C4: Detectors and accelerators

What limits particles being detected?

• Particle needs to be long lived enough to reach detector

• Other particles need to be reconstructed from decay products, so need to measure 4 momenta of daughter particles.

How to treat particles in detectors?

Detectors significantly larger than Compton wavelengths of particles → so sufficient to treat them as quasi-classical particles.

Properties of particles that can be measured.

• Existence (Geiger counter)

• Location (photons in imaging)

• Energy

• Complete 4-momentum of individual particles needed for full kinematic reconstruction

  • 3-momentum and energy, or mass

  • Mass can be known if particle is identified

  • Need tracking for direction of three-momentum (at least two points along trajectory, or >= 4 positions along curved track in magnetic field)

  • Energy from calorimetry

How do photons interact with matter?

Photoelectric effect

• Dominant up to ~1MeV

• Photon absorbed by an atom

  • Energy frees and electron, which escaped with E - E_photon - E_bind

  • For single atom E_bind is ionisation energy

  • For solids the parameter is the photoelectric work function, the minimum energy required to remove an electron from the solid to infinity.

• Below threshold for PE, material can be transparent (if no molecular resonances) - optical region.

• Because of shell and shielding effects no closed form description of cross-section.

Compton effect

Pair production

Radiation length

X₀ - the distance at which the energy of incoming electron has dropped by a factor 1/e (natural logarithm) due to Bremsstrahlung. Denser material, shorter radiation length.

Bremsstrahlung

• Cross sections may be calculated from QED (complicated due to screening)

• The coupling is proportional to Z, so squared in FGR to get Z² factor.

Interaction of charged particles with solid

Charged particles interact EM with nuclei and electrons

• Electrons are light compared to the incoming particle - the particle will “kick” electrons out of the way —> ionisation/excitation 

• Transfers energy to the electron. High density of charges results in quasi-continuous energy loss

• Nuclei are heavy so mostly elastic collisions. Will deflect the trajectory of the particle.

Range of charged particles in a material

• High stopping power for low momenta, so highest energy loss at the end of trajectory (Bragg peak) → radiotherapy

Cherenkov radiation

• Can be seen as luminar boom - the speed of the particle exceeds the speed of light in the material

• It is a (small) part of charged particle energy loss.

• emission angle given by Cherenkov angle:

  • cosθ_Ch​=v(c/n)​=(nβ)⁻¹

• Does not depend explicitly on the density, but index of refraction typically larger for a denser material.

Multiple scattering (not expression!)

Hadronic interactions

Number of ionisation pairs created in a length of detector material

To detect ionization charge

Drift in gases

Ion drift

Electron drift

Diffusion equation for ensemble of drifting charge carriers IGNORED

Drift in magnetic fields

Cyclotron frequency

ω = eB/m_e

Drift in liquids

• Need non-polar molecules

• Detectable ionisation charge smaller than generated charge, as time needed for thermalisation much shorter than in gases

  • Significant probability for recombination of a newly created electron-ion pair

  • Charge yield increases with electric field

• Easiest is noble gases (but need cryogenic).

• Need a liquid which wont absorb the electrons —> low electron affinity

Drift in semiconductors

• In semiconductors charges in conduction band are mobile

• Macroscopic drift velocity given by collisions.

• Scattering on phonons in the lattice, and on ionised impurities.

• At larger field strength, drift velocity saturates due to inelastic scattering of charge carriers with the emission of optical phonons.

Internal amplification

Amplification in gases

• Generates an avalanche of charges

• Ionisation in avalanche and excitation with subsequent photon emission

Photomultiplier tubes

• Photocathode has very low work function, so incoming photon creates photoelectron.

• Doesn’t have 100% efficiency => can’t measure single photons.

• Electrons accelerated by series of dynodes - amplify the number of electrons so get a big signal

  • Must be in a vacuum

  • Do not work well in a magnetic field => wrap in soft iron. Magnetic field would deflect electrons so don’t reach dynodes.

What are scintillation detectors?

Scintillation in liquids (e.g. argon)

Scintillation vs Cherenkov

Organic and inorganic scintillators

Organic scintillators => standard cheap detector. Response in molecule very fast.

Inorganic scintillators => much more dense, so stop particles in short distance but they are slower (due to time required for thermalisation of charge carriers).

Photon collection SKIP

Resistive plate chambers (RPCs) SKIP

Wire chambers

Multiwire proportion chambers

Micropattern gas detectors CUT

• Reduce instability and dimensional issues by mounting electrodes on an insulating substrate

• However issue where some charges stick to surface and a spark destroys the detector

• Solution is to reduce local gas gain by introducing additional amplification structures

Drift chambers

Resolution in drift chambers

Challenge for gaseous photon detectors

Low photon absorption cross-section

• In Cherenkov detectors, photons in visible or UV range. So either add chemical with low photo-ionisation threshold or a cathode coating with a low work function

• For X-ray photons transmission radiation detectors - use a gas with high-Z atoms (Xe for x-rays absorption length about 10mm)

Liquid TCPs CUT

Photon detection in liquids CUT- ALREADY MENTIONED

Semiconductors (not learnt expression)

p-n junction (haven’t learn expression)

Leakage current

Silicon pixel detectors

Advantages (4)

Disadvantages (2)

Silicon detectors with gain IGNORING FOR NOW

Momentum measurements in magnetic field JUST TO SEE!

Multiple scattering in detector layers (just to see)

What are calorimeters?

Error on calorimeter

EM showers

Resolution of a calorimeter

Sampling calorimeter

Energy resolution in sampling calorimeter

Hadronic showers

Particle flow in hadronic calorimeters

Particle identification

Time of flight (TOF) (looked at)

Cherenkov detectors

Choosing material for cherenkov detectors

Ring-imaging Cherenkov detectors (RICH) IGNORED FOR NOW

Linear vs circular accelerator

Bremsstrahlung in circular accelerators SPLIT?

Electron sources

Muon sources

Accelerating muons boosts their lifetime in the lab frame

Neutrino beams (electron and muon neutrino)

Generating antiprotons

Cavity optimisation SKIP

Phase stability SKIP

Bending magnets in accelerator

Focusing (weak and strong)

Strength of quadrupole CUT - WOULD BE GIVEN IF THEY WANTED IT!

Luminosity

Simple luminosity calculation

More accurate luminosity calculation

Interaction point

Measuring luminosity

Resolution for an EM calorimeter (repeated!)

Poisson equation

Explanation of silicon micro-strip detector

Uncertainty in detector divided into detecting strips width x

Useful to remember when converting uncertainties (differentials identity)

Drift chamber explanation

Ramo’s theorem

Electric field in concentric cylinders

Capacitance for cylindrical capacitor (per unit length)

Maxwell equations

Area of any conic section (eg ellipse) CUT

Babha scattering

Cherenkov detector

Choosing medium for Cherenkov detector

For such a large detector, the medium has to be cheap. Water is the obvious choice. Water is also a very good Cherenkov medium, being an insulator and transparent.

Luminosity and value of beta-function at the interaction point ISH

Beam emittance

What is the beta function

Describes the amplitude modulation. It varies around the ring as the focussing strength changes.

Normalised emmittance

If the energy is changed, it is the normalised emittance γε that is conserved, so ε decreases as the beam is accelerated. This allows the beampipe diameter to be reduced along a chain of accelerators. So need a chain of pre-accelerators to get the beam width small enough to be injected into a narrow high-energy accelerator such as the LHC.

Logarithmic method for error calculations