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Introduction to particle
accelerators
Walter Scandale
CERN - AT department
Roma, marzo 2006
Lecture I - what are accelerators ?
topics
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Fundamental discoveries in accelerator physics and technology
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Historical perspective
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Accelerator typologies
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Sources
Linear accelerators
Circular accelerators
Special accelerators
Synchrotrons
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Fixed target versus colliders
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Lepton versus hadron colliders
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Some relevant numbers
Introductory remarks
Particle accelerators are black boxes producing
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either flux of particles impinging on a fixed target
or debris of interactions emerging from colliding particles
In trying to clarify what the black boxes are one can
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list the technological problems
describe the basic physics and mathematics involved
Most of the phenomena in a particle accelerator can be described in terms of
 classical mechanics,
 electro-dynamics and
 restricted relativity
quantum mechanic is required in a couple of cases just for leptons (synchrotron radiation, pinch
effect)
However there are some complications:
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many non-linear phenomena
many particles interacting to each other and with a complex surroundings
the observables are averaged over large ensembles of particles
to handle high energy high intensity beams a complex technology is required
In ten hours we can only superficially fly over the
problems just to have a preliminary feeling of them
The everyone’s accelerator
Important discoveries
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1900 to 1925 radioactive source experiments à la Rutherford -> request for higher energy beams;
1928 to 1932 electrostatic acceleration ->
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Cockcroft & Walton -> voltage multiplication using diodes and oscillating voltage (700 kV);
Van der Graaf -> voltage charging through mechanical belt (1.2 MV);
1928 resonant acceleration -> Ising establish the concept, Wideroe builds the first linac;
1929 cyclotron -> small prototype by Livingstone (PhD thesis), large scale by Lawrence;
1942 magnetic induction -> Kerst build the betatron;
1944 synchrotron -> MacMillan, Oliphant and Veksel invent the RF phase stability (longitudinal focusing);
1946 proton linac -> Alvarez build an RF structure with drift tubes (progressive wave in 2p mode);
1950 strong focusing -> Christofilos patent the alternate gradient concept (transverse strong focusing);
1951 tandem -> Alvarez upgrade the electrostatic acceleration concept and build a tandem;
1955 AGS -> Courant, Snider and Livingstone build the alternate gradient Cosmotron in Brookhaven;
1956 collider -> Kerst discuss the concept of colliding beams;
1961 e+e- collider -> Touschek invent the concept of particle-antiparticle collider;
1967 electron cooling -> Budker proposes the e-cooling to increase the proton beam density;
1968 stochastic cooling -> Van der Meer proposes the stochastic cooling to compress the phase space;
1970 RFQ -> Kapchinski & Telyakov build the radiofrequency quadrupole;
1980 to now superconducting magnets -> developed in various laboratories to increase the beam energy;
1980 to now superconducting RF -> developed in various lab to increase the RF gradient.
The Livingstone’s diagram
In 1950 Livingstone plotted the
accelerator energy expressed in a semilogarithmic scale as a function of the year
of construction observing a linear growth.
The energy increase by a factor 33 every
decade, mostly due to discoveries and
technological advances.
Sources (1/3)
Penning source
Magnetron source
Ion sources:
 positive
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formed from electron bombardment of a gas
extracted from the resulting plasma:
species ranging from H to U (multiply charged)
 negative
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ions sources
ion sources: principal interest is in H-, for charge exchange injection
