
E
In particular the effects specific to hadronic showers give rise to non-Gaussian distributionsof the energy response. Therefore care must be used in performance comparisons, as different
parameterisations of the line shape and different definitions of the resolution are in use. In somecases, a linear rather than a quadratic addition of the stochastic and constant term may provide
a better description of the energy resolution as a function of energy. It should be noted that theindividual terms then lose the simplified interpretation discussed above, and care has to be taken
when comparing performance based on fits to the energy dependence of the resolution.
Typically, primarily the stochastic term — which is determined by the calorimeter design interms of material and geometry — is considered in order to describe the overall properties of acalorimeter. For the calorimeters of the multi-purpose experiments at the LHC, the stochastic
terms are 3 − 10% for electromagnetic and 50 − 80% for hadronic calorimeters. In practice, theenergy resolution of a calorimeter at high energies is limited by the constant term C, which in
the EM case mainly reflects the precision and stability of the mechanical construction, electronic
readout system and calibration. Typical constant terms are a few per-mil for EM and a few percent
for hadronic calorimeters. For concrete examples and references see Tables 35.11 and 35.13.
For sampling calorimeters, the stochastic term depends on the sampling fraction fsamp , i.e. theratio of energies deposited in the active and passive material. Also the sampling frequency enters,
which is determined by the number N of different sampling elements presentp
in the region in which
the shower develops. The stochastic
termA
scalesapproximately
with1/
fsamp , and for given√
fsamp and total depth, with 1/ N .
While the energy resolution for single hadrons (most commonly pions) is often used as the key
performance criterion for a hadronic calorimeter, it has to be noted that this value is only of limited
relevance in high-energy physics experiments. In most experiments, the calorimetric measurement of
hadrons is based on the combined system consisting of ECAL and HCAL. Moreover, for the physics
capabilities of a detector at a high-energy particle collider, also the combined calorimetric resolution
for single hadrons is not a sufficient criterion to fully characterise hadronic performance, but rather
the jet energy resolution, the resolution for missing (transverse) energy, and the capability tocope with high background and pile-up levels. These quantities cannot be measured directly with
prototypes in beam tests, and strongly depend on overall system aspects and reconstruction tools.
However, the performance in these observables can be reliably inferred from system simulations
once the simulated response to single particles and the simulated topology of showers has beenvalidated in detail by beam tests.
Besides energy resolution, response linearity is an important factor in the design of calorimeters.
While a non-linear response for single particles can be corrected for if appropriate calibration
measurements exist, such corrections deteriorate the energy resolution, in particular in the caseof superposition of several showers, as it often occurs in jets. Sources for non-linearities can be
intrinsic to the design, for example due to saturation effects in the active medium with increasingenergy density, due to leakage, or connected to shower physics as discussed in section 35.10.3.
The energy resolution for hadrons is intrinsically limited by large event-to-event fluctuationsof the shower evolution and of "invisible" components not contributing to the detector signal. It
remains the limiting factor for single particles and for the high-level performance for jets and total
event properties. This has motivated intense research in the past decades. One direction aims at
improving the hadronic resolution by extracting additional signals to disentangle the shower composition, e.g.with so-called dual read-out methods, and is explained in the hadron calorimeter section
35.10.3. Another, so-called "particle flow" approach described below optimises the combination of
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35. Particle Detectors at Accelerators

measurements of individual particles in different detector components. Ideally, both methods canbe combined.
35.10.1.2 Role of Simulations
Simulations have become indispensable for the design of detectors and the development of reconstruction algorithms. Since event-to-event fluctuations drive calorimeter performance, Monte
Carlo techniques that accurately model the evolution of particle cascades in material are required.
By far the most common computer code in use today is the GEANT4 toolkit [381, 382], which
provides a step-based simulation of the passage of particles through matter. Thanks to the relative simplicity of EM cascades, simulations of EM showers are typically highly accurate. The
modelling of hadronic showers is more complex, and suffers from larger uncertainties. Significant
improvement has been achieved in this area, moving from simpler parameterised models to physicsdriven interaction models. From early on, detailed codes and data describing nuclear break-up andneutron transport like CALOR [383] or FLUKA [384, 385] contributed crucially to the understanding of hadron calorimetry. The simulations reproduce the general features of the substructure ofhadronic showers, characterised by dense shower activity and sparser ionising track segments, andtheir accuracy is adequate for most purposes of quantitative design optimisations. Details of theimplementation of physics models in GEANT4 are discussed in [386].
35.10.1.3 Particle flow approach
In a typical collider experiment, the EM and hadronic calorimeter system surrounds a chargedparticle tracking volume devised for momentum measurement in a magnetic field. Matching tracks
to calorimetric energy deposits provides corrections for the magnetic deflection of the charged
particles, necessary for the reconstruction of invariant masses in multi-jet final states, or of thetotal momentum imbalance. Furthermore, for charged particles the track-based measurements are
far more precise for particles in jets with energies of up to several hundred GeV, so using theseinstead of calorimeter energies may optimise the jet energy resolution. This so-called "particle
flow" approach aims at reconstructing each particle individually, using a combination of the best
measurements from the detector.
About 60% of the energy in a typical jet is carried by charged particles, predominantly hadrons,
30% by photons and only 10% by long-lived neutral hadrons (KL0 and n), for which hadronic
calorimetry is unavoidable.
Assuming, as motivatedpp by detector designs proposed for a future
Higgs factory, 15%/ E(GeV) for photons and 55%/ E(GeV) forp hadrons, then, in the ideal case,where each particle is resolved,
a jet energy resolution of 19%/ E(GeV) could be obtained. Herepthe dominant part (18%/ E(GeV)) is still due to the calorimeter resolution for neutral hadrons.
The particle flow method places high demands on the imaging capabilities of the calorimeters,
and on the pattern recognition performance of the reconstruction algorithms. Only energy deposits
not associated with charged particles and not identified as photons, will be interpreted as neutral
hadrons. In practice, this cannot always be done unambiguously, and mis-assignments give riseto an additional measurement uncertainty, which is called confusion. For simulated detectors at
proposed future Higgs factories jet energy resolutions of 3-4% have been demonstrated, significantly
larger than in the ideal case, but sufficient for the required efficient separation of W and Z hadronic
final states.
Particle flow-like techniques√ were first applied in the ALEPH detector [387], which achieved a
jet energy resolution of 60%/ E, or 6.2 GeV for hadronic Z decays. More recently, particle flow
techniques are successfully used in the CMS experiment [388], for example improving the missing
energy resolution by one third over a wide range.
The Pandora particle flow algorithm (PFA) [389] is the most developed and best performing
today in the context of future lepton colliders. The algorithms make use of topological information,
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including the sub-structure of showers, as well as the compatibility of calorimetric and track-based
measurements. In this way the purely calorimetric performance for the jet is either retained or
improved. In the framework of studies for CLIC [390], it was shown that the required jet energy
resolution of 3.5% can be achieved with the PF technique for jet energies up to 1500 GeV.
For the use of energy-momentum matching in the assignment of energy depositions, and forenergy flow treatment of dense jets, particle flow calorimeters with their emphasis on imaging muststill feature a good energy resolution. Furthermore, the neutral hadron energy uncertainty is thedominant contribution to the jet resolution for low energy jets, where particles are well separated,while at higher energies the confusion effects take over.
High granularity in all three space dimensions comparable to or smaller than the length scalesof particle showers given by X0 and ρM for both ECAL and HCAL brings additional advantages;
for example it offers ideal conditions for the application of software compensation methods, which
improves the intrinsic resolution and also reduces "confusion" [391]. A particular strength is thepossibility to use topological information such as the reconstructed starting point of the shower
for the estimation of leakage. Moreover, the combination of fine-grained topological reconstruction
and cuts on cluster-wise timing with a precision of few tens of pico-seconds allows for powerfulpile-up rejection. This extends the application range of particle flow methods towards collider
environments with less benign background conditions, like multi-TeV e+ e− collisions, and it is anasset on its own for high-intensity hadron colliders, even if particle flow methods are difficult toapply.
The performance of highly granular calorimeters depends, among others, on the particle separation and pattern recognition capabilities and on the single particle energy and timing resolution.
They are thus not only optimised for energy measurement, but also for multi-dimensional showerreconstruction and particle separation in space and time. The potential of such calorimeters can befurther enhanced by combining a fine spatial segmentation with maximised information on energy,
time, and possibly the nature of the energy deposition, for example by using dual-readout methods.
This may be achieved, for example, by combining multiple optical materials sensitive to different
components in the shower in finely segmented sandwich calorimeters, or by using timing information to extract the position of the energy deposition along a fibre. For future collider experiments,
different approaches based on silicon, scintillator, noble liquid, fibre and crystal readout are being
pursued [392]. They all foresee, with different level of emphasis, high granularity to enable theapplication of particle flow methods, and in some cases to further enhance their performance byadditional information not exploited in current algorithms. One such example is the proposal [393]
to benefit from the superior electromagnetic energy performance of crystals to pair photons fromπ 0 decays and thereby resolve jet finding ambiguities to improve the jet energy resolution.
35.10.2 Electromagnetic calorimeters
Revised August 2023 by C.L. Woody (BNL) and R.-Y. Zhu (HEP California Inst. of Technology).
The development of electromagnetic showers is discussed in the section on “Passage of Particles
Through Matter” (Sec. 34 of this Review). Formulae are given which approximately describe average
showers, but since the physics of electromagnetic showers is well understood, a detailed and reliable
Monte Carlo simulation is possible. EGS4 [394] and GEANT [381] have emerged as the standards.
Electromagnetic calorimeters are devices that are designed to measure the total energy of electrons and photons by total absorption. They come in two general categories: homogeneous andsampling. In a homogeneous calorimeter, all of the particle’s energy is deposited in the active detector volume and is used to produce a measurable signal (either scintillation light, Cherenkov lightor charge). Homogeneous electromagnetic calorimeters are typically constructed using high density,
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35. Particle Detectors at Accelerators
Table 35.11: Resolution of typical electromagnetic calorimeters. E is in GeV.
Technology (Experiment)
NaI(Tl) (Crystal Ball)
Bi4 Ge3 O12 (BGO) (L3)
CsI (KTeV)CsI(Tl) (BaBar)
CsI(Tl) (BELLE)
CsI(Tl) (BES III)PbWO4 (PWO) (CMS)
PbWO4 (PWO) (ALICE)
Lead glass (OPAL)
Liquid Kr (NA48)
Scintillator/depleted U(ZEUS)
Scintillator/Pb (CDF)
SciFi/Pb spaghetti (KLOE)
SciFi/W (sPHENIX)
Liquid Ar/Pb (NA31)
Liquid Ar/Pb (SLD)
Liquid Ar/Pb (H1)
Liquid Ar/depl. U (DØ)
Liquid Ar/Pb accordion(ATLAS)

