Particle Accelerators and Detector Systems

Particle accelerators use electric fields to increase the energy of charged particles and magnetic fields to steer and focus them, and particle detectors record the products of collisions using layers of tracking chambers, calorimeters and muon systems; the momentum of a charged particle in a magnetic field B is found from the radius of its track, p = 0.2998 × B × r (p in GeV/c, B in tesla, r in meters). In brief: linear accelerators (linacs) accelerate particles in a straight line, while cyclotrons and synchrotrons bend them in circles to reuse the accelerating fields. Colliders bring two beams together head-on, so that the whole beam energy is available to create new particles. The Large Hadron Collider (LHC) at CERN has a circumference of 27 km and collides protons at up to 13.6 TeV.

The discoveries of the top quark, the W, Z and Higgs bosons were made with large accelerators and detectors, which are among the most complex scientific instruments ever built. This guide explains how accelerators work, why colliders are needed, how detectors identify particles, compares the types of accelerator and detector layers in tables, works through numerical examples and corrects common mistakes.

How do accelerators work?

A charged particle gains energy qV when it passes through a potential difference V (1 eV for an electron through 1 V). To reach high energies, accelerators use many stages:

• Linear accelerators (linacs): a series of cavities or drift tubes with alternating radio-frequency (RF) electric fields, timed so that the particle sees an accelerating field in each gap. The SLAC linac (3.2 km) accelerated electrons to 50 GeV; medical linacs, 6 to 20 MeV, are used for radiotherapy.
• Cyclotron: a charged particle moves in a circle in a uniform magnetic field, with a period T = 2πm ÷ qB independent of speed (at nonrelativistic energies), passing twice per turn through a gap with an alternating voltage of the same frequency (f = qB ÷ 2πm). The orbit radius grows with energy. Cyclotrons produce medical isotopes (proton energies of 10 to 30 MeV). At relativistic energies, the mass increases and the particles get out of step with the RF, so synchrocyclotrons and synchrotrons are needed.
• Synchrotron: the particles travel on a ring of fixed radius in a vacuum tube; the magnetic field of the bending magnets is increased in step with the momentum of the beam, and the RF frequency is synchronized. Quadrupole magnets focus the beam. Electrons lose a large fraction of energy by synchrotron radiation (∝ γ⁴/R), so ring electron-positron colliders are limited in energy; protons, which are heavier, can reach higher energies in the same ring; synchrotron radiation from electron rings is also exploited as an intense X-ray source.

The momentum is limited by the strength of the magnets and the size of the ring: p (GeV/c) = 0.2998 × B (T) × R (m). The LHC, with dipole magnets of 8.3 T made of superconducting niobium-titanium cooled to 1.9 K, bends 7 TeV protons on a radius of 2.8 km.

Why build colliders?

When a beam of energy E strikes a target at rest, momentum conservation requires the products to move on, so only a part of the energy is available for creating new particles: the center-of-mass energy is √(2mc²E) for E ≫ mc², which grows only as the square root of the beam energy. In a collider with two beams of equal energies colliding head-on, the total momentum is zero and all the energy, E_cm = 2E, is available. The price is a low interaction rate, since the beams are very dilute compared with a solid target. The measure of the interaction rate is the luminosity (collisions per second per unit cross section). The LHC has bunches of about 10¹¹ protons crossing every 25 ns, giving about a billion collisions per second at each experiment.

How do detectors work?

A general-purpose detector, such as ATLAS or CMS, is built in concentric layers around the collision point:

1. Tracking system (silicon sensors and wire chambers) inside a strong solenoid magnet (3.8 T in CMS). Charged particles leave a series of hits; the curvature of the track gives the momentum (p = 0.3Br) and the sign of the charge. Tracks that start away from the collision point show decays of long-lived particles (b quarks, tau leptons).
2. Electromagnetic calorimeter (dense crystals or lead and liquid argon): electrons and photons produce showers of particles, and the total light or charge measures their energy.
3. Hadronic calorimeter (steel or brass with scintillators): hadrons (protons, neutrons, pions) interact with the nuclei and produce showers; the energy of jets is measured.
4. Muon chambers on the outside: muons are the only charged particles that penetrate all the layers.