surface sources: in a plasma, H picks up electrons from an activated surface
volume sources: electron attachment or recombination in H plasma
polarized ion sources: e.g., optically pumped source -> some penalty in intensity,
relatively high (> 65 %) polarization
Volume source
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Surface source
QuickTime™ and a
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are needed to see this picture.
Electron sources
 electron
Sources (2/3)
production mechanism:
thermo ionic emission (pulse duration controlled by a pulsed
grid)
 photocathode irradiation by pulsed laser (laser pulse width
determines the pulse duration)
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 initial
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acceleration methods
DC HV guns -> 50-500 keV acceleration
RF guns: cathode forms one wall of the RF cavity
-> rapid acceleration to > 10 MeV in a few cells
-> mitigates space charge effects,
-> makes for low emittance
NLC Electron Source layout, for
polarized and un-polarized sources
QuickTime™ and a
TIFF (Uncompressed) decompressor
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Sources (3/3)
Positron sources
 “conventional”
positron source: can get from 10-3 :1 up to ~1:1 positron/electron as
electron energy rises from 0.2 to 20 GeV
target
0.2 to 20 GeV e-
 positron
e+
matching
solenoid
e+
RF linac
solenoid
production through high energy photons:
ehigh energy e-
g
eg
helical undulator sweep
magnet
Antiproton sources
80÷150 GeV p+
target p- horn lens To a storage ring
with stochastic
cooling
p+/p- yield typically ≈ 10-5
e+
converter
RF linac
e+
solenoid
m source is similar to p- source
Linear accelerators (1/2)
 electrostatic
accelerators
negative
ion source
high voltage terminal V ≤ 10 MV
-
Charging belt
 RF
linac
Wideroe (1928)
n+
Analysing
(n-1)+ Magnet
Stripping foil
tandem Van der Graaf,
pelletron
(n+1)+
positive ion beam
energy = 2qV
n+
V=V0*sin(t)
Focusing magnets
Alvarez (1946)
Linear accelerators (2/2)
 Induction
linac: the beam forms the secondary circuit of a high-current pulse
transformer
very low rep rates (a few Hz)
magnetic core
intermediate voltages (30-50 MeV)
accelerating gaps
 very high peak currents (>10 kA) in short (0.1÷1 µs) pulses
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 RFQ
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(RF quadrupole)
electric quadrupole, with a sinusoidal varying voltage on its electrodes;
the electrode tips are modulated in the longitudinal direction;
solenoid
this modulation results in a longitudinal accelerating field;
pulser
it is a capable of a few MeV of acceleration;
typically used between the ion source and the Alvarez linac in proton RF linacs.
Klystron - a microwave generator
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The e- beam enters in an RF cavity with Lcavity ≈ lRF 
In the cavity there is a velocity modulation of the e- beam
In the drift region the velocity modulation induces a beam bunching 
The bunched beam induces a wake modulation in the second cavity 
The initial RF power is amplified in the second cavity 
The residual e- beam is absorbed in a stopper 
If the two cavities are coupled we have instead an oscillator
QuickTi me™ a nd a
TIFF (Uncompre ssed ) decomp resso r
are need ed to se e th is p icture.
velocity modulation -> e- beam bunching -> coherent emission
Other RF power amplifier:
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the magnetron,
the travelling wave tube (TWT)
A microwave
oven magnetron
Circular accelerators (1/4)
 Betatron
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The betatron accelerate e- at relativistic speeds
It is essentially a transformer with a doughnut shaped vacuum tube as its secondary coil
The magnetic field B0 makes the electrons moving in a circle,
The change of magnetic flux within the orbit ∆ = πr2∆ <B>
produces an accelerating electric field E
U
1 d r d B
E 
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<B> = 2·B0 -> stable obit along a fixed radius r at all energies (Wideroe
condition)
2pr 2pr dt 2 dt
Energies up to 300 MeV have been obtained.
Betatrons are still used in industry and medicine as they are the very compact
accelerators for electrons. Cyclotrons are similarly compact but cannot accelerate
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electrons to useful energies.
p  erB0  dp  erdB0
1