Depth Energy resolution
1/4
20X0
2.7%/E√
22X0
2%/√E ⊕ 0.7%
27X02%/ E ⊕ 0.45%
16–18X0 2.3%/E 1/4 ⊕ 1.4%
16X0
1.7% for Eγ > 3.5 GeV
15X0
2.5%√for Eγ = 1 GeV
25X0
3%/ √
E ⊕ 0.5% ⊕ 0.2/E
19X0
3.6%/
√ E ⊕ 1.2%
20.5X05%/ √E
27X0
3.2%/ E⊕ 0.42% ⊕ 0.09/E√
20–30X0 18%/ E
18X0
15X0
20X0
27X0
21X0
20–30X0
20.5X025X0√
13.5%/√ E
5.7%/√ E ⊕ 0.6%
13%/ √E
7.5%/√ E ⊕ 0.5% ⊕ 0.1/E
8%/ √E12%/√E ⊕ 1%
16%/√E ⊕ 0.3% ⊕ 0.3/E
10%/ E ⊕ 0.4% ⊕ 0.3/E

Date
1983
1993
1996
1999
1998
2010
1997
2008
1990
1998
1988
1988
1995
2022
1988
1993
1998
1993
1996

high Z inorganic scintillating crystals such as BaF2 , BGO, CsI, CsI(Tl), LYSO, NaI(Tl) and PWO,
non-scintillating Cherenkov radiators such as lead glass and lead fluoride (PbF2 ), or ionizing noble
liquids such as liquid argon, liquid krypton or liquid xenon. The properties of some commonlyused inorganic crystal scintillators can be found in Table 35.4. Total absorption homogeneous
calorimeters such as those built with heavy crystal scintillators provide the best energy resolution
for measuring electromagnetic showers and are generally used when the best possible performanceis required, particularly at lower energies. Attention, however, needs to be paid to radiation damage in inorganic scintillators when exposed to the typical environment of high luminosity proton
colliders, as discussed below and in Section 35.4.
A sampling calorimeter consists of an active medium which generates a signal and a passive
medium which functions as an absorber. In this case, most of the particle’s energy is depositedin the absorber and only a fraction of the energy is detected in the active medium. The ratio ofenergy in the sampling medium to the total enegy in calorimeter is called the sampling fraction. The
active medium may be a scintillator, an ionizing noble liquid, a semiconductor, or a gas ionization
detector. The absorber is typically a heavy metal with a high Z such as lead, tungsten, iron,copper, or depleted uranium. The active material is interspersed with the passive absorber in avariety of ways, e.g. by using alternating plates of active material and absorber or embedding theactive material, such as scintillating fibers, into the absorber. The main difficulty in this approachis extracting the signal from the active material. One possibility is a simple stack of alternating
absorber and active material, which, however, usually leads to gaps for services and hence nonuniformities. This can be improved by using a so-called "spaghetti" design, where scintillating
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fibers are brought to the front or back of the detector and read out. This can also be done witheither wavelength shifting plates or fibers, such as in a so-called "shashlik" design where wavelength
shifting fibers run through the stack of alternating scintillator and absorber plates and are read out
at end, or embedding wavelength shifting fibers in the scintillating plates which are then brought
out to the edges or back of the detector and read out. For ionization detectors, there is also an"accordion" design which avoids all gaps for services and where the absorber plates are folded into
an accordion shape along with interspersed electrodes to collect the ionization charge [395]. Whilethese readout schemes are generally more complicated than those for homogeneous calorimeters,
the sampling calorimeter design allows the construction of large calorimeters at much lower costthan homogeneous calorimeters.
√
The energy resolution σE /E of a calorimeter can be parameterized as a/ E ⊕ b ⊕ c/E, where⊕ represents addition in quadrature and E and σE are in GeV. The stochastic term a represents
statistics-related fluctuations such as intrinsic shower fluctuations, photoelectron statistics, deadmaterial at the front of the calorimeter, and sampling fluctuations for minimum ionizing particles.
For a fixed number of radiation
lengths, the stochastic term a for a sampling calorimeter is expectedpto be proportional to t/f , where t is plate thickness and f is sampling fraction [396–398]. The
stochastic term a is typically of the order of a few percent for a homogeneous calorimeter, and isgenerally in the range of 8 to 20% for sampling calorimeters, depending on the sampling fraction.
The main contributions to the systematic, or constant, term b are detector non-uniformity andcalibration uncertainties. In √the case of hadronic cascades discussed below, non-compensation also
contributes deviations from E scaling. Another important contribution to the energy resolutionof calorimeters that are used in high radiation environments such as high lumnosity colliders isradiation damage of the active medium. Radiation damage can induce optical absorption in scintillating materials which reduces the measured light output and produces non-uniformities in lightcollection. This can be mitigated by developing radiation-hard active media [399], by reducing thesignal path length [400] and by frequent in situ calibration and monitoring [75, 398]. With effort,
the constant term b can be reduced to below one percent. The term c is due mainly to electronicnoise summed over the readout channels required to measure the shower energy (typically a few
Molière radii).
The position resolution depends on the effective Molière radius and the√ transverse granularityof the calorimeter. Like the energy resolution, it can be factored as a/ E ⊕ b, where a is thestochastic term, typically of the order of a few mm to 20 mm, and b can be as small as a fraction ofmm for a dense calorimeter with fine granularity. Fine granularity also helps particle flow analysis
discussed in the hadron calorimeters section below.
Electromagnetic calorimeters may also provide angular measurements for electrons and photons. This is particularly important for photon-related physics to identify the correct primaryvertex, since photons are not detected by the tracking√ system of the overall experiment. The
typical photon angular resolution is about 45 mrad/ E, which can be achieved by implementing
longitudinal segmentation [395] for a sampling calorimeter or by adding a preshower detector [401]for a homogeneous calorimeter without longitudinal segmentation.
There have been many electromagnetic calorimeters built and used in particle physics experiments for a variety of applications. Table 35.11 provides a short list of the major ones used insome of the larger experiments. Also listed are calorimeter depths in radiation lengths (X0 ) andthe achieved energy resolution. Whenever possible, the performance of the calorimeters in situ
is quoted, which is usually in good agreement with prototype test beam results as well as EGS
or GEANT simulations, provided that all systematic effects are properly included. Details about
detector design and performance can be found in Appendix C of reference [398] and Proceedingsof the International Conference series on Calorimetry in High Energy Physics.
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35.10.3 Hadronic calorimeters
Revised August 2021 by F. Sefkow (DESY, Hamburg) and F. Simon (KIT).
Hadronic calorimetry [380, 402, 403] is considerably more complex than electromagnetic (EM)calorimetry due to the wider range and different nature of physical processes contributing to shower
development and energy deposition, which in turn are characterised by different length and timescales. Hadronic showers are initiated by inelastic strong interactions of highly-energetic charged
and neutral hadrons with atomic nuclei. These interactions result in the production of secondary
particles, which drive the development of the shower. Among these are energetic hadrons, as well
as lower-energy nucleons, photons and nuclear fragments. Energy transferred to nuclear break-up,
excitation or recoil does not, in general, produce a signal, but remains invisible, and event-to-event
fluctuations of this invisible energy deposit ultimately limit the resolution of hadronic calorimeters(HCALs).
The length scale of the interaction of relativistic hadrons is given by the nuclear interaction
length λI . As discussed in Section 35.10.1, λI is a factor 10 to 30 larger than X0 for common
materials used in the construction of calorimeters. HCALs thus require a significantly larger geometrical depth for full containment than electromagnetic calorimeters (ECALs), albeit not by thefactor suggested by the ratio of λI /X0 due to the different nature of the showers. A key role isplayed by the production of π 0 s and their subsequent decay into two photons. These result in theformation of electromagnetic sub-showers which evolve on the scale given by the radiation length
X0 , and thus require sufficiently fine sampling of the shower activity to capture also this electromagnetic component. The two different length scales occurring in hadronic showers, and the large
fluctuations of hadronic, electromagnetic and invisible activity, result in significant event-to-event
variations of the energy response and of the shower topology. This topology is characterized by a
lumpy structure, with compact regions of high local energy density originating from electromagnetic
sub-showers, and sparser hadronic activity with minimum-ionizing hadrons.
Figure 35.35 (left) shows the distribution of the longitudinal position of the first inelastic interaction measured for pion-induced hadronic showers with the highly-granular scintillator-steel HCALof the CALICE collaboration [404]. The figure illustrates the exponential distribution, with a slope
consistent with the pion interaction length expected from the geometry and material compositionof the calorimeter. This distribution is well reproduced by simulations using GEANT4 [381, 386].
Figure 35.35 (right) shows the mean longitudinal shower profile, given by the mean energy deposition in each calorimeter layer, both relative to the front face of the calorimeter (dots, without
corrections for dead cells) and relative to the measured shower starting point given by the firstinelastic interaction (filled histogram). The latter is much more compact than the former, which
is a convolution of the latter with the distribution of shower starting point shown in the left panelof the figure. This shows that the detector depth required for adequate shower containment is significantly influenced by the fluctuations of the position of the first hadronic interaction. Detectionof this position allows for an estimate of leakage from a finite calorimeter volume, and it enables
stringent tests of shower evolution models. In the past years, motivated by precision needs at thenext generation of e+ e− colliders, the CALICE collaboration has constructed a number of prototypes with high 3-dimensional spatial granularity and recorded large sets of data at test beams,
allowing for studies of shower evolution processes in unprecedented detail. The refined simulations
support the trend to proceed from research focused on understanding the global intrinsic properties of showers, e.g. for the purpose of compensation, towards the study of detailed information, in
space, time, and energy deposition type, through many and multiple readout channels.
In an inelastic hadronic collision a significant fraction fem of the energy is removed from further
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105

0.08

DATA
fit DATAFTFP_BERT〈 Erec 〉 [MIP]n events

88

from front facefrom shower start.

