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ACCELERATORS
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Topics
 types of accelerators
 relativistic effects
 Fermilab accelerators
 Fermilab proton-antiproton collider
 beam cooling
CERN -- LHC
 summary
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Luminosity and cross section
 Luminosity is a measure of the beam intensity
(particles per area per second) ( L~1031/cm2/s )
 “integrated luminosity” is a measure of the amount of data
collected (e.g. ~100 pb-1)
 cross section s is measure of effective interaction area,
proportional to the probability that a given process will
occur.
o 1 barn = 10-24 cm2
o 1 pb = 10-12 b = 10-36 cm2 = 10-40 m2
 interaction rate:
dn / dt  L  s
 n  s  Ldt
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How to make qq collisions
 Quarks are not found free in nature!
 But (anti)quarks are elements of (anti)protons.
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 So, if we collide -protons and anti-protons we should get some qq
collisions.
 Proton structure functions give the probability that a single quark (or
gluon) carries a fraction x of the proton momentum (which is 980
GeV/c at the Tevatron)
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ACCELERATORS
 are devices to increase the energy of charged particles;
 use magnetic fields to shape (focus and bend) the trajectory of the
particles;
 use electric fields for acceleration.
 types of accelerators:
 DC)accelerators
o Cockcroft-Walton accelerator (protons up to 2 MeV)
o Van de Graaff accelerator (protons up to 10 MeV)
o Tandem Van de Graaff accelerator (protons up to 20 MeV)
 resonance accelerators
o cyclotron (protons up to 25 MeV)
o linear accelerators
 electron linac: 100 MeV to 50 GeV
 proton linac: up to 70 MeV
 synchronous accelerators
o synchrocyclotron (protons up to 750 MeV)
o proton synchrotron (protons up to 900 GeV)
o electron synchrotron (electrons from 50 MeV to 90 GeV)
 storage ring accelerators (colliders)
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DC Accelerators
 electrostatic accelerators:
 generate high voltage
between two electrodes
 charged particles
move in electric field,
energy gain = charge
times voltage drop;
 Cockcroft-Walton and
Van de Graaff
accelerators differ in
method to achieve high
voltage.
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Cockcroft-Walton generator
 C-W generator uses diodes and capacitors in a
rectifier and voltage-multiplier circuit
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Van de Graaff accelerator
 use power supply to deposit charges on belt; pick charges
off at other end of belt and deposit on “terminal”
 now rubber belt replaced by “pellet” chain – “pelletron”
http://www.pelletron.com/charging.htm
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Van de Graaff accelerator -- 2
 tandem – VdG: use potential difference twice, with change
of charges in the middle (strip off electrons)
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Proton Linac
 proton linac (drift tube accelerator):
 cylindrical metal tubes (drift tubes) along axis of large vacuum
tank
 successive drift tubes connected to opposite terminals of AC
voltage source
 no electric field inside drift tube  while in drift tube, protons
move with constant velocity
 AC frequency such that protons always find accelerating field
when reaching gap between drift tubes
 length of drift tubes increases to keep drift time constant
 for very high velocities, drift tubes nearly of same length
(nearly no velocity increase when approaching speed of light)
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CYCLOTRON
 cyclotron
 consists of two hollow metal chambers called (“dees” for their shape, with
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open sides which are parallel, slightly apart from each other (“gap”)
dees connected to AC voltage source - always one dee positive when other
negative  electric field in gap between dees, but no electric field inside
the dees;
source of protons in center, everything in vacuum chamber;
whole apparatus in magnetic field perpendicular to plane of dees;
frequency of AC voltage such that particles always accelerated when
reaching the gap between the dees;
in magnetic field, particles are deflected: p = qBR
p = momentum, q = charge, B = magnetic field strength,
R = radius of curvature
radius of path increases as momentum of proton increases time for passage
always the same as long as momentum proportional to velocity;
this is not true when velocity becomes too big (relativistic effects)
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Cyclotron
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Accelerators:
“relativistic effects”
 “relativistic effects”
 special relativity tells us that certain approximations made in
Newtonian mechanics break down at very high speeds;
________
 relation between momentum and velocity in “old” (Newtonian)
mechanics: p = m v
relativistically this becomes p = mv , with  = 1/1 - (v/c)2
m = “rest mass”, i.e. mass is replaced by rest mass times 
- “relativistic growth of mass”
 factor  often called “Lorentz factor”; ubiquitous in relations from
special relativity; energy: E = mc2
 acceleration in a cyclotron is possible as long as relativistic effects
are negligibly small, i.e. only for small speeds, where momentum is
still proportional to speed; at higher speeds, particles not in
resonance with accelerating frequency; for acceleration, need to
change magnetic field B or accelerating frequency f or both;
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more types of Accelerators
 electron linac
 electrons reach nearly speed of light at small energies
(at 2 MeV, electrons have 98% of speed of light);
no drift tubes; use travelling e.m. wave inside resonant
cavities for acceleration.
 synchrocyclotron:
 B kept constant, f decreases;
 synchrotron :
 B increases during acceleration, f fixed (electron
synchrotron) or varied (proton synchrotron);
radius of orbit fixed.
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Fermilab
 Fermi National Accelerator Laboratory
(http://www.fnal.gov/)
 Founded 1972
 One of the top laboratories for high energy physics
 Near Batavia, Illinois (45 mi West of Chicago)
 Until 2009 world’s highest energy accelerator:
Tevatron = proton synchrotron, Emax=980GeV
 Operated as collider: proton – antiproton collisions
at Ecm = 1.96 TeV
 collider operation ended 30 Sept 2011
 Physics Program
 Collider experiments CDF, DØ, CMS
 neutrino physics: Minos, Mini-Boone,..
 Astrophysics: Auger Observatory, Sloan Sky Survey,
DES,..
 ………….
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The TeVatron Collider
 Tevatron collider
 Colliding bunches of protons and antiprotons;
 bunches meet each other every 396 ns in
the center of two detectors (DØ and CDF)
 steered apart at other places
 Each particle has ~ 980 GeV of energy,
so the total energy in the center of mass
is 1960 GeV = 1.96 TeV
 About 2,500,000 beam bunch crossings
per second
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Fermilab aerial view
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Fermilab accelerator chain: 0 to 400 MeV
Plasma ion source:
H- ions, 18keV
Cockroft-Walton
H- ions, 18keV to 750keV
Linac :
H- ions,
750keV to 400 MeV
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FNAL Cockcroft-Walton acc.
 The Cockcroft-Walton preaccelerator provides the
first stage of acceleration;
hydrogen gas is ionized to
create negative ions, each
consisting of two electrons
and one proton.
 ions are accelerated by a
positive voltage and reach
an energy of 750,000
electron volts (750 keV).
(about 30 times the energy
of the electron beam in a
television's picture tube.)
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FNAL Linac
 Next, the negative
hydrogen ions enter a linear
accelerator, approximately
500 feet long.
 Oscillating electric fields
accelerate the negative
hydrogen ions to 400
million electron volts (400
MeV).
 Before entering the third
stage, the ions pass
through a carbon foil,
which removes the
electrons, leaving only the
positively charged protons.
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Fermilab Linac
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Fermilab accelerator chain: 400 MeV to 980 GeV
Booster:
H- ions, stripped to p
400 MeV to 8 GeV
Main Injector:
Protons,
8GeV to 150GeV
TeVatron
Protons and
Antiprotons
150GeV to 980GeV
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Main Injector and recycler
 recycler:
 antiproton storage ring
 fixed momentum
(8.9 GeV/c),
 permanent magnets
Main Injector:
 proton synchrotron; cycle
period 1.6-3 seconds;
 delivers 120 GeV protons
to pbar production target.
 Also delivers beam to a
number of fixed target
experiments.
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Fermilab TeVatron tunnel
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Antiproton manufacture
 120 GeV protons from
Main Injector
 extract, shoot on target
(Ni)
 collect with Lithium lens
 select 8GeV
antiprotons
 transfer to debuncher
 reduce beam spread by
stochastic cooling
 store in accumulator
(“stacking”)
 transfer to “recycler”
when stack reaches 1012
pbars
 when enough antiprotons:
 extract from
accumulator or recycler
 transfer to Main
Injector
 accelerate to 150 GeV
 transfer to Tevatron
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Antiprotons -- target and collection
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pbars from target have wide angular distribution;
Li lens focuses
bend magnet selects 8 GeV pbars
efficiency: 8 pbars per 1 M protons hitting target make it into accumulator
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Debuncher
 pbars from target are in
“bunches” (small time
spread), wide energy
spread (4%);
 debuncher performs
“bunch rotation” to swap
large energy spread and
small time spread into
narrow energy spread and
large time spread
 low momentum pbars have
shorter path  arrive
earlier at RF cavity  get
stronger accelerating kick
 after sufficient turns,
energy spread reduced
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Debuncher and accumulator
debuncher
accumulator
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Accumulator
 accumulates antiprotons
 successive pulses of antiprotons from
debuncher stacked over a day or so
 momentum stacking: newly injected pbars
are decelerated by RF cavity to edge of
stack
 stack tail cooling system sweeps beam
deposited by RF towards core of the stack
 additional core cooling systems keep
antiprotons in core at desired energy and
minimize beam size
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Beam Cooling
 Beam cooling: reduce size and energy spread of a
particle beam circulating in a storage ring (without
any accompanying beam loss)
 motion of individual beam particles deviate from
motion of beam center (ideal orbit)
 transverse deviations in position and angle –
“betatron oscillations”
 longitudinal deviations due to energy
(momentum) spread -- “synchrotron oscillations”
 motions of particles with respect to beam center
similar to random motion of particles in a gas
 beam temperature = measure of average energy
corresponding to these relative motions
 “beam cooling” = reduction of these motions -decrease of beam temperatures
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Phase space
Transverse Phase space
x’
x
x’
x
 Phase Space = space defined by
coordinates describing motion wrt
beam center
 Emittance = region of phase space
where particles can orbit, also its
size (phase space volume)
 Liouville’s Theorem:
phase space volume = constant
(cannot be changed by
conservative forces)
 L.T. only for continous particle
stream (liquid) – discrete particles
 can swap particles and empty
phase space – reduce area occupied
by beam
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Beam cooling -- 2
 beam cooling beats constraints of Liouville theorem (phase
space volume is constant) because phase space volume is not
reduced, only occupancy (distribution of particles) within
phase space volume is changed
 Cooling is, by definition, not a conservative process. The
cooling electronics act on the beam through a feedback loop to
alter the beam's momentum or transverse oscillations.
 Two types of beam cooling have been demonstrated and used
at various laboratories: electron cooling which was pioneered
by G. I. Budker, et. al., at Novosibirsk, and stochastic cooling,
developed by Simon van der Meer of CERN.
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Stochastic cooling -- 1