B

B

0
2
1
p  eE  dp  edE  2 erd B
Cross section of a Betatron
Steel
r
<B>
B0
Bguide= <B>/2
p=erBguide
Coil
Vacuum
chamber
Bguide = 1/2 Baverage
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Principle of Betatron Acceleration
Circular accelerators (2/4)
 Cyclotron
The cyclotron accelerate ions at non-relativistic speeds
A constant magnetic field imposes circular orbits;
The RF accelerating field in the Dee’s gap can be
substantially reduced respect to a linear accelerator;
 The acceleration process is resonant and similar to a
parametric resonator.
 Used in the industry and medicine to accelerate protons
and ions
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The centripetal force is the Lorenz
force: F = eE+evB
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The instantaneous radius of curvature r
is: evB
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= mv2/r -> r = p/eB
The cyclotron frequency  is:
 = v/r = eB/m
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The maximal kinetic energy depends on
the magnetic field and radius:
Ecin = 1/2 mv2 = 1/2 e2B2r2/m
 Isochronous
Circular accelerators (3/4)
cyclotron
The isochronous cyclotron (sector cyclotron) accelerate ions at relativistic speeds
B varies with the azimuth:
 mimic the alternate gradient principle, focusing the beam also in the vertical
direction
 B varies with r
 shape B(r) to keep  constant whilst m and the kinetic energy Ecin increase
above the relativistic limit
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The PSI Ring Cyclotron: a separated sector cyclotron with a fixed beam energy of 590
MeV, commissioned in 1974, produces a proton beam with the highest power in the world.
The protons are accelerated in the ring
cyclotron to almost 0.8c, corresponding
to an energy of 590 MeV.
 The proton current amounts presently to
almost 2 mA, which results in a beam
power of over 1 MW.
 The principle components of the ring
cyclotron are eight sector magnets, with
a total weight of 2000 t, and four
accelerator cavities (50 MHz frequency)
each having a peak voltage of 730 kV.
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QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
 Synchro-cyclotron
Circular accelerators (4/4)
A synchrocyclotron accelerate ions at relativistic speed
It is simply a cyclotron with the accelerating supply frequency decreasing as the
particles become relativistic and begin to lag behind.
 Although in principle they can be scaled up to any energy they are not built any more as
the synchrotron is a more versatile machine at high energies.
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2pr 2pm0g
Trev 

v
eB
 RF
ec 2 B

m 0c 2  E cin
The revolution period increases with the energy since
the path length increases faster than the speed
The radiofrequency decreases with the energy: a
variable capacity modifies the RF resonant circuit
 Microtron
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Special accelerators
A microtron accelerate e- at relativistic speed
It is simply a cyclotron for e- containing an RF linac and a bending field region
Turn after turn Trev increases by a multiple of TRF so that the e- are always in
phase with the accelerating RF

2pm0
T


 RF eBh  k 

h

2
E

m
c
0

 cin
hk

2p
2
T

 rev,1 ec 2 B m0c  E cin  hTRF first turn

T  2p E  kT
change per turn
rev
cin
RF
2

ec B
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Cebaf concept: disentangle RF for magnet
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The orbits are separated by large space
A magnetic system for each consecutive orbit
Orbit lengths shaped to keep synchronicity for an optimal
RF system (large k) within limited space and costs
Special accelerators
 FFAG
Fixed Field Alternate Gradient
A FFAG accelerate e- at relativistic speed recent versions accelerate p or m beams at
high rate
 It allows strong focussing, RF synchronisation, fixed B field -> fast cycling
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m complex
A modern synchrotron
Main components of a modern accelerator
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Source of charged particles;
Acceleration element (RF cavities);
Guiding magnets (quadrupole, dipoles, correctors);
Vacuum system;
Beam diagnostics;
Physics detectors in an experimental area
Extraction devices
 special magnets
 high voltage septa
 high power targets
Fixed target versus collider rings
Collider
Fixed target
Advantage
A
l
beam population
N1
N1 particles
target density
r
cross section