0.06

4

10

CALICE Fe−AHCALCALICE Fe−AHCAL

0.04

103
0.02

500

0

1000

Shower starting point z [mm]

0

500

1000
z position [mm]Figure 35.35: Longitudinal profile of hadronic showers induced by 45 GeV negative pions measured
in he CALICE highly-granular steel-scintillator sampling calorimeter [404]. Left: Reconstructed position of the first inelastic interaction, compared to simulations (GEANT4 9.4p03, FTFP_BERT),
and an exponential fit yielding a slope consistent with the expected pion interaction length. Right:
Longitudinal shower profile measured from the front face of the calorimeter (dots, without corrections for dead cells) and relative to the position of the shower start given by the first inelastic
interaction (filled histogram). The visible energy is given in units of the most probable energy lossof a minimum-ionizing particle (MIP). The integrals of the distributions are normalized to unity.
energy electromagnetic showers. Charged secondaries (π ± , p, . . . ) deposit energy via ionizationand excitation, but also interact with nuclei, producing evaporation neutrons, spallation protons
and neutrons, and heavier spallation fragments. The charged collision products produce detectableionization, as do the showering γ-rays from the prompt de-excitation of highly excited nuclei. The
recoiling nuclei generate little or no detectable signal, as mentioned previously. The neutrons lose
kinetic energy in elastic collisions which generate ionization signals via recoiling protons, thermalize
on a time scale of several µs, and are finally captured, with the production of more γ-rays—usuallyoutside the acceptance gate of the electronics. Between endothermic spallation losses, nuclear
recoils, and late neutron capture, a significant fraction of the hadronic energy (20%–40%, dependingon the absorber and energy of the incident particle) is used to overcome nuclear binding energies
and is therefore lost or “invisible.”
In a hadron-nucleus collision a large fraction of the incident energy is carried by a “leading
particle” with the same quark content as the incident hadron. If the projectile is a charged pion,
the leading particle is usually a pion, which can be neutral and hence contributes to the EM sector.
This is not true for incident protons. The result is an increased mean hadronic fraction for incident
protons.
The complexity of hadronic showers also has a significant impact on the energy measurement.
In contrast to EM showers, hadronic cascade processes are characterised by the production of relatively few high-energy particles. The number multiplicity of these particles produced in hadronicinteractions increases only logarithmically with energy. The lost energy and fem are highly variable from event to event, and on average increase with increasing energy [405]. Electromagnetic
sub-showers typically result in a higher response than the hadronic parts of the cascade, where undetectable energy loss due to nuclear dissociation, the long time scales and the material dependence
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89

(b)

(a)

readout
interface

PMT
waveshifter
fiber

É

iiiiiiiiiites

Kt.si
iiii'iiii
i

SiPM

i

scintillator
tile
φ r

integrated electronics

hadronsz

absorber plateTgranular scintillator elements

Hadrons

Figure 35.36: Two examples of geometrical structures of scintillator-based HCALs. (a) A wedge of
the ATLAS central tile calorimeter consisting of scintillator tiles in iron, read out via wavelengthshifting fibers and PMTs [406]. The coordinate system is that of the ATLAS calorimeter within
the experiment, with the z axis along the beam direction, r pointing radially outward, and φ being the azimuthal angle. (b) An illustration of the “SiPM-on-tile” structure used in the CALICE
analogue HCAL prototype, and in the CMS High-Granularity Calorimeter (HGCAL), highly granular calorimeters with steel absorbers and small scintillator tiles directly read out via SiPMs withembedded electronics [403, 407–409].

of neutron signals, as well as other effects reduce the measured signal. This difference in response
is often expressed by the hh/ei ratio, a calorimeter-dependent quantity which is smaller than unity
for many, but not all, HCALs. The increase of the electromagnetic fraction with energy thus introduces a non-linear contribution to the response. Combined with the significant event-by-event
fluctuations between electromagnetic and hadronic fractions of the showers and between different hadronic processes the non-equality of h and e deteriorates the energy resolution of HCALs.
Different strategies to address this exist, as discussed further below.
Most large HCALs are parts of complex 4π detectors at colliding beam facilities. To date, allthese HCALs are sampling calorimeters. This choice is imposed by the physics of hadronic showers,
both by the required depth for containment which favours high-density materials with short λI ,and by the differences in response to electromagnetic and hadronic parts of the cascade, which
are particularly severe for homogeneous calorimeters. Common absorber materials are Fe, Cu,
Pb, and U, with W also used occasionally. A large variety of different active materials are used,
depending on application and optimisation, from plastic scintillators (plates, tiles, bars, fibers),
crystals and Cherenkov media, silicon, liquid argon (LAr), to gaseous detectors. The energy loss ofparticles in the active medium is either detected directly by collecting charge, or via scintillation
or Cherenkov light observed with conventional photomultipliers (PMTs), photodiodes or silicon
photomultipliers (SiPMs). The choice of both active and passive materials is driven by different,
sometimes conflicting, constraints, including performance requirements, space and other mechanicalboundary conditions, radiation tolerance, and cost considerations.
A wide range of different geometries of absorbers and sensors is used, with design choices
depending on the chosen priorities of addressing these constraints, also considering the need to bring
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the signals to the outside of the detector while achieving a hermetic coverage and other constraints.
In this context it is important to note that a classic sandwich structure with absorber plates andactive elements approximately perpendicular to the particle incidence is not required, and arbitrary
orientations are viable for good calorimetric measurements, as long as channelling, meaning theextended passage of primary particles through low-density active regions, is excluded. Figure
35.36 shows two examples of plastic scintillator-based calorimeters to illustrate differences in design
between coarsely-segmented and highly-granular calorimeters. The ATLAS tile calorimeter [406]uses scintillator tiles coupled to wavelength-shifting fibers which collect the light from the tiles andguide them to PMTs outside of the active region of the calorimeter. The calorimeter is segmented
in φ (azimuthal angle) and η (pseudorapidity, defined as η = − ln tan(θ/2), where θ is the angle
relative to the beam axis), with coarse longitudinal segmentation. The technological prototypeof the CALICE analog HCAL, a highly granular SiPM-on-tile calorimeter is based on scintillator
tiles directly coupled to SiPMs, which, together with the front-end electronics, are embedded insideof the the active volume of the calorimeter. The CMS HGCAL [409] uses the same concept inpart of the detector, and in addition embeds elements for digital data concentration and power
distribution in the active volume. Other detector solutions include scintillating fibres threading anabsorber [410], liquid-argon-filled tubes [411] and the “accordion” LAr detector [412]. The latterhas zig-zag absorber plates to minimize channeling effects; the calorimeter is hermetic (no cracks),and plates are oriented so that cascades cross the same plate repeatedly.
In particular, but not exclusively, the combination of heavy absorber materials (Pb, U) withplastic scintillators allows the construction of HCALs that have a near-equal response to electromagnetic and hadronic parts of the cascade, so-called compensating calorimeters [413]. In this firststudy, it was recognized that nuclear fission can amplify the hadronic signal when using uranium
absorbers. However, the key drivers of compensation are the reduction of the electromagnetic
response with high-Z absorbers and an increased sensitivity to neutrons, which are strongly correlated to otherwise invisible energy loss due to nuclear dissociation, with a hydrogeneous active
medium [414–418]. Since the electromagnetic cross section increases, and the critical energy decreases with Z, and since most of the energy of an electromagnetic shower is deposited by low-energy,
short-range electrons, a disproportionate fraction of the total electromagnetic energy is depositedin the absorber in the high-Z case. Hydrogenous active media, such as organic scintillators, have ahigh sensitivity to spallation neutrons via elastic n−p scattering. The number of produced neutrons
is highly correlated with the invisible energy of the hadronic cascade. Increasing the sensitivity
to these particles can thus boost the visible hadronic signal. Achieving compensation requires
carefully-chosen sampling fractions and frequencies, with the response to the hadronic parts of theshower also sensitive to the integration time of the electronics due to the time structure of theneutron component of the signal.
Since Cherenkov light, for example in quartz plates or fibers, or in crystals, is produced only
by relativistic particles in the cascade and thus predominantly by the electromagnetic componentof the shower, such media are less common in hadronic than in ECALs. Notable exceptions areapplications that require high radiation tolerance, and dual-readout calorimeters which specifically
exploit this feature, as discussed below.
Silicon offers high compactness, high granularity, high radiation tolerance, long-term stability
and fast charge collection, and is thus an interesting active material for sampling calorimeters. A
thorough overview of the development and of the features of this technology can be found in a recent
review paper [419]. The first silicon-based calorimeter in a collider experiment was a HCAL, theH1 PLUG calorimeter [420] covering the very forward region of the H1 experiment at HERA. The
SICAPO collaboration has demonstrated the conceptual possibility of constructing compensating
HCALs using silicon sensors [421]. Silicon is currently the technology of choice for several ECALs
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35. Particle Detectors at Acceleratorsfor future Higgs factories [422–424]. It is also being used extensively in the CMS HGCAL [409] inboth electromagnetic and hadronic sections, complemented by scintillator tiles with on-tile SiPM
readout where the radiation levels allow.
More generally, high-granularity calorimeters play an increasingly important role, in particular motivated by the use of particle-flow algorithms for global event reconstruction (see Section
35.10.1). The associated technologies for both electromagnetic and HCALs have been pioneeredby the CALICE collaboration, which has built and tested an increasingly sophisticated series of“imaging” calorimeters with a highly granular readout [425]. In the area of HCALs, this includes
the scintillator-based analog HCAL [426] with the latest SiPM-on-tile technological prototype withfully-integrated electronics having approximately 22, 000 channels [407, 408], as well as digital [427]and semidigital [428] calorimeters using gas detectors, such as RPCs (Sec. 35.6.7) and micropatterngas detectors (Sec. 35.6.4), with channel counts of up to 500, 000. The large numbers of channelsof high-granularity calorimeters presents a significant integration challenge for full detector systems, and requires the full integration of the front-end electronics inside of the active volume of thedetector, as well as very compact data concentration and interface units. The first such detector
in construction for a collider experiment is the CMS HGCAL [409]. Beam tests with a combined prototype using both silicon and scintillator-SiPM instrumented active layers have confirmed
simulation-based expectations [429]. The total silicon area of the full HGCAL amounts to about
600 m2 , and about 240,000 SiPMs are foreseen. The calibration of such calorimeters requires themonitoring of a large number of cells, which is achieved in-situ using reconstructed track segments
within hadronic showers [409, 430] or externally identified muons. For this method, the capability
to detect the most probable energy loss of a minimum-ionizing particle in a single cell is essential.
This is required over the full lifetime of the detector, also after the active elements have received
significant radiation damage, resulting in increased noise and reduced charge or signal collection
efficiency. Due to the large number of cells contributing to the measurement of one shower, therequirements on the precision of the calibration of individual cells is relaxed relative to the global
energy calibration of the calorimeter.
The energy resolution of HCALs is severely affected by fluctuations between different components of the cascade, exacerbated by differences in response to purely hadronic and to electromagnetic sub-showers. In many detectors, fluctuations in the electromagnetic energy fraction,
fem , and the related, consequential variations in nuclear energy dissociation losses, represent thebiggest single contribution to the hadron energy resolution. One strategy to address this problem
is the construction of intrinsically-compensating calorimeters, which imposes stringent constraints
on materials and geometries as discussed above. Compensating calorimeters are not used in current
large collider experiments, and are at the moment not considered for future collider detectors. Two
different strategies are presently followed to improve the energy resolution in non-compensating
calorimeters: Offline weighting or software compensation in longitudinally-segmented or in highlygranular calorimeters; and dual-readout calorimetry.
Software compensation techniques exploit the fact that electromagnetic sub-showers typicallyhave a higher spatial density than the purely hadronic parts of the cascade. Amplitude (or energydensity) dependent weights are applied in the reconstruction to reduce the effects of shower-toshower fluctuations. These techniques were pioneered by the CDHS collaboration for a longitudinally segmented steel-plastic scintillator calorimeter [431], where an improvement of the energy
resolution of 10% (at 10 GeV) to 30% (at 140 GeV) for charged pion showers was achieved. Similar
techniques were successfully√ applied in the H1 [432] liquid argon calorimeter system resulting in astochastic term of 51%/ E, and in the√ATLAS [433] endcap calorimeters, also based on liquid argon, with an energy resolution of 84%/ E. Inspired by these approaches, a software compensation
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technique using the detailed spatial information provided by highly-granular calorimeters of the
CALICE collaboration has been developed, achieving up to 25% improvement of the energy resolution√compared to the resolution without software compensation, resulting in a stochastic term of
45%/ E [434] in a scintillator tile calorimeter with steel absorbers. This technique has also beensuccessfully transferred to particle-flow reconstruction [435], resulting in an improvement of thejet-energy resolution in simulated events by 8% - 15%, depending on jet energy. Highly-granularcalorimeters with software compensation and particle-flow reconstruction are currently studied as
the baseline configuration for several Higgs-factory detectors.
The dual-readout method, originally proposed by Mockett in 1983 [436], measures fem event by
event in parallel to the total deposited energy. It uses the fact that most of the relativistic particles
in the shower originate from the electromagnetic part, and that only those produce Cherenkov light,
while the signal of the hadronic part is mostly due to non-relativistic protons. In practice either two
different active media, e.g. scintillator and quartz, are used to register scintillation and Cherenkov
light, respectively, or the optical signals from the two processes occurring in heavy crystals are
disentangled, using their different spectral, directional or timing properties.
The Cherenkov and scintillation signals, normalised to the response for electrons, are given by
C = [fem + (h/e)C (1 − fem )]E ,(35.44)S = [fem + (h/e)S (1 − fem )]E ,(35.45)

