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Cobbled together from: i ) “The quest for luminosity”, by Dr. Rob Appleby ii) “An introduction to particle accelerators,” by Erik Adli. Particle accelerators are everywhere!. Daily applications TV, computer monitor Microwave oven, oscilloscopes Industrial Food sterilization

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

particle accelerators are everywhere
Particle accelerators are everywhere!
  • Daily applications
    • TV, computer monitor
    • Microwave oven, oscilloscopes
  • Industrial
    • Food sterilization
    • Electron microscopes
    • Radiation treatment of materials
    • Nuclear waste treatment
particle accelerators are everywhere1
Particle accelerators are everywhere!
  • Medical applications
    • Cancer therapy, Radiology
    • Instrument sterilization
    • Isotope production
  • Research tools for many scientific fields
    • High energy physics experiments
    • Light sources for chemistry, biology etc
    • Optics, neutron sources
    • Inertial fusion
the technologies used
The technologies used
  • Large scale vacuum
  • High power microwaves
  • Superconducting technology
  • Very strong and precise magnets
  • Computer control
  • Large scale project management
  • Accelerator physics (beam dynamics)
what is an accelerator
What is an accelerator?
  • Put simply, an accelerator takes a stationary particle, with energy E0, and accelerates it to some final energy E.
  • This is achieved using electric fields for acceleration and magnetic field for beam control
  • The uses are many…we are interested mainly in colliding beam applications
why do we need them
Why do we need them?
  • We want to study the building blocks of nature
    • Very small structure, 10-10m to 10-15m
  • Our probe is electromagnetic radiation
    • To probe 10-15m, we need =10-15m
a basic 9ev accelerator
A basic 9eV accelerator

(The simplest in the universe!)

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

an aside on electron volts
An aside on electron volts
  • Make sure you understand the units of particle and accelerator physics!

1 eV = 1.602 x 10-19 joules

  • So we speak of GeV (Giga-electron-volts) and TeV (Tera-electron volts)
the development of accelerators
The development of accelerators
  • Accelerators have gone through a long development process, including
    • Electrostatic accelerators
    • The Van de Graaff accelerator
    • The Cyclotron
    • The Synchrotron
the cyclotron
The Cyclotron
  • A vertical B-field provides the force to maintain the electron’s circular orbit
  • The particles pass repeatedly from cavity to cavity, gaining energy.
  • As the energy of the particles increases, the radius of the orbit increases until the particle is ejected

AC voltage between “D”s timed so electric field always accelerates

the first million volt cyclotron
The first million volt cyclotron


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

Lawrence and Livingston at Berkeley

modern particle accelerators
Modern Particle Accelerators

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

accelerating cavities
Accelerating cavities
  • Modern machines use a time-dependent electric field in a cavity to accelerate the particles
how we manipulate the beam
How we manipulate the beam
  • The charged particle beam is then manipulated by the use of powerful magnets
  • In analogy with light optics, we call this process magnetic beam optics
  • The beam is bent using dipole magnets and focusing using quadrupole magnets
  • The magnets are very strong, often several Tesla, and use normal conducting, superconducting or permanent magnet technology
lorentz equation
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 3108 V/m (NOT feasible)
    • FB is by far the most effective in order to change the particle direction
magnetic lattices


F Quadrupole

D Quadrupole

Magnetic lattices
  • Magnets are combined to form a magnet lattice
  • The lattice steers and focuses the beam
a mini tour
A mini tour
  • Now we’ll look at some of the world’s biggest circular accelerators
    • Just LEP and the LHC
  • Note that I only scratch the surface, miss many out and spend very little time on non-colliding machines
  • There is much more life than I show!
what was lep
What was LEP?
  • LEP was a circular electron-positron collider, built at Cern, Geneva.
  • The ring design (c=27km) meant that the accelerating structures are seen many times by the circulating beams of particles
  • The ring had 4 experimental sites - ALEPH, DELPHI, L3 and OPAL.
  • Final collision energy was 209 GeV (2 x Ebeam)
  • It almost discovered the Higgs boson!
the lep tunnel
The LEP tunnel

(this is one of LEPs superconducting cavities)

acceleration techniques rf 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
From pill-box to real cavities

(from A. Chao)

LHC cavity module

ILC cavity

why circular accelerators
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
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)
focusing field quadrupoles
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:

inevitable due to Maxwell

optics analogy
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
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”
conclusion transverse dynamics
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 energy
But particles radiate energy!

Synchrotron Radiation from

an electron in a magnetic field:

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

Energy loss must be replaced by RF systemcost scaling $ Ecm2

~3400 MeV for

LEP200 (18 MW)

end of the road
End of the road?
  • So, because of the low mass of an electron, LEP is the end of the road for circular electron machines!
  • The higher proton mass means that we can build the LHC (what matters is =E/E0)
  • So the next generation of electron colliders cannot use a ring…so we need to stretch out that ring into a straight line
a linear machine


A linear machine



~15-20 km

For a Ecm = 1 TeV machine:

Effective gradient G = 500 GV / 14.5 km

= 35 MV/m

Note: for LC, $totµE

the international linear collider
The International Linear Collider
  • The International Linear Collider (ILC) is a proposed machine, to complement the LHC
  • It shall collider electron and positrons together at a centre-of-mass energy of 1 TeV
  • The anticipated cost is a cool $8,000,000,000!
  • Currently, a detailed physics case and accelerator design is being formulated, in an attempt to get someone to pay for it!
the key parameters
The key parameters
  • The linear collider is driven by 2 key parameters
    • The collision energy
    • The luminosity
  • The two beams collide head-on, so the collision energy is the sum of the beam energies E=2Ebeam
  • The luminosity tells us the probability of the two beams interacting – essentially the overlap of the two colliding beams
event rate vs luminosity
Event rate vs. Luminosity

Rate = L*s

e+e- annihilation cross-section approximately

L=10E34/cm2s = 0.00001/fb/s luminosity results in rate 0.0015/s = 5.4/hr.

Presumably interested in much more rare processes

High luminosity is very important at high energy

how to get luminosity
How to get Luminosity
  • To increase probability of direct e+e- collisions (luminosity) and birth of new particles, beam sizes at IP must be very small

Beam size: 250 * 3 * 110000 nanometers

(x y z)

(We shall derive this next lecture)

the large hadron collider
The large hadron collider
  • The large hadron collider (LHC) uses the same tunnel as LEP, at Cern in Geneva
  • The machine is a 14 TeV proton-proton collider, so each stored beam will have an energy of 7 TeV
  • It is being built now, and shall start operation sometime in 2007no2009oops 2011
  • There are a number of experiments
lhc layout
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 long

FODO = focus-drift-defocus-drift

lhc main parameters at collision energy
LHC main parametersat collision energy

4000 in 2012

1400 in 2011-2

colliding proton antiproton beams
Colliding Proton/Antiproton Beams

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 colliders











Timeline of Proton Colliders





CDF/D0 Detectors

LHC Collider

CMS/Atlas Detectors

SPS Collider

UA1/UA2 Detectors


Top quark

W/Z bosons

Higgs, Supersymmetry


proton antiproton collisions at fermilab chicago
Proton-Antiproton Collisions at Fermilab (Chicago)
  • The Tevatron accelerator, 6 km circumference

The CDF (Collider Detector at Fermilab) experiment

  • Bibliography:
    • 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