Particle Accelerators and Detectors

Creating collisions at extreme energies

In 1967, Jerome Friedman, Henry Kendall, and Richard Taylor at SLAC aimed 20 GeV electrons at stationary protons. Most electrons passed through with small deflections — but some scattered at enormous angles, as if they had struck a hard, small object inside the proton. This was the same pattern Rutherford had seen when alpha particles hit gold foil in 1909 — evidence of point-like internal structure. To resolve structure at 10⁻¹⁷ m, you need particles with de Broglie wavelengths that small: by $\lambda = h/p$, this requires enormous momentum — and hence enormous energy. Additionally, Einstein's $E = mc^2$ means that creating massive particles (like the Higgs boson at 125 GeV or the top quark at 173 GeV) requires at least that much collision energy.

Linear accelerators (linacs): Particles are accelerated in a straight line by oscillating electric fields. Each accelerating stage adds energy. Linacs are used as injectors for larger machines and for applications like medical radiation therapy. The Stanford Linear Accelerator (SLAC) reached 50 GeV electrons over a 3 km track.

Synchrotrons: Particles travel in a circular path, gaining energy from radio-frequency (RF) cavities each lap. A system of dipole magnets bends the trajectory; quadrupole magnets focus the beam. As energy increases, the magnetic field must increase to keep particles on the same radius. The Large Hadron Collider (LHC) at CERN is a synchrotron with a 27 km circumference, accelerating protons to 6.8 TeV per beam (13.6 TeV centre-of-mass energy).

Colliders vs fixed-target experiments: In colliders, two counter-rotating beams collide head-on, maximising the centre-of-mass energy available to create new particles. For two beams of equal mass $m$ and energy $E$ colliding head-on:

In fixed-target experiments, a beam hits a stationary target. Most of the beam energy goes into the kinetic energy of the products rather than mass creation:

For the same beam energy, a collider gives dramatically higher centre-of-mass energy, making it far more efficient for producing heavy particles.

High energy needed: E = mc² to create massive particles; λ = h/p to resolve small structures. Linac: single-pass straight, limited by length (SLAC: 3 km, 50 GeV). Synchrotron: circular, RF cavities boost energy each lap (LHC: 27 km, 6.8 TeV/beam). Collider: √s = 2E_beam. Fixed-target: √s ≈ √(2m_target c²·E_beam) — much less efficient.

Write both √s formulas — the collider vs fixed-target comparison is a Band 5 exam question.

Reconstructing collisions from debris

We just saw that synchrotrons achieve massive centre-of-mass energies through repeated acceleration over many laps. That raises a question: once a collision happens and produces exotic particles that live for 10⁻²² s, how do we actually detect them? This card answers it → onion-layered detectors — tracking, EM calorimeter, hadronic calorimeter, muon detectors — each capture different particles; neutrinos appear as missing transverse momentum.

Modern detectors like ATLAS and CMS at the LHC are onion-like structures arranged in concentric layers, each optimised to detect different types of particles. By combining information from all layers, physicists reconstruct the entire collision event — identifying particles, measuring their energies and momenta, and searching for exotic signatures of new physics.

Inner tracking detectors: The innermost layer, closest to the beam pipe. Charged particles leave trails of ionisation in silicon pixels or drift chambers. A strong magnetic field bends their trajectories — the radius of curvature gives momentum via $p = qBr$. Neutral particles leave no track. The sign of charge is determined from the direction of curvature.

Electromagnetic (EM) calorimeters: Electrons and photons initiate electromagnetic cascades and deposit all their energy in this layer. Made of dense materials (lead, liquid argon, or scintillating crystals) to absorb the shower completely. Hadrons mostly pass through.

Hadronic calorimeters: Hadrons (protons, neutrons, charged pions) penetrate further and shower in steel or brass interspersed with scintillating tiles. Measures jet energies — the collimated sprays of hadrons produced by quarks and gluons.

Muon detectors: The outermost layer. Muons are too heavy to shower in the calorimeters and interact only electromagnetically and weakly — they penetrate all other layers and reach the outer detectors. Identifying muons is crucial for many discovery channels, e.g., Higgs $\rightarrow ZZ^* \rightarrow 4\mu$.

Neutrinos: Escape the detector entirely, appearing as "missing" transverse energy and momentum. Their presence is inferred from momentum imbalance — if all visible particle momenta do not cancel, something invisible carried the rest.

Detector layers (inside out): tracking (p = qBr; charged particles only — no track for neutrals), EM calorimeter (e⁻ and γ stop here), hadronic calorimeter (p/n/π stop here), muon detectors (outermost). Neutrinos escape entirely — inferred from missing transverse momentum. Higgs discovered via H→γγ and H→ZZ*→4ℓ (clean signatures in EM calorimeter).

Draw the concentric detector layers and write which particle stops in each — this diagram question appears almost every year.