respectively, which can be solved for the fraction fem and the energy
E = (ξS − C)/(ξ − 1) ,(35.46)

where ξ = [1 − (h/e)C ]/[1 − (h/e)S ] and (h/e)C,S denote the average ratios of hadronic to electromagnetic response in the Cherenkov and scintillator parts, respectively. This is illustrated in
Figure 35.37, which shows their correlation for a set of simulated negative pion events [437] using
FLUKA [385].
It was noted that the method demands a steep slope ξ, which implies that the scintillator readout should be as compensating as possible, which however reduces the room for improvement byadding Cherenkov information.
The method was tested by the DREAM/RD52 collaboration [438, 439], using a 1 ton copper
matrix with embedded quartz and scintillatingfibers. The value of ξ was about 3 in this detector.
pWith this detector, a resolution of 70%/ E(GeV ) was obtained for single hadrons [440]. Due tothe small size of the module, this includes contributions from transverse leakage which preventthe full exploitation of key features of dual readout, and thus underestimates the potential of themethod.
The separate Cherenkov read-out evidently provides excellent pion-electron separation for particle identification. In another RD52 prototype, each fiber is read out individually by SiPMs, giving
also a superior transverse granularity. A fiber-based calorimeter with full solid-angle coverage requires a pointing geometry due to the limited or missing longitudinal segmentation. The resulting
challenges for a mechanical design are studied in the framework of the IDEA detector concept [441].
Table 35.12 shows selected examples of the energy resolution of HCALs for single charged pions
achieved in beam tests. The examples are selected to illustrate the performance achieved withdifferent designs ranging from intrinsic compensation to software compensation and dual readout,with a focus on results by R&D projects. It should be noted that the exact values of the different
resolution terms depend on the functional form used in the fit, here the addition in quadrature isused for the cases where more than just the stochastic term is quoted. The results shown in the table
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93

100 GeV MC
Incident γ
Incident π−

1.0
0.8

Slope ξ =1 − h/e C
1 − h/e S

C /E

0.6

fem = 1

0.4

fem = 0

h/e S

0.2

h/e C

0.0
0.0

0.2

0.4

0.6

S/E

0.8

1.0

Figure 35.37: Scatter plot of Monte Carlo C/E (Cherenkov) vs S/E (scintillator) signals forindividual events in a dual-readout calorimeter for 100 GeV negative pions and photons. Hadronic
events are shown in blue, and scatter about the indicated event locus. Electromagnetic events
cluster about (C/E, S/E) = (1,1). In this case worse resolution (fewer p.e.’s) was assumed for the
Cherenkov events, leading to the “elliptical” distribution.
Table 35.12: Energy resolution of selected hadron calorimeters for single charged hadrons obtained
in beam tests.
Calorimeter

Passive Active

Resolution√
Scintillator layers
44.2%/√E §Scintillator tiles
44.3%/√E ⊕ 1.8% †§Scintillator tiles
57.9%/√ E] ⊕ 4.6% ⊕ 0.065/E
Scintillator layers
58%/√E
Scint.+ Quartz fibers 70%/√E ∗Scintillator layers
34%/ √
E§
Scintillating fibers
33.3%/ E ⊕ 2.2% §Ref.

Bernardi et al.
CALICE AHCALCALICE W-AHCAL
CDHSDREAM/RD52
HELIOSSPACAL

Pb
Fe
W
Fe
Pb
U
Pb

[442]
[434]
[443]
[431]
[440]
[444]
[445]

§ Bernardi et al., CALICE W-AHCAL, HELIOS, SPACAL: (near-)compensating calorimeters.
† CALICE AHCAL: Local software compensation exploiting the high granularity of the calorimeter.
] CDHS: Offline weighting using longitudinal information.
* DREAM/RD52: Due to the relatively small transverse size of the detector lateral leakage was significant,deteriorating the energy resolution with respect to the full potential of the dual readout method.

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94

illustrate that (close to) compensating calorimeters with optimized sampling fraction and frequency,such as HELIOS (U-plastic scintillator) and SPACAL (Pb-plastic scintillator), achieve a very goodenergy resolution. The comparison with Bernardi et al., which has the same Pb/scintillator ratio
by volume as SPACAL, but coarser sampling in a sandwich structure, illustrates the importanceof the geometrical details. Beyond the examples shown in the table, liquid argon has also been
explored as an active medium, for example in the context of the SLD detector with different
absorber options [446]. Due to the reduced sensitivity to neutrons in the shower, not the same
resolution as for plastic-scintillator-based systems is achieved. This technology has also been usedin the D0 experiment, as discussed below. The dual-readout method has the potential to reach or
surpass this performance, but would require a prototype sufficiently large for full longitudinal andtransverse shower containment for an experimental demonstration. The two CALICE calorimeters
shown, which use the same active elements (5 mm thick scintillator tiles) but different absorbers(21.4 mm Fe vs 10 mm W + 4 mm Fe) per layer, illustrate the impact of the absorber choiceon energy resolution and reconstruction possibilities. While the tungsten-based W-AHCAL setup
is very close to compensating, the steel-based AHCAL achieves a better energy resolution whensoftware compensation is applied, profiting from the finer sampling of the electromagnetic parts ofthe cascade and the correction for shower-to-shower fluctuations of the electromagnetic fraction in
the reconstruction. In the case of tungsten, software compensation does not significantly improvethe energy resolution, as expected. The comparison of the CALICE AHCAL performance with theone of CDHS illustrates the benefits of higher granularity for software compensation techniques,
but it should be noted that the absorber thickness of the latter is 25 mm, with the same scintillator
thickness as in the case of CALICE.
As explained in the introduction, in most high-energy physics experiments, the HCAL follows
after an ECAL, making the response of the latter to hadronic cascades highly relevant for the overall
performance of the combined ECAL HCAL system. For scenarios where the electromagnetic and the
HCAL have very different hh/ei, as is typically the case for crystal-based ECALs, the fluctuations of
the fraction of the hadronic shower contained within the ECAL result in a significant deteriorationof the energy resolution for hadrons. A deterioration of the hadronic performance also results fromlarger amounts of not-instrumented material, e.g. supports and services, between electromagnetic
and hadronic sections. In particle-flow calorimeters, a large value of the λI /X0 ratio of the absorbermaterial, like in tungsten, maximises the longitudinal separation of electromagnetic and hadronic
showers. This is reflected in the design of particle-flow-based detector concepts for future Higgs
Factories.
Table 35.13: Energy resolution of selected combined electromagnetic and hadronic calorimetersystems in past and present high-energy collider experiments for single hadrons. The results aretaken from beam tests of prototypes with the electromagnetic calorimeter upstream of the hadronic
calorimeter.
Experiment technology (ECAL, HCAL)

Reference

H1
ZEUS

[447]
[448]

CDF
D0
ATLAS
CMS

Combined hadronic resolution√
Pb/LAr, Steel / LAr46%/√E ⊕ 2.6% ⊕ 0.73/E
depleted U / plastic scintillator
35%/ E√Pb/plastic scint., Steel/plastic scint. 68%/ √E ⊕ 4.1%
depleted U / LAr
44.6%/ E ⊕ 3.9%√
Pb/LAr, Steel/plastic scintillator
52%/ √
E ⊕ 3.0% ⊕ 1.6/E
PbWO4 , brass/plastic scintillator
84.7%/ E ⊕ 7.4%
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[449]
[450]
[451]
[452]

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35. Particle Detectors at Accelerators

