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Elementary Particles
Instrumentation
Accelerators
Dec 15, 2014
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First accelerator: cathode ray tube
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Efield = V / D
heated
filament
With electron charge q:
F = q . Efield
distance D
Potential diffence V
electron kinetic energy:
Ee- =  F dD = q.V
Ee- independent of:
- distance D
- particle mass
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ElectronVolt: eV
Energy unit: ElectronVolt:
eV
1000 eV = 1 keV = 103 eV
1 MeV = 106 eV
1 GeV = 109 eV
1 TeV = 1012 eV
1 eV = |q| Joules = 1.6 x 10-19 Joules
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Wimshurst’s electricity generator, Leidsche Flesschen
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Van de Graaff accelerator
Corona discharge
deposits charge
on belt
Left: Robert van de Graaff
Vertical construction
is easier as support
of belt is easier
From: Principles of Charged
Particle Acceleration
Stanley Humphries, Jr.,
on-line edition, p. 222.
http://www.fieldp.com/cpa/cpa.html
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Faraday Cage!
HV = 10 kV
gnd
belt
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Beam pipe
From: Principles of Charged
Particle Acceleration
Stanley Humphries, Jr.,
on-line edition, p. 223.
http://www.fieldp.com/cpa/cpa.html
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Hoogspanning (hoge potentiaal) met:
Rumkorffse Klos
transformator
bobine
vonkenzender
Marconi
bobine:
ontsteking voor
explosie motoren
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Practical limit to transformers
Cockcroft-Walton
high-voltage generator
Sir John Douglas Cockroft
Ernest Walton
Nobel Prize 1951
From: Principles of Charged
Particle Acceleration
Stanley Humphries, Jr.,
on-line edition, p. 210
http://www.fieldp.com/cpa/cpa.html
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Cockroft Walton generator
at Fermilab, Chicago, USA
High voltage = 750 kV
Structure in the foreground:
ion (H-) source
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Motion of charged particle in magnetic field
Lorentz force:
dp
 q v B
dt
The speed of a charged particle, and therefore its g, does not change by a static
magnetic field
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Motion of charged particle in magnetic field
If magnetic field direction perpendicular to the velocity:
g mv 2

 q v  B which can be written as : p =  q B → p = 0.2998 B 
radius of curvature
(p in GeV/c, B in T,  in m,
for 1 elementary charge
unit = 1.602177x10-19 C,
and obtained using
1 eV/c2 = 1.782663x10-36 kg
and c = 299792458 m/s )
D
Sh
ρ
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Force on charged particle due to electric and magnetic fields:
dp
= q(E + v ´ B)
dt
perpendicular to
motion: deflection
In direction of
motion -> acceleration
or deceleration
-> For acceleration an electric field needs to be produced:
• static: need a high voltage: e.g. Cockroft Walton generator,
van de Graaff accelerator
• with a changing magnetic field: e.g. betatron
• with a high-frequent voltage which creates an accelerating field across one
or more regions at times that particles pass these regions: e.g. cyclotron
• with high-frequency electro-magnetic waves in cavities
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The cyclotron
"Dee": conducting,
non-magnetic box
Top view
Constant
magnetic field
Side view
~
r.f. voltage
Ernest O.Lawrence at the controls
of the 37" cyclotron in 1938,
University of California at Berkeley.
1939 Nobel prize for "the invention
and development of the cyclotron,
and for the results thereby attained,
especially with regard to artificial
radioelements."
(the 37" cyclotron could accelerate
deuterons to 8 MeV)
Speed increase smaller if particles become relativistic:
special field configuration or synchro-cyclotron (uses particle
bunches, frequency reduced at end of acceleration cycle)
http://www.lbl.gov/Science-Articles/Archive/early-years.html
http://www.aip.org/history/lawrence/
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From: S.Y. Lee and K.Y. Ng, PS70_intro.pdf in: http://physics.indiana.edu/~shylee/p570/AP_labs.tar.gz
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From: S.Y. Lee and K.Y. Ng, PS70_intro.pdf in: http://physics.indiana.edu/~shylee/p570/AP_labs.tar.gz
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Superconducting cyclotron (AGOR), KVI, Groningen
Protons up to ~ 190 MeV, heavy ions (C, N, Ar, ...) ~ 50-60 MeV per nucleon
http://www.kvi.nl
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Eindhoven: new cyclotron for isotope production (2002)
IBA Cyclone 30, 18 - 30 MeV protons, 350 mA
http://www.accel.tue.nl/tib/accelerators/Cyclone30/cyclone30.html
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Linear Drift Tube accelerator, invented by R. Wideröe
~
r.f. voltage: frequency
matched to velocity particles,
so that these are accelerated
for each gap crossed
Particles move through
hollow metal cylinders in
evacuated tube
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Linear Drift Tube accelerator, Alvarez type
Metal tank
~
small antenna injects e.m. energy
Particles move through
into resonator, e.m. wave in tank
hollow metal cylinders in
accelerates particles when they cross
evacuated tube
gaps, particles are screened from e.m.
wave when electric field would decelerate
Luis Walter Alvarez
Nobel prize 1968, but not for his work on accelerators:
"for his decisive contributions to elementary particle physics,
in particular the discovery of a large number of resonance states,
made possible through his development of the technique of using
hydrogen bubble chamber and data analysis"
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Inside the tank of the
Fermilab Alvarez type
200 MeV proton linac
http://www-linac.fnal.gov/linac_tour.html
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R.f. cavity with drift tubes as used in the
SPS (Super Proton Synchrotron) at CERN
NB: traveling e.m. waves are used
Frequency = 200.2 MHz
Max. 790 kW
8MV accelerating voltage
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Standing waves in cavity:
particles and anti-particles
can be accelerated at the same time
Superconducting cavity for the LEP-II
e+e- collider (2000: last year of operation)
t1
"iris"
t2
The direction of E is indicated
Cavities in cryostat in LEP
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Non-superconducting cavity as used in LEP-I.