Neutrinos pass through unseen, and their presence is inferred from “missing” momentum. Computing systems filter the 40 million crossings a second to select a few hundred events per second to be recorded (triggers). Particle identification uses the combination of signals: an electron leaves a track and an electromagnetic shower; a photon, only a shower; a muon, a track through everything; a jet of hadrons, a track and a hadronic shower; a neutral long-lived particle, a gap in the tracks. Older detectors: the cloud chamber, bubble chamber and spark chamber.

Accelerator types compared

Worked example: cyclotron frequency, bending radius and collision energy

1. Cyclotron frequency. A proton in a magnetic field of 1.5 T: f = qB ÷ (2πm) = 1.602 × 10⁻¹⁹ × 1.5 ÷ (2π × 1.673 × 10⁻²⁷) = 2.29 × 10⁷ Hz = 22.9 MHz. The same field for an electron gives 42 GHz.
2. Energy of a cyclotron. If the maximum radius is 0.50 m and B = 1.5 T, the proton momentum p = qBr = 1.602 × 10⁻¹⁹ × 1.5 × 0.50 = 1.2 × 10⁻¹⁹ kg·m/s (= 0.225 GeV/c). The kinetic energy: KE = p² ÷ 2m = 4.3 × 10⁻¹² J = 27 MeV (nonrelativistic, accurate to about 3 percent).
3. Bending radius for the LHC. p = 7.0 TeV/c = 7,000 GeV/c, B = 8.33 T: r = p ÷ (0.2998 × B) = 7,000 ÷ (0.2998 × 8.33) = 2,803 m, in agreement with the 2.8 km bending radius of the dipoles, which fill about two thirds of the 27 km circumference (2π × 2,803 m = 17.6 km of dipoles).
4. Track in a detector. A muon of 10 GeV/c in the 3.8 T field of a detector has a radius of curvature r = 10 ÷ (0.2998 × 3.8) = 8.8 m. A 1 GeV/c particle has r = 0.88 m, so it curls up inside the tracker.
5. Fixed target versus collider. A 7 TeV proton hitting a stationary proton has E_cm = √(2m_pc²E + 2m_p²c⁴) = √(2 × 0.938 × 7,000 + 2 × 0.880) = 114.6 GeV. Two 7 TeV beams colliding head-on give 14 TeV, about 120 times the energy.
6. Energy gain in a linac. An electron linac with an accelerating gradient of 20 MV/m needs 50 GeV ÷ 20 MeV/m = 2,500 m to reach 50 GeV, close to the 3.2 km length of the SLAC accelerator.

How did accelerators develop?

John Cockcroft and Ernest Walton built a voltage multiplier in 1932 and split the lithium nucleus with 0.7 MeV protons. Ernest Lawrence invented the cyclotron in 1929 to 1931, and was awarded the Nobel Prize in Physics in 1939. The Bevatron (1954) produced antiprotons; SLAC (1966) discovered the quark structure of the proton; CERN’s Super Proton Synchrotron, converted to a collider, found the W and Z in 1983. The Tevatron at Fermilab (1.96 TeV) found the top quark in 1995. The LHC started in 2008, discovered the Higgs boson in 2012, and began operation at 13.6 TeV in 2022. Future colliders under discussion include a larger circular collider of about 91 km.

Which mistakes are common?

Mistake 1: Thinking that the magnetic field accelerates the particles

Magnetic fields only bend the path; they do no work. The energy is supplied by electric fields.

Mistake 2: Using the beam energy as the energy available for new particles in fixed-target experiments

Much of the energy goes into the motion of the products. Only the center-of-mass energy is available.

Mistake 3: Believing that detectors “see” particles directly

They record the effects of particles (ionization, light, showers), and the particles are identified from the patterns of those signals.

Mistake 4: Saying that a bigger ring is only for more particles

A larger radius lets the beam reach a higher momentum for a given magnetic field and reduces energy losses by synchrotron radiation.