Table 35.13 summarizes the single hadron energy resolution obtained from test beams of the
combined ECAL and HCAL systems of the large multi-purpose experiments at HERA, the Tevatron and at the LHC. These systems are examples of different optimization strategies. D0 and
ZEUS are near-compensating systems with the same technology in ECAL and HCAL emphasizing
hadronic performance. ATLAS and H1 use sampling ECALs with good electromagnetic resolution
and weighting techniques exploiting longitudinal and transverse shower information for hadronicenergy reconstruction. CMS, with a crystal ECAL and a scintillator-brass HCAL, prioritizes electromagnetic performance, with very different hh/ei in the electromagnetic and hadronic system.
Of the detectors shown in the table, CMS has the best electromagnetic resolution by a comfortable margin, but consequently the weakest hadronic resolution. The best hadronic performance isachieved with the compensating calorimeter of ZEUS, which however has a weaker electromagnetic
performance than the other calorimeter systems shown here. It should be noted that an excellent
single-hadron resolution in general does not fully propagate into the jet-energy performance. Inactive material in front of the calorimeter can significantly worsen the energy resolution for jets, with
an impact in particular on lower-energy particles. For example, the core of the invariant mass distribution of hadronically-decaying Z 0 bosons measured in ZEUS, which had a superconducting coilin front of the calorimeter, is well described by a Gaussian with a σ of 6 GeV [453], approximately
40% wider than would be expected for a jet-energy resolution that is identical to the single-hadron
performance.
35.10.4 Free electron drift velocities in liquid ionization chambers
Revised August 2009 by W. Walkowiak (Siegen U.).
Drift velocities of free electrons in LAr [290] are given as a function of electric field strength fordifferent temperatures of the medium in Fig. 35.38. The drift velocites in LAr have been measured
using a double-gridded drift chamber with electrons produced by a laser pulse on a gold-plated
cathode. The average temperature gradient of the drift velocity of the free electrons in LAr is
described [290] by∆vd= (−1.72 ± 0.08) %/K.
(35.47)∆T vd
Previous measurements [454, 455, 457, 458] range from 13% higher [455] to 18% lower [457] thanthese measurements. They used different techniques and show drift velocities for free electrons
which cannot be explained by the temperature dependence mentioned above.
Drift velocities of free electrons in LXe [454] as a function of electric field strength are also displayed in Fig. 35.38. The drift velocity saturates for |E | > 3 kV/cm, and decreases with increasing
temperature for LXe as well as measured e.g. by [459].
The addition of small concentrations of other molecules like N2 , H2 and CH4 in solution to theliquid typically increases the drift velocities of free electrons above the saturation value [454, 457],
see example for CH4 admixture to LAr in Fig. 35.38. Therefore, actual drift velocities are criticallydependent on even small additions or contaminations.

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35. Particle Detectors at Accelerators

968

97.0 K7

LAr + 0.5% CH4

Vd (mm/µs)

6587.0 K
89.8 K
93.9 K

LAr

4
3

LXe

2

Shibamura et al. (1976)
Walkowiak (2000)
Miller et al. (1968)1

163.0 K

0
0

2

4

6

8

10

12

14

E (kV/cm)
Figure 35.38: Drift velocity of free electrons as a function of electric field strength for LAr [290],
LAr + 0.5% CH4 [454] and LXe [455]. The average temperatures of the liquids are indicated.
Results of a fit to an empirical function [456] are superimposed. In case of LAr at 91 K the error
band for the global fit [290] including statistical and systematic errors as well as correlations of thedata points is given. Only statistical errors are shown for the individual LAr data points.

35.11 Accelerator-based neutrino detectors
Written by M.O. Wascko (Imperial Coll. London). Minor revision in August 2023 by A. Fava
(FNAL) and F. Pietropaolo (CERN; INFN, Padova).
35.11.1 Introduction
Accelerator-based neutrino experiments span many orders of magnitude in neutrino energy, froma few MeV to hundreds of GeV. This wide range of neutrino energy is driven by the many physics
applications of accelerator-based neutrino beams. Foremost among them is neutrino oscillation,
which varies as the ratio L/Eν , where L is the neutrino baseline (distance traveled), and Eν is theneutrino energy. But accelerator-based neutrino beams have also been used to study the nature of
the weak interaction, to probe nucleon form factors and structure functions, and to study nuclear
structure.
The first accelerator-based neutrino experiment used neutrinos from the decays of high energy
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35. Particle Detectors at Accelerators

pions in flight to show that the neutrinos emitted from pion decay are different from the neutrinos
emitted by beta decay [460]. The field of accelerator-based neutrino experiments would likely
not have expanded beyond this without Simon van der Meer’s invention of the magnetic focusing
horn [461], which significantly increased the flux of neutrinos aimed toward the detector. In thismini-review, we focus on experiments employing decay-in-flight beams—pions, kaons, charmed
mesons, and taus—producing fluxes of neutrinos and antineutrinos from ∼ 10 MeV to ∼ 100 GeV.
Neutrino interactions with matter proceed only through the weak interaction, making the crosssection extremely small and requiring high fluxes of neutrinos and large detector masses in orderto achieve satisfactory event rates. Therefore, neutrino detector design is a balancing act taking
into account sufficient numbers of nuclear targets (often achieved with inactive detector materials),
adequate sampling/segmentation to ensure accurate reconstruction of the tracks and showers produced by neutrino-interaction secondary particles, and practical readout systems to allow timely
analysis of data.
35.11.2 Signals and Backgrounds
The neutrino interaction processes available increase with increasing neutrino energy as interaction thresholds are crossed; in general neutrino-interaction cross sections grow with energy; for a
detailed discussion of neutrino interactions see [462]. The multiplicity of secondary particles fromeach interaction process grows in complexity with neutrino energy, while the forward-boost due toincreasing Eν compresses the occupied phase space in the lab frame, impacting detector designs.
Because decay-in-fight beams produce neutrinos at well-defined times, leading to very small duty
factors, the predominant backgrounds usually stem from unwanted beam-induced neutrino interactions, i.e. neutrinos interacting via other processes than the one being studied. A noteworthy
exception is time projection chambers, wherein the long drift times can admit substantially morecosmic backgrounds than most other detection methods. Cosmic backgrounds are more rare athigher energies because the secondary particles produced by neutrino interactions yield detector
signals that resemble cosmic backgrounds less and less.
Below, we describe a few of the dominant neutrino interaction processes, with a focus on the
final state particle content and topologies.
35.11.2.1 Charged-Current Quasi-Elastic Scattering and Pion Production
Below ∼ 2 GeV neutrino energy, the dominant neutrino-nucleus interaction process is quasielastic (QE) scattering. In the charged current (CC) mode, the CCQE base neutrino reactionis ν` n → `− p, where ` = e, µ, τ , and similarly for antineutrinos, ν ` p → `+ n. The final stateparticles are a charged lepton, and perhaps a recoiling nucleon if it is given enough energy toescape the nucleus. Detectors designed to observe this process should have good single-particle track
resolution for muon neutrino interactions, but should have good µ/e separation for electron neutrino
interactions. Because the interaction cross section falls sharply with Q2 , the lepton typically carries
away more of the neutrino’s kinetic energy than the recoiling nucleon. The fraction of backwardscattered leptons is large, however, so detectors with 4π coverage are desirable. The dominantbackgrounds in this channel tend to come from single pion production events in which the pion is
not detected.
Near 1 GeV, the quasi-elastic cross section is eclipsed by pion production processes. A typical single pion production (CC1π) reaction is ν` n → `− π + n, but many more final state particle
combinations are possible. Single pion production proceeds through the coherent channel andmany incoherent processes, dominated by resonance production. With increasing neutrino energy,
higher-order resonances can be excited, leading to multiple pions in the final state. Separating theseprocesses from quasi-elastic scattering, and indeed from each other, requires tagging, and ideallyreconstructing, the pions. Since these processes can produce neutral pions, electromagnetic (EM)
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35. Particle Detectors at Accelerators

shower reconstruction is more important here than it is for the quasi-elastic channel. The predominant backgrounds for pion production change with increasing neutrino energy. Detection of pion
processes is also complicated because near threshold the quasi-elastic channel creates pion backgrounds through final state interactions of the recoiling nucleon, and at higher energies backgrounds
come from migration of multiple pion events in which one or more pions is not detected.
35.11.2.2 Deep Inelastic Scattering
Beyond a few GeV, the neutrino has enough energy to probe the nucleon at the parton scale,leading to deep inelastic scattering (DIS). In the charged-current channel, the DIS neutrino reactionis ν` N → `− X, where N is a nucleon and X encompasses the entire recoiling hadronic system. The
final state particle reconstruction revolves around accurate reconstruction of the lepton momentum
and containment and reconstruction of the hadronic shower energy. Because of the high neutrinoenergies involved, DIS events are very forward boosted, and can have extremely long particle tracks.
For this reason, detectors measuring DIS interactions must be large to contain the hadronic showers
in the detector volume.
35.11.2.3 Neutral Currents
Neutrino interactions proceeding through the neutral current (NC) channel are identified by thelack of a charged lepton in the final state. For example, the NC elastic reaction is νl N → νl N , andthe NC DIS reaction is νl N → νl X. NC interactions are suppressed relative to CC interactions bya factor involving the weak mixing angle; the primary backgrounds for NC interactions come fromCC interactions in which the charged lepton is misidentified.
35.11.3 Instances of Neutrino Detector Technology
Below we describe many of the actual detectors that have been built and operated for use inaccelerator-based neutrino beams.
35.11.3.1 Spark Chambers
In the first accelerator-based neutrino beam experiment, Lederman, Schwartz, and Steinberger[460] used an internally-triggered spark chamber detector, filled with 10 tons of Al planes andsurrounded by external scintillator veto planes, to distinguish muon tracks from electron showers,
and hence muon neutrinos from electron neutrinos. The inactive Al planes served as the neutrino
interaction target and as radiators for EM shower development. The detector successfully showed
the presence of muon tracks from neutrino interactions. It was also sensitive to the hadronic showers
induced by NC interactions, which were unknown at the time. In 1963, CERN also built and ran
a large (20 ton) Al plane spark chamber in a wideband beam based on the PS accelerator [463].
More than a decade later, the Aachen-Padova [464] experiment at CERN employed a 40 ton Al
spark chamber in the PS-WBB.
35.11.3.2 Bubble Chambers
Several large bubble chamber detectors were employed as accelerator neutrino detectors in
the 1970s and 80s, performing many of the first studies of the properties of the weak interaction.
Bubble chambers provide exquisite granularity in the reconstruction of secondary particles, allowing
very accurate separation of interaction processes. However, the extremely slow and labor-intensive
acquisition and analysis of the data from photographic film led to them being phased out in favorof electronically read out detectors.
The Gargamelle [465] detector at CERN used Freon and propane gas targets to make the firstobservation of neutrino-induced NC interactions and more. The BEBC [466] detector at CERN wasa bubble chamber that was alternately filled with liquid hydrogen, deuterium, and a neon-hydrogenmixture; BEBC was also outfitted with a track-sensitive detector to improve event tagging, andsometimes used with a small emulsion chamber. The SKAT [467] Freon bubble chamber was
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35. Particle Detectors at Accelerators

Table 35.14: Properties of detectors for accelerator-based neutrino beams. Revised in August2023 by A. Fava (FNAL) and F. Pietropaolo (CERN; INFN, Padova).
Name
Lederman et al.
CERN-spark.
Serpukhov
Aachen-Padova
Gargamelle
BEBC
SKAT
ANL-12ft
BNL-7ft
Fermilab-15ft
CITF
CDHS
MINOS
MINOS+INGRID
SuperKamiokande
SuperK-Gd
HyperK
K2K-1kt
MiniBooNE
ANNIE
HWPF
LSND
NOvA
SciBarSciBooNE,
Captain MillsICARUSICARUS
Argoneut
MicroBooNE
SBND
DUNE
FNAL-E-531
CHORUS
DONuT
OPERA
NINJA
FASERνCHARM
CHARM-II
BNL-E-734
BNL-E-776
NOMAD
CCFR
NuTeV
MINERvA
T2K-ND280
COHERENT
SND@LHC