The copper sphere was used for low-loss temporary storage of the
e.m. power in order to reduce the power load of the cavity
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Generation of r.f. e.m waves with a klystron
* The electron gun 1 produces a flow of electrons.
* The bunching cavities 2 regulate the speed of the electrons so
that they arrive in bunches at the output cavity.
* The bunches of electrons excite microwaves in the output cavity 3
of the klystron.
* The microwaves flow into the waveguide 4, which transports
them to the accelerator.
* The electrons are absorbed in the beam stop 5.
from http://www2.slac.stanford.edu/vvc/accelerators/klystron.html
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Synchrotron : circular accelerator with r.f. cavities
for accelerating the particles and with separate magnets
for keeping the particles on track. All large circular
accelerators are of this type.
Injection
During acceleration
the magnetic field
needs to be
"ramped up".
Focussing magnet
r.f. cavity
Vacuum beam line
Bending magnet
Extracted beam
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CERN, Geneve
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During acceleration the magnetic field needs to be "ramped up".
Slow extraction
Fast extraction
of part of beam
At time of operation of LEP
Fast extraction
of remainder of beam
SPS used as
injector for LEP
For LHC related
studies
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Collider: two beams are collided to obtain a high Centre of Mass
(CM) energy.
Colliders are usually synchrotrons (exception: SLAC).
In a synchrotron particles and anti-particles can be accelerated
and stored in the same machine (e.g. LEP (e+e-), SppS and
Tevatron (proton - anti-proton). This is not possible for e.g. a
proton-proton collider or an electron-proton collider.
Important parameter for colliders : Luminosity L
N = L s cross-section
number of events /s
Unit L: barn-1 s-1 or cm-2 s-1
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CERN accelerator complex
to Gran-Sasso (730 km)
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Charged particles inside accelerators and in external beamlines
need to be steered by magnetic fields. A requirement is that
small deviations from the design orbit should not grow without
limit. Proper choice of the steering and focusing fields makes this
possible.
Consider first a charged particle moving in a uniform field
and in a plane perpendicular to the field:
design orbit
displaced orbit
In the plane a deviation from the design
orbit does not grow beyond a certain
limit: it exhibits oscillatory behavior.
However, a deviation in the direction
perpendicular to the plane grows in
proportion to the number of revolutions
made and leads to loss of the particle
after some time.
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To prevent instabilities a restoring force in the vertical direction is
required. Possible solution : "weak focusing" with a
"combined function magnet"
pole
shoe
design orbit
plane (seen
from the side)
pole
shoe
field
component
causes
downward
force
field
component
causes
upward
force
Components of magnetic field
parallel to the design orbit plane
force particles not moving in the
plane back to it, resulting in
oscillatory motion1) perpendicular
to plane. The field component
perpendicular to the plane now
depends on the position in the
design orbit plane: the period
of the oscillatory motion1) in this
plane around the design orbit
becomes larger than a single
revolution.
1)
"betatron oscillations"
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Dipoles and quadrupoles in LEP
Quadrupole
Dipole
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Large Hadron Collider LHC:
proton-proton collider
Interaction
point
Bunch size squeezed
near interaction point
• Crossing angle to avoid long range beam beam
interaction
• R ~4 km, E ~ 7 TeV (2x!)  B ~ 7 T!
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Superconducting magnets: no pole shoes
Current distributions
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LHC dipoles
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pp collisions
2) heavy collisions:
A proton is a bag filled with quarks en gluons
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With van de Graaff accelerator: simple:
E = q V, so E = V eV
From Einstein’s Special Theory on Relativity:
E2 = mo2 c4 + p2c2
With:
 = v / c, and the Lorentz factor γ:
relativistic mass mr = γ m0
γ = 1 / sqrt(1- 2), and  = sqrt(γ2 -1) / γ
So: total energy E = m0 c2 sqrt(1+ 2 γ2) [= rest mass eq. + kinetic energy]
= γ m0 c 2 = mr c 2
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Remember:
TOTAL energy E2 = mo2 c4 + p2c2
Note ‘restmass’ term and ‘kinetic’ term (squared!)
relativistic mass mr = γ m0
p = m v = γ m0 v (for high energy particles: p = γ m0 c)
γ = 1 / sqrt(1- 2)
For high-energy particles (E >> m0c2):
E2 = mo2 c4 + p2c2 = E2 = p2c2  E = pc  p = E/c
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Examples: electron: rust mass m0 = 511 keV
With total energy 1 GeV: kinetic energy = 1 GeV
Momentum p: 1GeV/c
Other example: electron with [kinetic] energy of 1 MeV (~1/2 m0 c2)
Total energy ET = 1 MeV + 511 keV = 1511 keV
Momentum p follows from ET2 = mo2 c4 + p2c2
Gamma factor γ = ET / moc2
Speed follows from γ = 1 / sqrt(1- 2), and  = sqrt(γ2 -1) / γ
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