1

Cobbled together from:

i) “The quest for luminosity”, by Dr. Rob Applebyii) “An introduction to particle accelerators,” by Erik Adli

Particle accelerators are Particle accelerators are everywhere!everywhere!

Daily applicationsDaily applications TV, computer monitorTV, computer monitor Microwave oven, oscilloscopesMicrowave oven, oscilloscopes

IndustrialIndustrial Food sterilizationFood sterilization Electron microscopesElectron microscopes Radiation treatment of materialsRadiation treatment of materials Nuclear waste treatmentNuclear waste treatment

Particle accelerators are Particle accelerators are everywhere!everywhere!

Medical applicationsMedical applications Cancer therapy, RadiologyCancer therapy, Radiology Instrument sterilizationInstrument sterilization Isotope productionIsotope production

Research tools for many scientific Research tools for many scientific fieldsfields High energy physics experimentsHigh energy physics experiments Light sources for chemistry, biology etcLight sources for chemistry, biology etc Optics, neutron sourcesOptics, neutron sources Inertial fusionInertial fusion

The technologies usedThe technologies used

Large scale vacuumLarge scale vacuum High power microwavesHigh power microwaves Superconducting technologySuperconducting technology Very strong and precise magnetsVery strong and precise magnets Computer controlComputer control Large scale project managementLarge scale project management Accelerator physics (beam Accelerator physics (beam

dynamics)dynamics)

What is an accelerator?What is an accelerator?

Put simply, an accelerator takes a Put simply, an accelerator takes a stationary particle, with energy Estationary particle, with energy E00, and , and accelerates it to some final energy E.accelerates it to some final energy E.

This is achieved using electric fields for This is achieved using electric fields for acceleration and magnetic field for acceleration and magnetic field for beam controlbeam control

The uses are many…we are interested The uses are many…we are interested mainly in colliding beam applicationsmainly in colliding beam applications

Why do we need them?Why do we need them?

We want to study the building blocks of We want to study the building blocks of naturenature Very small structure, 10Very small structure, 10-10-10m to 10m to 10-15-15mm

Our probe is electromagnetic radiationOur probe is electromagnetic radiation To probe 10To probe 10-15-15m, we need m, we need =10=10-15-15mm

102 10hc

E h J

91.2 10

e

e

E eU

EeE E U V

e

The best accelerator in the universe…

A basic 9eV acceleratorA basic 9eV accelerator

The single electron passes through a potential difference of 1.5 volts, thus gaining 1.5 electron-volts of energy

(The simplest in the universe!)

An aside on electron An aside on electron voltsvolts

Make sure you understand the units Make sure you understand the units of particle and accelerator physics!of particle and accelerator physics!

1 eV = 1.602 x 10-19 joules

So we speak of GeV (Giga-electron-So we speak of GeV (Giga-electron-volts) and TeV (Tera-electron volts)volts) and TeV (Tera-electron volts)

The development of The development of acceleratorsaccelerators

Accelerators have gone through a Accelerators have gone through a long development process, includinglong development process, including Electrostatic acceleratorsElectrostatic accelerators The Van de Graaff acceleratorThe Van de Graaff accelerator The CyclotronThe Cyclotron The SynchrotronThe Synchrotron

The CyclotronThe Cyclotron

A vertical B-field A vertical B-field provides the force to provides the force to maintain the electron’s maintain the electron’s circular orbitcircular orbit

The particles pass The particles pass repeatedly from cavity repeatedly from cavity to cavity, gaining to cavity, gaining energy. energy.

As the energy of the As the energy of the particles increases, the particles increases, the radius of the orbit radius of the orbit increases until the increases until the particle is ejectedparticle is ejectedAC voltage between “D”s timed so electric field always accelerates

The first million volt The first million volt cyclotroncyclotron

“we were concerned about how many of the protons would succeed in spiralling around a great many times without getting  lost on the way."