Type
TargetTotal Mass (fiducial) [t]hEν i [GeV]
Location
Dates
Spark
Al
10
[0.2-3]
BNL
1962
Spark
Al
20
1.5
CERN
1963
Spark
Al
20
[3-30]
IHEP
1974-82Spark
Al
40(20)
1.4
CERN
1976-77
BubbleFreon
12[1-10]
CERN
1970-79
Bubble
H,D,Ne-H
2-42[50-150],20
CERN
1977-84
Bubble
Freon
8
7
IHEP
1976-1987
Bubble
H,D
1-2
0.5
ANL
1970
BubbleHD
0.4-0.9
1.3,3
BNL
1976-82
BubbleD, Ne
1,20[50-180],[25-100]
FNAL
1973-92
IronFe
92[50-180]
FNAL
1974-83Iron
Fe
1250(520)
10-200
CERN
1976-84IronFe
980(23.7), 5.5k (4.2k)
3
FNAL, SUL 2005-2012
Iron
Fe
980, 5.5k
4-10
FNAL, SUL 2013-2016
Iron
Fe
160
0.6-3
J-PARC
2010Cherenkov
H2 O
50k (22.5k)
0.6
Kamioka
1996-2018
Cherenkov H2 O doped with Gd
50k (22.5k)
0.6
Kamioka
2020Cherenkov
H2 O
260k(190k)
0.6
Kamioka
2027Cherenkov
H2 O
25
0.8
KEK
1998-2004
Cherenkov
CH2
818(440)
0.5
FNAL
2002-19
Cherenkov H2 O with GD sulfate
26
0.8
FNAL
2021Scintillation
CH2 , Fe
160
[50-180]
FNAL
1974-78
Scintillation
CH2
167
0.003-0.06
LANL
1993-1998
Scintillation
CH2300, 14k
2
FNAL,Ash River 2014Scintillation
CH
15(9.5)
0.6
KEK
2003-2004
Scintillation
CH
15(9.5)0.8
FNAL
2007-08
Scintillation
Ar
10
0.003-0.06
LANL
2022-2024
LArTPCAr
760(476)
17
LNGS
2006-12LArTPCAr
760(476)
0.8
FNAL
2020LArTPC
Ar
0.025
3
FNAL
2009-10LArTPCAr
170(85)
0.8
FNAL
2014-21LArTPCAr
220(112)0.8
FNAL
2024LArTPC
Ar
70(40)
3
FNAL,SURF
2027Emulsion
Ag, Br
0.009
22
FNAL
1984
EmulsionAg, Br
0.8
27
CERN
1994-97
Emulsion
Fe
0.26
53
FNAL
1997
Emulsion
Pb
1.25k
17
LNGS
2008-12
EmulsionFe0.002(0.001)
0.6
J-PARC
2015EmulsionW
1.2[360-6300]
CERN (LHC)2022Hybrid
CaCO3(27),156(122)20
CERN
1978-84
Hybrid
glass
692
20
CERN
1984-91
Hybrid
CH2
172
1.3
BNL
1981-86
Hybridconcrete
240
1.4
BNL
1986
HybridCH
2.9(2.7)
27
CERN
1995-98
HybridFe
690[30-260]
FNAL
1985-88
HybridFe
690[70-180]
FNAL
1996-97
Hybrid CH,H2 O,Fe,Pb,C,He
8
3.8
FNAL
2010-19
HybridCH,H2 O
2
0.6
J-PARC
2010Hybrid
severalbetween 0.01 and 1.3
0.03
ORNL
2015Hybrid
Emulsions & SciFi
0.81[100-1000]
CERN (LHC)2022-

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35. Particle Detectors at Accelerators