Stochastic cooling:
 pick-up electrode
detects excursions of a
particle from its central
orbit
 sends signal to a “kicker”
downstream
 kicker applies a
correction field to
reduce this amplitude.
Short cut, (n+¼)
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Stochastic cooling - 2
 The cooling process can be
looked at as a competition
between two terms:
 (a) the coherent term
which is generated by the
single particle,
 (b) the incoherent term
which results from
disturbances to the single
particle.
 (a)=linear with gain
(b)=quadratic
 by suitable choice of
gain, overall cooling can
be achieved
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Stochastic Cooling - 3
 Particle beams are not just a single particle, but
rather, a distribution of particles around the
circumference of the storage ring. Each particle
oscillates with a unique amplitude and random initial
phase. The cooling system acts on a sample of
particles within the beam rather than on a single
particle.
 Since stochastic cooling systems cannot resolve the
motion of a single antiproton, only a phenomenon
called mixing makes cooling possible. Mixing arises
because particles with different momenta take
different times to travel around the ring, and get
spread out over the beam. After a few turns around
the ring, the noise averages to zero for accumulating
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antiprotons.
Stochastic Cooling in the Pbar Source
 Standard Debuncher operation:
 108 pbars, uniformly distributed
 ~600 kHz revolution frequency
 To individually sample particles
 to resolve 10-14 seconds, would need 100 THz
bandwidth
 Don’t have good pickups, kickers, amplifiers in the
100 THz range
 Sample Ns particles -> Stochastic process
o Ns = N/2TW where T is revolution time and W bandwidth
o Measure <x> deviations for Ns particles
 The higher the bandwidth the better the cooling
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Betatron Cooling
 With correction ~ g<x>, where g is gain of system
 New position: x - g<x>
 Emittance Reduction: RMS of kth particle
(W = bandwidth and N = number of circulating particles),
 xk
 g  x 
 x 
2
1
Ns