08/01/32

Lawrence and Livingston at Berkeley

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Modern Particle Modern Particle AcceleratorsAccelerators

The particles gain energy by surfing on the electric fields of well-timed radio oscillations (in a cavity like a microwave oven)

Accelerating cavitiesAccelerating cavities Modern machines use a time-dependent electric Modern machines use a time-dependent electric

field in a cavity to accelerate the particlesfield in a cavity to accelerate the particles

How we manipulate the How we manipulate the beambeam

The charged particle beam is then The charged particle beam is then manipulated by the use of powerful manipulated by the use of powerful magnetsmagnets

In analogy with light optics, we call this In analogy with light optics, we call this process magnetic beam opticsprocess magnetic beam optics

The beam is bent using dipole magnets The beam is bent using dipole magnets and focusing using quadrupole magnets and focusing using quadrupole magnets

The magnets are very strong, often The magnets are very strong, often several Tesla, and use normal several Tesla, and use normal conducting, superconducting or conducting, superconducting or permanent magnet technologypermanent magnet technology

Lorentz equation

• The two main tasks of an accelerator– Increase the particle energy– Change the particle direction (follow a given trajectory, focusing)

• Lorentz equation:

• FB v FB does no work on the particle

– Only FE can increase the particle energy

• FE or FB for deflection? v c Magnetic field of 1 T (feasible) same bending power as en electric field of 3108 V/m (NOT feasible)

– FB is by far the most effective in order to change the particle direction

BE FFBvqEqBvEqF

)(

Magnetic latticesMagnetic lattices

Magnets are Magnets are combined to form combined to form a magnet latticea magnet lattice

The lattice steers The lattice steers and focuses the and focuses the beam beam Dipole

F Quadrupole

D Quadrupole

A mini tourA mini tour

Now we’ll look at some of the Now we’ll look at some of the world’s biggest circular acceleratorsworld’s biggest circular accelerators Just LEP and the LHCJust LEP and the LHC

Note that I only scratch the surface, Note that I only scratch the surface, miss many out and spend very little miss many out and spend very little time on non-colliding machinestime on non-colliding machines

There is much more life than I show!There is much more life than I show!

What was LEP?What was LEP? LEP was a circular electron-positron LEP was a circular electron-positron

collider, built at Cern, Geneva.collider, built at Cern, Geneva. The ring design (c=27km) meant that the The ring design (c=27km) meant that the

accelerating structures are seen many accelerating structures are seen many times by the circulating beams of particlestimes by the circulating beams of particles

The ring had 4 experimental sites - The ring had 4 experimental sites - ALEPH, ALEPH, DELPHI, L3 and OPAL.DELPHI, L3 and OPAL.

Final collision energy was 209 GeV (2 x Final collision energy was 209 GeV (2 x EEbeambeam))

It almost discovered the Higgs boson!It almost discovered the Higgs boson!

LL(arge)(arge)EE(lectron)(lectron)PP(ositron)(ositron)

The LEP tunnel The LEP tunnel

(this is one of LEPs superconducting cavities)

Acceleration techniques: RF cavities

• Electromagnetic power is stored in a resonant volume instead of being radiated

• RF power feed into cavity, originating from RF power generators, like Klystrons

• RF power oscillating (from magnetic to electric energy), at the desired frequency

• RF cavities requires bunched beams (as opposed to coasting beams)– particles located in bunches separated in space

From pill-box to real cavities

LHC cavity module ILC cavity

(from A. Chao)

Why circular accelerators?