exposed to wideband neutrino and antineutrino beams at the Serpukhov laboratory in the former
Soviet Union. A series of American bubble chambers in the 1970’s and 1980’s made measurements
on free nucleons that are still crucial inputs for neutrino-nucleus scattering predictions. The 12-footbubble chamber at ANL [468] in the USA used both deuterium and hydrogen targets, as did the
7-foot bubble chamber at BNL [469]. Fermilab’s 15 foot bubble chamber [470] used deuterium andneon targets.
35.11.3.3 Iron Tracking Calorimeters
Because of the forward boost of high energy interactions, long detectors made of magnetized ironinterspersed with active detector layers have been very successfully employed. The long magnetized
detectors allow measurements of the momentum of penetrating muons. The iron planes also act
as shower-inducing layers, allowing separation of EM and hadronic showers; the large numberof iron planes provide enough mass for high statistics and/or shower containment. Magnetizediron spectrometers have been used for studies of the weak interaction, measurements of structure
functions, and searches for neutrino oscillation. Non-magnetized iron detectors have also beensuccessfully employed as neutrino monitors for oscillation experiments and also for neutrino-nucleus
interaction studies.
The Caltech-Fermilab counter (CITF) [468] combined a 92 ton iron-scintillator target-calorimeter
detector with a downstream toroidal magnet to perform early studies of weak interactions—
including observations of neutral currents. The CDHS [471] detector used layers of magnetizediron modules interspersed with wire drift chambers, with a fiducial mass of 1250 t, to detector
neutrinos in the range 10–200 GeV. Within each iron module, 5 cm (or 15 cm) iron plates wereinterspersed with scintillation counters. The MINOS [472] detectors, a near detector of 980 t at
FNAL and a far detector of 5500 t in the Soudan Underground Laboratory (SUL), were functionally identical magnetized iron calorimeters, comprised of iron plates interleaved with layers of
4 cm wide plastic scintillator strips in alternating orientations. The T2K [473] on-axis detector,
INGRID, consists of 16 non-magnetized iron scintillator sandwich detectors, each with nine 6.5 cm
iron plane (7.1 t total) interspersed between layers of 5 cm wide plastic scintillator strips readoutout by multi-pixel photon counters (MPPCs) coupled to WLS fibers. Fourteen of the INGRID
modules are arranged in a cross-hair configuration centered on the neutrino beam axis.
35.11.3.4 Cherenkov Detectors
Open volume water Cherenkov detectors were originally built to search for proton decay. Largevolumes of ultra-pure water were lined with photomultipliers to collect Cherenkov light emitted
by the passage of relativistic charged particles. See Sec. 36.3.1 for a detailed discussion of deep
liquid detectors for rare processes. The Cherenkov light, which has significant production in thevisible range, appears on the walls of the detectors in distinctive ring patterns, and topologicalcharacteristics of the rings are employed to separate muon-induced rings from electron-inducedwith very high accuracy. As neutrino detectors, Cherenkov detectors optimize the design balancesince the entire neutrino target is also active detector medium.
When used to detect ∼ GeV neutrinos, the detector medium acts as a natural filter for final
state particles below the Cherenkov threshold; this feature has been exploited successfully by the
K2K, MiniBooNE (using mineral oil instead of water), and T2K neutrino oscillation experiments.
This makes event reconstruction simple and robust since electrons and muons have very different
signatures, but does require making assumptions when inferring neutrino energy since not all final
state particles are observed. At higher energies Cherenkov detectors become less accurate because
the overlapping rings from many final state particles become increasingly difficult to resolve.
The second-generation Cherenkov detector in Japan, Super-Kamiokande [86] (Super-K), comprises 22.5 kt of water viewed by 50 cm photomultiplier tubes with 40% photocathode coverage;
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it is surrounded by an outer detector region viewed by 20 cm photomultipliers. Super-K is the far
detector for K2K and T2K, and is described in greater detail elsewhere in this review. The K2K
experiment also employed a 1 kt water Cherenkov detector in the suite of near detectors [474], with
40% photocathode coverage. The MiniBooNE detector at FNAL was a 0.8 kt [475] mineral oil
Cherenkov detector, with 20 cm photomultipliers giving 10% photocathode coverage, surrounded
by a veto detector also with 20 cm photomultipliers. The ANNIE detector also at FNAL consistsof a 26-ton water Cherenkov detector loaded with gadolinium sulfate (Gd2O12S3), complemented
by a muon range detector and a veto wall. In addition to traditional PMTs, it exploits novel Large
Area Picosecond Photodetectors (LAPPDs) for the detection of the Cherenkov light.
35.11.3.5 Scintillation Detectors
Liquid and solid scintillator detectors also employ fully (or nearly fully) active detector media.
Typically organic scintillators, which emit into the ultraviolet range, are dissolved in mineral oilor plastic and read out by photomultipliers coupled to wavelength shifters (WLS). Open volume
scintillation detectors lined with photomultipliers are conceptually similar to Cherenkov detectors, although energy reconstruction is calorimetric in nature as opposed to kinematic (see alsoSec. 36.3.1). For higher energies and higher particle multiplicities, it becomes beneficial to use
segmented detectors to help distinguish particle tracks and showers from each other.
The HWPF collaboration [476] employed a 2 t liquid scintillator total-absorption hadron calorimeter followed by a magnetic spectrometer to observe neutral current events in the early days of
Fermilab. The LSND [477] detector at LANL was a 130 t open volume liquid scintillator detector
employed to detect relatively low energy (<300 MeV) neutrinos. The NOvA [478] detectors use
segmented volumes of liquid scintillator in which the scintillation light is collected by WLS fibers inthe segments that are coupled to avalanche photodiodes (APDs) at the ends of the volumes. The
NOvA far detector, located in Ash River, MN, is comprised of 896 layers of 15.6 m long extruded
PVC scintillator cells for a total mass of 14 kt; the NOνA near detector is comprised of 214 layersof 4.1 m scintillator volumes for a total mass of of 300 t. Both are placed in the NuMI beamline
at 0.8◦ off-axis. The SciBar (Scintillation Bar) detector was originally built for K2K at KEK in
Japan and then re-used for SciBooNE [479] at FNAL. SciBar used plastic scintillator strips with
1.5 cm×2.5 cm rectangular cross section, read out by multianode photomultipliers (MAPMTs)
coupled to WLS fibers, arranged in alternating horizontal and vertical layers. Both SciBooNE
and K2K employed an EM calorimeter downstream of SciBar and a muon range detector (MRD)
downstream of that.
The Coherent Captain Mills (CCM) detector is an upright cylindrical cryostat 2.58 m in diameter and 2.25 m high that holds 10 tons of LAr and is designed to be movable for distances between
20 m to 40 m from the neutrino source. It is instrumented with 120 8-inch PMTs, out of which 96
are coated with Tetraphenyl Butadiene (TPB) wavelength shifter.
35.11.3.6 Liquid Argon Time Projection Chambers
Liquid argon time projection chambers (LAr-TPCs) were conceived in the 1970s as a way toachieve a fully active detector with sub-centimeter track reconstruction [480]. A massive volume of
purified liquid argon is put under a strong electric field (hundreds of V/cm), so that the liberated
electrons from the paths of ionizing particles can be drifted to the edge of the volume and readout, directly by collecting charge from wire planes or non-destructively through charge inductionin the wire planes. Dual-phase readout methods have also been developed, in which the charge
is drifted vertically and then passed through an amplification region inside a gas volume above
the liquid volume; the bottom of the liquid volume is equipped with a PMT array for detecting
scintillation photons form the liquid argon. The first large scale LAr-TPC was the ICARUS T-600
module [481], comprising 760 t of liquid argon with a charge drift length of 1.5 m read out by wires
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35. Particle Detectors at Acceleratorswith 3 mm pitch, which operated in LNGS, both standalone and also exposed to the CNGS highenergy neutrino beam. The ICARUS detector has been transported to Fermilab and installed andpresently operated in an on-axis position in the Booster Neutrino Beamline at 600 m from target,
where it is also exposed to off-axis neutrinos from the NuMI beamline. It will be complemented by
the SBND detector(100 m from BNB target, 112 t fiducial mass), currently in the final phases of
installation to search for possible anomalies in short baseline neutrino oscillation in the context of
the SBN Program.
The ArgoNeuT [482] detector at FNAL, with fiducial mass 25 kg of argon read out with 4 mm
pitch wires, was exposed to the NuMI neutrino and antineutrino beams. The MicroBooN [483]detector at FNAL comprises 170 t (85t active) of liquid Ar, read out with 3 mm wire pitch, whichbegan collecting data in the Booster Neutrino Beam Oct 2015. A LAr-TPC has also been chosen
as the multi-kton detector design for the future DUNE [484] neutrino oscillation experiment, fromFNAL to Sanford Underground Research Facility. The design choices for the first two DUNE far
detector modules (each with a total LAr mass of 17 kt) are being validated in the NP04 (horizontal
drift) and the NP02 (vertical drift) experiments at the CERN Neutrino Platform facility [485,486].
35.11.3.7 Emulsion Detectors
Photographic film emulsions have been employed in particle physics experiments since the 1940s[487]. Thanks to advances in scanning technology and automation [488], they have been successfully
employed as neutrino detectors. Emulsions are used for experiments observing CC tau neutrino
interactions, where the short lifetime of the tau, ττ = 2.90 × 10−13 s, leading to the short mean
path length, c × τ = 87µm, requires extremely precise track resolution. They are employed in
hybrid detectors in which the emulsion bricks are embedded inside fine-grained tracker detectors.
In the data analysis, the tracker data are used to select events with characteristics typical of atau decay in the final state, such as missing energy and unbalanced transverse momentum. The
reconstructed tracks are projected back into an emulsion brick and used as the search seed for aneutrino interaction vertex.
E531 [489] at Fermilab tested many of the emulsion-tracker hybrid techniques employed by later
neutrino experiments, in a detector with approximately 9 kg of emulsion target. The CHORUS [488]experiment at CERN used 1,600 kg of emulsion, in a hybrid detector with a fiber tracker, highresolution calorimeter, and muon spectrometer, to search for νµ → ντ oscillation. The DONuT [490]experiment at FNAL used a hybrid detector, with 260 kg of emulsion bricks interspersed with fiber
trackers, followed by a magnetic spectrometer, and calorimeter, to make the first direct observationof tau neutrino CC interactions. The OPERA [491] [492] [493] experiment used an automatedhybrid emulsion detector, with 1,25x0 t of emulsion, to make the first direct observation of theappearance of ντ in a νµ beam. Recently, the NINJA collaboration has developed an emulsion
cloud chamber detector to observe neutrinos in the J-PARC neutrino beam [494].
FASERν [495] (a sub-detector of the FASER [496] experiment) is designed to detect and study
all neutrino flavors produced at the LHC in the far-forward region of the ATLAS interaction pointat the TeV energies scale. It consists of emulsion films interleaved with tungsten plates with a total
target mass of 1.2 tons, enabling the identification of the leptons in charged current ν interactions.
Placed 480m downstream of ATLAS, FASERν will measure neutrino cross sections at energies
where they are currently unconstrained and will bound models of forward particle production.
35.11.3.8 Hybrid Detectors
In the previous neutrino detector examples, one can point to a specific detection technology or
configuration that defines a category of detectors. In this section we look at detectors that combine
multiple elements or techniques, without one facet being specifically dominant or crucial; we callthese detectors hybrids.
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The CHARM detector [497] at CERN was built to study neutral-current interactions and search
for muon neutrino oscillation. It was a fine-grained ionization calorimeter tracker with approximately 150 t of marble as neutrino target, surrounded by a magnetized iron muon system for
tagging high angle muons, and followed downstream by a muon spectrometer. The CHARM II
detector [498] at CERN comprised a target calorimeter followed by a downstream muon spectrometer. Each target calorimeter module consists of a 4.8 cm thick glass plate followed by a layer ofplastic streamer tubes, with spacing 1 cm, instrumented with 2 cm wide pickup strips. Every fifth
module is followed by a 3 cm thick scintillator layer. The total mass of the target calorimeter was
692 t.
The Brookhaven E-734 [499] detector was a tracking calorimeter made up of 172 t liquid scintillator modules interspersed with proportional drift tubes, followed by a dense EM calorimeter anda muon spectrometer downstream of that. The detector was exposed to a wideband horn-focused
beam with peak neutrino energy near 1 GeV. The Brookhaven E-776 [500] experiment comprised afinely segmented EM calorimeter, with 2.54 cm concrete absorbers interspersed with planes of drift
tubes and acrylic scintillation counters, with total mass 240 t, followed by a muon spectrometer.
The FNAL Lab-E neutrino detector was used by the CCFR [501] and NuTeV [502] collaborations to perform a series of experiments in the Fermilab high energy neutrino beam (50 GeV<Eν < 300 GeV). The detector was comprised of six iron target calorimeter modules, with 690 t
total target mass, followed by three muon spectrometer modules, followed by two drift chambers.
Each iron target calorimeter module comprised 5.2 cm thick steel plates interspersed with liquid
scintillation counters and drift chambers.
The NOMAD [503] detector at CERN consisted of central tracker detector inside a 0.4 T dipole
magnet (the magnet was originally used by the UA1 experiment at CERN) followed by a hadronic
calorimeter and muon detectors downstream of the magnet. The main neutrino target is 3 t ofdrift chambers followed downstream by transition radiation detectors which are followed by an EM
calorimeter. NOMAD was exposed to the same wideband neutrino beam as was CHORUS.
MINERvA [504] is a hybrid detector based around a central plastic scintillator tracker: 8.3 tof plastic scintillator strips with triangular cross section read out by MAPMTs coupled to WLS
fibers. The scintillator tracker is surrounded by electromagnetic and hadronic calorimetry, whichis achieved by interleaving thin lead (steel) layers between the scintillator layers for the ECAL(HCAL). MINERvA is situated upstream of the MINOS near detector which acts as a muon
spectrometer. Upstream of the scintillator tracker is a nuclear target region containing inactive
layers of C (graphite), Pb, Fe (steel), and O (water). MINERvA’s physics goals span a wide rangeof neutrino-nucleus interaction studies, from form factors to nuclear effects.
T2K [473] in Japan employs two near detectors at 280 m from the neutrino beam target, one
centered on the axis of the horn-focused J-PARC neutrino beam and one placed 2.5◦ off-axis. The
on-axis detector, INGRID, is described above. The 2.5◦ off-axis detector, ND280, employs theUA1 magnet (at 0.2 T) previously used by NOMAD. Inside the magnet volume are three separate
detector systems: the trackers, the Pi0 Detector (P0D), and several ECal modules. The tracker
detectors comprise two fine-grained scintillator detectors (FGDs), read out by MPPCs coupled to
WLS fibers, interleaved between three gas TPCs read out by micromegas planes. The downstream
FGD contains inactive water layers in addition to the scintillators. Upstream of the tracker is theP0D, a sampling tracker calorimeter with active detector materials comprising plastic scintillator
read out by MPPCs and WLS fibers, and inactive sheets of brass radiators and refillable water
modules. Surrounding the tracker and P0D, but still inside the magnet, are lead-scintillator EM
sampling calorimeters.
The COHERENT collaboration aims to measure CEvNS (Coherent Elastic Neutrino-Nucleus
Scattering) using the high-quality pion-decay-at-rest neutrino source at the Spallation Neutron
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Source in Oak Ridge, Tennessee. For doing so, it is deploying a suite of detector systems in a
hallway in the basement of the SNS target hall with a phased approach. This includes CsI[Na]crystal, LAr scintillation detector, NaI[Tl], interwoven EJ200 scintillator and gadolinium-doped
Mylar, thorium-232 metal plates and Germanium detectors.
The SND@LHC experiment [505] will perform measurements with high-energy neutrinos (100 GeV–
1 TeV) produced at the LHC in the pseudo-rapidity region 7.2 < η < 8.6. It allows the identificationof all neutrino flavours with high efficiency. It is located 480 m downstream and off-axis with respect
to the ATLAS interaction point and consists of a target region followed by a muon identification
system. The target (810 kg) is instrumented with nuclear emulsions and Scintillating Fibre (SciFi)
planes. The muon identification system is made of iron slabs interleaved with scintillating bars
planes. SND@LHC is complementary to FASERν as it intercepts different components of theneutrino flux from LHC collisions, mainly those produced in heavy flavour decays, mostly charm.
35.11.4 Outlook
Detectors for accelerator-based neutrino beams have been in use, and constantly evolving, forsix decades now. The rich program of neutrino oscillation physics and attendant need for newer andbetter neutrino-nucleus scattering measurements means that more neutrino detectors with broader
capabilities will be needed in the coming decades.
One of the most intriguing prospects is a large volume, high pressure gas time projection
chamber (HPTPC). With the prospect of megawatt power accelerator-based neutrino beams, it isentirely feasible to collect high statistics data sets with a gas target. The low momentum thresholds
for particle detection, and excellent momentum resolution and particle identification capabilities, ofan HPTPC would open a new window into the physics of neutrino-nucleus scattering. Moreover, theability to change the gas mixtures in the HPTPC would allow measurements in the same detector
on multiple nuclear targets, which would, in turn, allow unprecedentedly accurate constraints andtuning of neutrino-nucleus interaction models.