 xk2  2 gxk  g 2  x 2
xi 
i
1
1
xk 
Ns
Ns
x
ik
i
Average over all particles and do lots of algebra
d  x 2
 2g x2 
g2


 x 2  , where n is ' sample'
dn
Ns
Ns
 Cooling rate
1


2W
N
2 g  g 
2
 Must also consider noise (characterized by U = Noise/Signal)
 Mixing:
 Randomization effects M = number of turns to completely
randomize sample
 Cooling rate
1

2W
N
2 g  g M

 Net cooling effect if g sufficiently small
2

U 
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Momentum cooling
Momentum cooling systems reduce the longitudinal energy
spread of a beam by accelerating or decelerating particles in the
beam distribution towards a central momentum.
 The sum signal is used for longitudinal cooling and the
difference for betatron cooling.

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AntiProton Source
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Electron cooling
 invented by G.I. Budker (INP, Novosibirsk) in 1966 as a way to
increase luminosity of p-p and p-pbar colliders.
 first tested in 1974 with 68 MeV protons in the NAP-M ring at
INP.
 cooling of ion beams by a co-moving low emittance electron beam
is a well-established technique for energies up to hundreds of
MeV per nucleon
 at higher energy, expect slower cooling, but may still give
enhancement in the performance of high energy colliders as well.
 was used for cooling of 8 GeV antiprotons in the Fermilab
recycler ring
 GSI project for cooling antiprotons
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How does electron cooling work?
 velocity of electrons made equal to velocity of ions
(antiprotons)
 ions undergo Coulomb scattering in the “electron gas” and
lose energy which is transferred from the ions to the costreaming electrons until thermal equilibrium is attained
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Electron cooling
electron collector
electron gun
high voltage platform
magnetic field
electron beam
ion beam
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CERN
(Conseil Européen pour la Recherche Nucléaire)
European
Laboratory for
Particle Physics,
near Geneva,
Switzerland
(about 9km West
of Geneva, between
Meyrin,
and St.Genis,
straddling the
Swiss-French
border)
http://www.cern.ch
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CERN accelerators
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http://public.web.cern.ch/public/en/LHC/LHC-en.html
Large Hadron Collider (LHC)
 Proton beams travel around the 27 km
ring
 in opposite directions, separate beam
pipes.
 In ultrahigh vacuum, 10-10 Torr.
 time for a single orbit, 89.92 μs.
 beams controlled by superconducting
electromagnets
o 1232 dipole magnets, 15 m each, bends
beam.
o 392 quadrupole magnets, 5-7 m, focus
beams.
o 8 inner triplet magnets are used to
'squeeze' the particles closer for
collisions. Similar to firing needles 10
km apart with enough precision to
meet in the middle.
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LHC – some numbers
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Circumference
Dipole operating temperature
Number of magnets
Number of dipoles
Number of quadrupoles
Number of RF cavities
Nominal energy, protons
Nominal energy, ions
Peak magnetic dipole field
Min. distance between bunches
Design luminosity
No. of bunches per proton beam
No. of protons per bunch (at start)
Number of turns per second
Number of collisions per second
26 659 m
1.9 K (-271.3°C)
9300
1232
858
8 per beam
7 TeV
2.76 TeV/nucleon
8.33 T
7 m
1034 cm-2 s-l
2808
1.1 x 1011
11 245
600 million
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LHC Experiments
Atlas
CMS
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LHC Detectors
ATLAS
CMS
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CMS Collaboration
Austria
Belgium
USA
Bulgaria
Finland
CERN
France
Germany
Greece
Hungary
Russia
Uzbekistan
Ukraine
Slovak Republic
Georgia
Belarus
Armenia
Italy
UK
Turkey
Iran
Serbia
Pakistan
India
Korea
Estonia
Cyprus
Poland
Portugal
Spain
China, PR
Switzerland
China (Taiwan)
Croatia
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Summary
 many different types of accelerators have been developed
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for nuclear and particle physics research
different acceleration techniques suitable for different
particles and energy regimes
most accelerators in large research laboratories use several
of these techniques in a chain of accelerators
beam cooling has become important tool in improving beam
quality and luminosity
active research going on to develop new accelerating
techniques for future applications
many types of accelerators have found applications in fields
other than nuclear and particle physics (e.g. medicine, ion
implantation for electronics chips, condensed matter research,
biology,….)
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