• Technological limit on the electrical field in an RF cavity (breakdown)

• Gives a limited E per distance

Circular accelerators, in order to re-use the same RF cavity

• This requires a bending field FB in order to follow a circular trajectory (later slide)

The synchrotron

• Acceleration is performed by RF cavities

• (Piecewise) circular motion is ensured by a guide field FB

• FB : Bending magnets with a homogenous field

• In the arc section:

• RF frequency must stay locked to the revolution frequency of a particle (later slide)

• Synchrotrons are used for most HEP experiments (LHC, Tevatron, HERA, LEP, SPS, PS) as well as, as the name tells, in Synchrotron Light Sources (e.g. ESRF)

]/[

][3.0][

11 F 1

2

B cGeVp

TBm

p

qBvm

Focusing field: quadrupoles

• Quadrupole magnets gives linear field in x and y:Bx = -gy

By = -gx

• However, forces are focusing in one plane and defocusing in the orthogonal plane:

Fx = -qvgx (focusing)

Fy = qvgy (defocusing)

• Opposite focusing/defocusing is achieved by rotating the quadrupole 90

• Analogy to dipole strength: normalized quadrupole strength:

]/[

]/[3.0][ 2

cGeVp

mTgmk

p

egk

inevitable due to Maxwell

Optics analogy

• Physical analogy: quadrupoles optics

• Focal length of a quadrupole: 1/f = kl– where l is the length of the quadrupole

• Alternating focusing and defocusing lenses will together give total focusing effect in both planes (shown later)

– “Alternating Gradient” focusing

The Lattice

• An accelerator is composed of bending magnets, focusing magnets and non-linear magnets (later)

• The ensemble of magnets in the accelerator constitutes the “accelerator lattice”

Example: lattice components

Conclusion: transverse dynamics

• We have now studied the transverse optics of a circular accelerator and we have had a look at the optics elements,

– the dipole for bending– the quadrupole for focusing– the sextupole for chromaticity correction

• All optic elements (+ more) are needed in a high performance accelerator, like the LHC

But particles radiate But particles radiate energy!energy!

B

Synchrotron Radiation froman electron in a magnetic field:

2222

2BEC

ceP

4

/EC

revE

Energy loss per turn of a machine with an average bending radius :

Energy loss must be replaced by RF systemcost scaling $ Ecm2

~3400 MeV forLEP200 (18 MW)

End of the road?End of the road?

So, because of the low mass of an So, because of the low mass of an electron, LEP is the end of the road for electron, LEP is the end of the road for circular electron machines!circular electron machines!

The higher proton mass means that we The higher proton mass means that we can build the LHC (what matters is can build the LHC (what matters is =E/E=E/E00))

So the next generation of electron So the next generation of electron colliders cannot use a ring…so we need colliders cannot use a ring…so we need to stretch out that ring into a straight to stretch out that ring into a straight line line

A linear machineA linear machine

e+ e-

~15-20 km

For a Ecm = 1 TeV machine:

Effective gradient G = 500 GV / 14.5 km

= 35 MV/m

Note: for LC, $tot E

The International Linear The International Linear ColliderCollider

The International Linear Collider (ILC) is a The International Linear Collider (ILC) is a proposed machine, to complement the LHCproposed machine, to complement the LHC

It shall collider electron and positrons It shall collider electron and positrons together at a centre-of-mass energy of 1 together at a centre-of-mass energy of 1 TeVTeV

The anticipated cost is a cool The anticipated cost is a cool $8,000,000,000!$8,000,000,000!

Currently, a detailed physics case and Currently, a detailed physics case and accelerator design is being formulated, in accelerator design is being formulated, in an attempt to get someone to pay for it!an attempt to get someone to pay for it!

The parts of a linear The parts of a linear collidercollider

The key parametersThe key parameters The linear collider is driven by 2 key parametersThe linear collider is driven by 2 key parameters

The collision energyThe collision energy The luminosityThe luminosity

The two beams collide head-on, so the collision energy is the The two beams collide head-on, so the collision energy is the sum of the beam energies E=2Esum of the beam energies E=2Ebeambeam

The luminosity tells us the probability of the two beams The luminosity tells us the probability of the two beams interacting – essentially the overlap of the two colliding beamsinteracting – essentially the overlap of the two colliding beams

Event rate vs. Event rate vs. LuminosityLuminosity

Rate = L*s Rate = L*s ee++ee-- annihilation cross-section approximately annihilation cross-section approximately

L=10EL=10E3434/cm/cm22s = 0.00001/fb/s luminosity results s = 0.00001/fb/s luminosity results in rate 0.0015/s = 5.4/hr.in rate 0.0015/s = 5.4/hr.