35.12 Superconducting magnets for collider detectors
Revised March 2024 by Y. Makida (KEK).
35.12.1 Solenoid Magnets
In all cases SI unit are assumed, so that the magnetic field, B, is in Tesla, the stored energy,
E, is in joules, the dimensions are in meters, and vacuum permeability of µ0 = 4π × 10−7 .
The magnetic field (B) in an simple solenoid with a flux return iron yoke, in which the magnetic
field is lower than magnetic saturation of < 2 T, is given byB=µ0 n I
L(35.48)where n is the number of turns, I is the current and L is the coil length.
In an air-core solenoid case, the central field is given by
B(0, 0) = µ0 n I √1
L2 + 4R2,(35.49)where R is the coil radius.
In most cases, momentum analysis is made by measuring the circular trajectory of the passing
particles according to p = mv = qrB, where p is the momentum, m the mass, q the charge, r thebending radius. The sagitta, s, of the trajectory is given bys = q B `2 /8p ,31st May, 2024

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35. Particle Detectors at Accelerators

Figure 35.39: Geometric relation of sagitta between path length.
where ` is the path length in the magnetic field as shown in Fig. 35.39 .
In a practical momentum measurement in colliding beam detectors, it is more effective toincrease the magnetic volume than the field strength, since
dp/p ∝ p/B `2 ,(35.51)

where ` corresponds to the solenoid coil radius R. The energy stored in the magnetic field of
any magnet is calculated by integrating B 2 over all space:
E=

1
2µ0

Z

B 2 dV(35.52)

If the coil thin and inside an iron return yoke , (which is the case if it is to superconductingcoil), thenE ≈ (B 2 /2µ0 )πR2 L .
(35.53)For a detector in which the calorimetry is outside the aperture of the solenoid, the coil must betransparent in terms of radiation and absorption lengths. This usually means that the superconducting solenoid and its cryostat is of minimum real thickness and is made of a material with longradiation length. There are two major contributors to the thickness of a thin solenoid:
1. The conductor consisting of the current-carrying superconducting material (usually Nb-Ti/Cu)
and the quench protecting stabilizer (usually aluminum) are wound on the inside of a structural support cylinder (usually aluminum alloy). The coil thickness scales as B 2 R, so thethickness in radiation lengths (X0 ) is
tcoil /X0 = (R/σh X0 )(B 2 /2µ0 ) ,31st May, 2024

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35. Particle Detectors at Accelerators

106

Table 35.15: Progress of superconducting magnets for particle physics detectors.
Experiment

Laboratory

B
[T]
1.2
1.5
0.75
3
1.5
1.5
1.2
1.8
1.2
1.5
2.0
1.5
1.0
2.0
1
1
4
5
4
5
4
6

Radius
[m]
1.45
1.5
1.75
1.29
1.55
2.75
2.8
1.5
2.8
1.5
0.6
1.8
1.475
1.25
4.7–9.75
0.825–5.35
6
2.9
3.8
2.8
3.8
6

TOPAZ*KEK
CDF*
Tsukuba/Fermi
VENUS*KEK
AMY*
KEK
CLEO-II*
Cornell
ALEPH*
Saclay/CERN
DELPHI*
RAL/CERN
ZEUS*
INFN/DESY
H1*
RAL/DESYBaBar*
INFN/SLAC
D0*
Fermi
BELLE*KEK
BES-IIIIHEPATLAS-CS ATLAS/CERNATLAS-BT ATLAS/CERNATLAS-ET ATLAS/CERN
CMS
CMS/CERN
SiD**
ILC
ILD**
ILC
SiD**
CLIC
ILD**
CLIC
FCC**
∗ No longer in service∗∗ Conceptual design in future† EM calorimeter is inside solenoid, so small X/X is not a goal0

Length Energy X/X0
E/M
[m]
[MJ]
[kJ/kg]
5.4
20
0.70
4.3
5.07
30
0.84
5.4
5.64
12
0.52
2.8
3
40
†
3.8
25
2.5
3.7
7.0
130
2.0
5.5
7.4
109
1.7
4.2
2.85
11
0.9
5.5
5.75
120
1.8
4.8
3.46
27
†
3.6
2.73
5.6
0.9
3.7
4
42
†
5.3
3.5
9.5
†
2.6
5.3
38
0.66
7.0
26
1080 (Toroid)†5
2 × 250 (Toroid)†
12.5
2600
†
12
5.6
1560
†
12
7.5
2300
†
13
6.2
2300
†
14
7.9
2300
†
13
23
54000
†
12

where tcoil is the physical thickness of the coil, X0 the average radiation length of the coil/stabilizer material, and σh is the hoop stress in the coil [506]. B 2 /2µ0 is the magnetic pressure.
In large detector solenoids, the aluminum stabilizer and support cylinders dominate the thickness; the superconductor (Nb-TI/Cu) contributes a smaller fraction. The main coil and support cylinder components typically contribute about 2/3 of the total thickness in radiation
lengths.
2. Another contribution to the material comes from the outer cylindrical shell of the vacuum
vessel. Since this shell is susceptible to buckling collapse, its thickness is determined by thediameter, length and the modulus of the material of which it is fabricated. The outer vacuum
shell represents about 1/3 of the total thickness in radiation length.
35.12.2 Properties of collider detector magnets
The physical dimensions, central field stored energy and thickness in radiation lengths normal
to the beam line of the superconducting solenoids associated with the major collider are given in
Table 35.15 [507]. Fig. 35.40 shows thickness in radiation lengths as a function of B 2 R in various
collider detector solenoids.
The ratio of stored energy to cold mass (E/M ) is a useful performance measure. It can also be
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35. Particle Detectors at Accelerators

Figure 35.40: Magnet wall thickness in radiation length as a function of B 2 R for various detector
solenoids. Gray entries are for magnets no longer in use.
expressed as the ratio of the stress, σh , to twice the equivalent density, ρ, in the coil [506]:
E
E
σh
=
≈
M
ρ 2πtcoil RL2ρ

(35.55)The E/M ratio in the coil is approximately equivalent to H,¶¶ the enthalpy of the coil, and it
determines the average coil temperature rise after energy absorption in a quench:
E/M = H(T2 ) − H(T1 ) ≈ H(T2 )(35.56)

where T2 is the average coil temperature after the full energy absorption in a quench, and T1 is
the initial temperature. E/M ratios of 5, 10, and 20 kJ/kg correspond to ∼65, ∼80, and ∼100 K,
respectively. The E/M ratios of various detector magnets are shown in Fig. 35.41 as a functionof total stored energy. One would like the cold mass to be as small as possible to minimize thethickness, but temperature rise during a quench must also be minimized. An E/M ratio as large
as 12 kJ/kg is designed into the CMS solenoid, with the possibility that about half of the stored
energy can go to an external dump resistor. Thus the coil temperature can be kept below 80 K if
the energy extraction system works well. The limit is set by the maximum temperature that thecoil design can tolerate during a quench. This maximum local temperature should be <130 K (50K + 80 K), so that thermal expansion effects, which are remarkable beyond 80 K, in the coil aremanageable less than 50 K.
¶¶

The enthalpy, or heat content, is called H in the thermodynamics literature. It is not to be confused with themagnetic field intensity B/µ.

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35. Particle Detectors at Accelerators

Figure 35.41: Ratio of stored energy to cold mass for major detector solenoids. Gray indicatesmagnets no longer in operation.
35.12.3 Toroidal magnets
Toroidal coils uniquely provide a closed magnetic field without the necessity of an iron fluxreturn yoke. Because no field exists at the collision point and along the beam line, there is, inprinciple, no effect on the beam. On the other hand, the field profile generally has 1/r dependence.
The particle momentum may be determined by measurements of the deflection angle combinedwith the sagitta. The deflection (bending) power BL is
BL ≈

Z R0
Ri

Bi Ri dR
Bi Ri=ln(R0 /Ri ) ,R sin θsin θ

(35.57)

where Ri is the inner coil radius, R0 is the outer coil radius, and θ is the angle between theparticle trajectory and the beam line axis . The momentum resolution given by the deflection may
be expressed aspp sin θ∆p∝≈.
(35.58)p
BL
Bi Ri ln(R0 /Ri )The momentum resolution is better in the forward/backward (smaller θ) direction. The geometry has been found to be optimal when R0 /Ri ≈ 3–4. In practical designs, the coil is divided into
6–12 lumped coils in order to have reasonable acceptance and accessibility. This causes the coil
design to be much more complex. The mechanical structure needs to sustain the decentering force
between adjacent coils, and the peak field in the coil is 3–5 times higher than the useful magnetic
field for the momentum analysis [508].

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35. Particle Detectors at Accelerators

109

35.13 Measurement of particle momenta in a uniform magnetic field
The trajectory of a particle with momentum p (in GeV/c) and charge ze in a constant magnetic→−
field B is a helix, with radius of curvature R and pitch angle λ. The radius of curvature and→−momentum component perpendicular to B are related byp cos λ = 0.3 z B R ,(35.59)where B is in tesla and R is in meters.
The distribution of measurements of the curvature k ≡ 1/R is approximately Gaussian. The
curvature error for a large number of uniformly spaced measurements on the trajectory of a charged
particle in a uniform magnetic field can be approximated by(δk)2 = (δkres )2 + (δkms )2 ,(35.60)where δk= curvature error
δkres = curvature error due to finite measurement
resolution
δkms = curvature error due to multiple scattering.
If many (≥ 10) uniformly spaced position measurements are made along a trajectory in a
uniform medium,s
720
δkres = 0 2,(35.61)L
N +4
where N = number of points measured along track
L0 = the projected length of the track onto thebending plane = measurement error for each point,
perpendicular to the trajectory.
If a vertex constraint is applied at the origin of the track, the coefficient under the radical becomes320.
For arbitrary spacing of coordinates si measured along the projected trajectory and with variablemeasurement errors i the curvature error δkres is calculated from:(δkres )2 =4Vss,
w Vss Vs2 s2 − (Vss2 )2where V are covariances defined as Vsm sn = hsm sn −ism hsn with ism = w−1
P
w = i −2 .
The contribution due to multiple Coulomb scattering is approximately(0.016)(GeV/c)zδkms ≈
Lpβ cos2 λwhere p
z
L
X0

=
=
=
=

s

L
,
X0

(35.62)(si m /i 2 ) andP(35.63)

momentum (GeV/c)charge of incident particle in units of e
the total track length
radiation length of the scattering medium(in units of length; the X0 definedelsewhere must be multiplied by density)
β = the kinematic variable v/c.
More accurate approximations for multiple scattering may be found in the section on Passage ofParticles Through Matter (Sec. 34 of this Review). The contribution to the curvature error is given2
rms
approximately by δkms ≈ 8srms
plane /L , where splane is defined there.
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35. Particle Detectors at Accelerators

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