no. of target particles
N2 = rlA
effective interaction area Aeff = N2 = rlA
probability of interaction
P = Aeff/A = rl
reaction rate
R = P•dN1/dt = rl•dN1/dt
Luminosity
bunch population in beam 1 N1
bunch population in beam 2 N2
rms beam radius 
beam areap2
L = R/ = rl•dN1/dt =
N2/A•dN1/dt
L = fN1N2/4p2
Synchrotron radiation
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Polarized light
Fan in the bending plane
Energy loss per turn
e 2  3g 4
U
30 r
E 4 GeV 
U MeV   0.0885
rm
Lepton versus hadron circular colliders
RF is a major concern
(At the parton level )
->
magnets are a major concern
Type of accelerators (1990)
Main accelerators for research
Colliders in operation (2001)
Type
e+e- two rings
e+e- single ring
e+e- single ring
e+e- two rings
e+e- two rings
e+e- single ring
Pbar-p single ring
ep two rings
e+e- linear collider
Facility
DAFNE (Italy)
BEPC (China)
CESR (US)
SLAC PEP-II (US)
KEK-B (Japan)
CERN LEP (Europe)
Fermilab Tevatron (US)
DESY HERA (Germany)
SLAC SLC (US)
Ecm (GeV)
1.05
3.1
10.4
10.4
10.4
200
1800
300
100
Luminosity (1033cm-2 s-1)
0.01
0.05
0.8
0.6
0.3
0.05
0.02
0.02
0.002
Main accelerators for research
Colliders under investigation or in construction (2006)
Type
pp two rings
e+-e- linear collider
µ+-µ- single ring
pp two rings
Facility
CERN LHC
NLC – JLC -TESLA - CLIC
Muon collider
VLHC
Ecm (GeV)
14000
500-3000
100-3000
100000
Luminosity (1033cm-2 s-1)
10
10
0.1-100
10
Accelerators in operation for nuclear physics research (2006)
Type
AuAu two ring collider
Electron Microtron
Electron linac
Proton synchrotron
Isochronous he avy-ion cyclotron
Isochronous cyclotron
Isochronous cyclotron
Facility
Ecm (GeV)
Luminosity (1033cm-2 s-1)
BNL RHIC (US)
100/nucleon
10-6
CEBAF (US)
4
Bates (US)
0.3-1.1
IUCF (US)
0.5
MSU NSCL (US.)
0.5
TRIUMF(Canada)
0.5
PSI (Switzerland)
0.5
-
Other applications
Field
Accelerator
Topics of study
Atomic Physics
Low energy ion beams
Condensed matter
physics
Condensed matter
physics
Material science
Synchrotron radiation
sources
Spallation neutron
sources
Ion beams
Atomic collision processes - study of excited
states - electron-ion collisions - ele ctronic
stopping power in solids
X-ray studies of crystal structure
Chem istry and
biology
Synchrotron radiation
sources
Neutron scattering studies of metals and
crystals - liquids and amorphous materials
Proton and X-ray activation analysis of
materials - X-ray emission studies accelerator mass spectrometry
Chem ical bonding studies: dynamics and
kinetics - protein and virus crystallography biological dynamics
Other applications
 Oil
well logging with neutron sources from small linacs
 Archaeological
 Medical
dating with accelerator mass spectrometry
diagnostics using accelerator-produced radioisotopes
 Radiation
therapy for cancer: X-rays from electron linacs, neutrontherapy from proton linacs, proton therapy; pion and heavy-ion therapy
 Ion
implantation with positive ion beams
 Radiation
processing with proton or electron beams:
polymerization,vulcanization and curing, sterilization of food, insect
sterilization,production of micro-porous membranes
 X-ray
microlithography using synchrotron radiation
 Inertial
confinement fusion using heavy-ion beams as the driver
 Muon-catalyzed
 Tritium
fusion
production, and radioactive waste incineration, using high energy
proton beams
How many accelerators today?
CATEGORY
Ion implanters and surface modifications
Accelerators in industry
Accelerators in non-nuclear research
Radiotherapy
Medical isotopes production
Hadrontherapy
Synchrotron radiation sources
Research in nuclear and particle physics
TOTAL
NUMBER
7'000
1'500
1'000
5'000
200
20
70
110
15'000
Lecture I - what are accelerators ?
reminder
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The accelerators are basic tools for physics discovery: new ideas
and technological breakthrough sustained an impressive
exponential progress of their performance for more than 80
years
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Many different type of accelerator are used for particle and
nuclear physics research, however the large majority of the
existing accelerators is used for a multitude of practical
applications
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The synchrotrons are the backbone of accelerator complex,
however old ideas and concepts are still revisited and upgraded to
achieve more demanding requirements
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Colliders are the master tool in the quest of the highest energy,
whilst fixed target operation allow reaching the highest rates
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Hadron and lepton colliders play complementary roles