• Accelerators & Detectors
• Luminosity and cross-sections
• Fixed target vs collider
• linac vs circular
• Detectors: fixed target, collider
• Detector elements

1

High Energies in Accelerators

• Produce new particles
• e.g. W, Z,
• … Higgs ?
• Probe small scale structure
• p=h/λ, e.g. proton structure

2

Accelerators

• Electric Fields to accelerate stable charged particles to high energy
• Simplest Machine – d.c. high V source
• 20MeV beam
• High frequency a.c. voltage
• Time to give particles successive kicks

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3

> MeV Energy speed ~c, hence length of tubes same

Linear Accelerator - Linac

Fermilab linac

Synchrotron

• pp,ep collider – need different magnets
• p anti-p, or e^-e⁺
• One set of magnets,one vacuum tube
• LEP (e+e-), Tevatron(p anti-p)
• Need to produce anti-particles
• Positron – OK, anti-protons difficult
• from proton nucleus collisons

4

radius

B field (bending) and

E-field (accelerating cavity)

Synchronised with particle

velocity

Magnets

• International Linear Collider plan for 35 MV/m
• Length for 500 GeV beams ?

5

Accelerating Cavities

Niobium, superconducting

1200 dipole superconducting (1.9K) magnets, 14.3m long, 8.35 T

Proton energy 7 TeV,

minimum ring circumference ?

Energy considerations: �1)Fixed Target vs Collider

• Linac Energy
• length & voltage per cavity
• Synchrotron Energy
• Radius, max B-field
• Synchrotron radiation

6

Higher E = bigger machine

• Energy
• Achieve higher sqrt(s) at collider
• Direct new particle searches
• Stable particles
• Colliding beam expts use p,e^- (muons?)
• Rate
• Higher luminosity at fixed target

2) Linac vs synchrotron

Energy: Fixed Target Experiment

7

b at rest:E_b=m_b

for

Energy: Colliding Beam

Symmetric beams – lab frame =CM frame Particle & anti-particle collision

Synchrotron Radiation

8

ρ is radius of curvature of orbit

So for relativistic particles β≈1

Limits energy for a electron/positron machine

< ~ 100GeV/beam

Also a useful source of high energy photons for material studies

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Diamond Synchrotron started operation recently in Oxfordshire

Hence, LHC proton collider

Energy lost as particles

bent to travel in circle

Synchrotron: Beam Stability

• Particles accelerated in bunches LHC N=10¹⁰
• Particle accelerated just enough to keep radius constant – in reality…
• Synchrotron Oscillations
• Movement of particles wrt bunch
• out of phase with ideal, stability ensured

9

Particle B arriving early receives a larger RF pulse

moves to a larger orbit and arrives later next time

Particle C arriving late received smaller acceleration, smaller orbit, earlier next time

V

Early

C

Focussing

• Particles also move in transverse plane
• Betatron oscillations
• Origin - natural divergence of the originally injected beam and small asymmetries in magnetic fields.
• Beams focussed using quadropole magnets.

10

N.B. Dipoles=bending, Quadropoles=focussing

Focussing in vertical/ horizontal planes

Force towards centre of magnet.

Alternate vertical / horizontal

net focussing effect in both planes.

+ve particle

into paper

Cooling

• Initially particles have a wide spread of momentum and angle of emission at production
• Need to “cool” to bunch
• One methods – stochastic cooling used at CERN for anti-protons
• Sense average deviation of particles from ideal orbit
• Provide corrective kick
• Note particles travelling at c and so does does electrical signal !

11

Particle

accelerator

Cross-Sections

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We perform an experiment:

How many pions do we expect to see ?

• Duration of expt(t)
• Volume of target seen by beam (V)
• Density of p in target (ρ)
• Beam incident /sec/Unit area (I)
• Solid angle of detector (ΔΩ)
• Efficiency of experiment (trigger/analysis) (ε)
• (I t) (Vρ) ΔΩ ε
• (1/Area)(N_o) ΔΩ ε

Smashing beam into a target

The constant of proportionality – the bit with the real physics in !

– is the differential cross-section

ΔN

Integration over 4π gives total cross-section

Can divide total xsec into different reactions e.g.

xsec measured in barn, pb etc…

Luminosity

13

For colliding beams no V (target volume) term.

Require two narrow beams with complete overlap at collision point

Typical beam sizes 10-100μm in xy and cm in z

Interaction rate is

n₁,n₂ are number of particles in a bunch

f is the frequency of collisions

e.g. rotation in circular collider, this can be high, LHC 40 MHz!

a is the bunch area of overlap at collision point (100% overlap)

jn s^-1

is known as the luminosity

LHC plans up to 10³⁴ cm^-2 s^-1

Number of events = lumi x xsec x time

Typically good machine running time is ~1/3 yr (1x10⁷s)

Linac – one shot machine

Synchrotron – particles circulate for many hours

Fixed target luminosity can be higher

e.g. 10¹² p on 1m long liquid-H target gives~10³⁷cm^-2 s^-1

Electrons vs Protons ?

• Useful centre-of-mass energy electron vs proton
• Proton is composite, ~10% root(s) useful energy
• 100 GeV LEP, 1TeV Tevatron had similar reach

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• Electron-positron much cleaner environment
• No extra particles
• Can detect missing energy e.g. neutrinos, new neutral particles
• Proton
• Higher energies, less synchrotron radiation
• Electron-positron – “high precision machine”
• Proton-proton – “discovery machine”

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14

Tevatron

Event

LEP

Event

15

A typical modern particle physics experiment

DELPHI experiment @ LEP collider

Example Particle Detector- ATLAS

16

Detector Components:

Tracking systems, ECAL/HCAL, muon system

+ magnet – several Tesla - momentum measurement

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Tracking: Spatial Resolution 5-200μm

ECAL:

HCAL:

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Energy Resolution

Time Resolution:

LHC 40Mz=25ns

Elements of Detector System

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• Sensitive Detector Elements: e.g.
• Tracking - silicon sensors, gaseous ionisation detectors
• Calorimeters – lead, scintillators
• Electronic readout:e.g.
• Custom designed integrated circuits, custom pcbs,
• Cables, power supplies.
• Support Services: e.g.
• Mechanical supports
• Cooling
• Trigger System
• LHC 40 MHz, write to disk 2kHZ
• Which events to take ?
• Parallel processing, pipelines
• Trigger levels
• Add more detector components at higher levels

Computing in HEP

Each event 100kB-1MB

1000MB/s, 1PB/year

Cannot analyse on

single cluster

Worldwide computing

Grid

Example Neutrino Detector

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18

But not all detectors look like previous examples

Example – neutrino detector

• Very large volume
• Low data rate

Super-Kamiokande

half-fill with water

50,00 tonnes of water

11000 photomultiplier tubes

Neutrinos interact

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Chereknov light cone given off

and detected by photomultipliers

Accelerator Summary

19

Considerations for an accelerator.

• Reaction to be produced
• Energy required
• Luminosity required
• Events expected

Particles are accelerated by electric field cavities.

Achievable Electric fields few MV/m

Higher energy = longer machine

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Fixed target expt. – not energy efficient but sometimes unavoidable

(e.g. neutrino expts)

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Particles are bent into circles by magnetic fields.

Synchrotron radiation – photons radiated as particle travels in circle

E lost increases with γ⁴, so heavy particles or bigger ring

Or straight line…

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Synchrotron oscillations controlled by rf acceleration

Quadropole magnets used to focus beams in transverse plane

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Linac – repetition rate slower as beams are not circulating

Synchrotron – beams can circulate for several hours

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