Presumably interested in much more rare Presumably interested in much more rare processesprocesses

High luminosity is very important at high High luminosity is very important at high energyenergy

To increase probability of direct eTo increase probability of direct e++ee-- collisions (luminosity) and birth of new collisions (luminosity) and birth of new particles, beam sizes at IP must be very particles, beam sizes at IP must be very small small

How to get LuminosityHow to get Luminosity

Dyx

brep HNnf

L

2

4

Beam size: 250 * 3 * 110000 nanometers(x y z)

(We shall derive this next lecture)

The Livingstone plotThe Livingstone plot

The large hadron colliderThe large hadron collider

The large hadron collider (LHC) uses the The large hadron collider (LHC) uses the same tunnel as LEP, at Cern in Genevasame tunnel as LEP, at Cern in Geneva

The machine is a 14 TeV proton-proton The machine is a 14 TeV proton-proton collider, so each stored beam will have collider, so each stored beam will have an energy of 7 TeVan energy of 7 TeV

It is being built now, and shall start It is being built now, and shall start operation sometime in operation sometime in 2007no2007no 2009oops2009oops 20112011

There are a number of experimentsThere are a number of experiments

The LHC tunnelThe LHC tunnel

LHC layout

• circumference = 26658.9 m

• 8 interaction points, 4 of which contains detectors where the beams intersect

• 8 straight sections, containing the IPs, around 530 m long

• 8 arcs with a regular lattice structure, containing 23 arc cells

• Each arc cell has a FODO structure, 106.9 m longFODO = focus-drift-defocus-drift

LHC main parametersat collision energy

Particle type p, Pb

Proton energy Ep at collision 7000 GeV

Peak lumin. (ATLAS, CMS) 1034 cm-2s-1

Circumference C 26 658.9 m

Bending radius 2804.0 m

RF frequency fRF 400.8 MHz

# particles per bunch np 1.15 x 1011

# bunches nb 2808 1400 in 2011-2

4000 in 2012

Colliding Proton/Antiproton Colliding Proton/Antiproton BeamsBeams

No problem with synchrotron radiation energy loss, but…

Like throwing bags of marbles at each other at high velocity:

Marble-marble collisions are interesting, not bag-bag collisions

Fortunately, the number and arrangements of the “marbles” has been measured by other experiments

Timeline of Proton Timeline of Proton CollidersColliders

1975 1980 1985 1990 1995 2000 2005 2010 2015 2020

W/Z bosons Top quark Higgs, Supersymmetryetc

Proton-proton

Proton-antiproton

Proton-proton

Proton-Antiproton Collisions at Proton-Antiproton Collisions at Fermilab (Chicago)Fermilab (Chicago)

The Tevatron The Tevatron accelerator, 6 km accelerator, 6 km circumferencecircumference

The CDF (Collider Detector at Fermilab)

experiment

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LHC Dipole Design

50

LHC Dipole Magnet (3D)

51

ReferencesBibliography:

K. Wille, The Physics of Particle Accelerators, 2000

...and the classic: E. D. Courant and H. S. Snyder, "Theory of the Alternating-Gradient Synchrotron", 1957

CAS 1992, Fifth General Accelerator Physics Course, Proceedings, 7-18 September 1992

LHC Design Report [online]

Other references:USPAS resource site, A. Chao, USPAS january 2007

CAS 2005, Proceedings (in-print), J. Le Duff, B, Holzer et al.

O. Brüning: CERN student summer lectures

N. Pichoff: Transverse Beam Dynamics in Accelerators, JUAS January 2004

U. Amaldi, presentation on Hadron therapy at CERN 2006