PHYS 3446 – Lecture #15
Monday, Oct. 30, 2006
Dr. Jae Yu
1. Particle Accelerators
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Electro-static Accelerators
Cyclotron Accelerators
Synchrotron Accelerators
2. Elementary Particle Properties
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Monday, Oct. 30, 2006
Forces and their relative magnitudes
Elementary particles
Quantum Numbers
Gell-Mann-Nishijima Relations
Production and Decay of Resonances
PHYS 3446, Fall 2006
Jae Yu
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Announcements
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Quiz in class Wednesday, Nov. 1
LPCC Workshop Saturday, Nov. 4
Homework: Carry out Fourier transformation and
derive equations 9.3 and 9.5
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Particle Accelerators
• How can one obtain high energy particles?
– Cosmic ray  Sometimes we observe 1000TeV cosmic rays
• Insufficient statistics due to low flux
• Cannot control momenta too well
• Need to look into small distances to probe the fundamental
constituents with full control of particle energies and fluxes
– Particle accelerators
• What else do you think accelerators have do other than particle
acceleration?
– Track them
– Maneuver (focus or turn) them
– Constrain their motions to the order of 1mm
• Why?
– Must correct particle paths and momenta to increase fluxes and control
momenta
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Particle Accelerator Types
• Depending on what the main goals of physics are, one needs
different kinds of accelerator experiments
• Fixed target experiments: Probe the nature of the nucleons 
Structure functions
– Use neutrinos or charged leptons (electrons or muons) to probe proton
or neutron internal structure
– Results also can be used for producing secondary particles for further
accelerations  Tevatron anti-proton production
• Colliders: Probes the interactions between fundamental
constituents
– Hadron colliders: Wide kinematic ranges and high discovery potential
• Proton-anti-proton: TeVatron at Fermilab, Sp`pS at CERN
• Proton-Proton: Large Hadron Collider at CERN (late 2007)
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Particle Accelerator Types
– Lepton colliders: Very narrow kinematic reach, so it is used
for precision measurements
• Electron-positron: LEP at CERN, Petra at DESY, PEP at SLAC,
Tristan at KEK, ILC in the med-range future
• Muon-anti-muon: Conceptual accelerator in the far future
– Lepton-hadron colliders: HERA at DESY
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Probe deep inside the hadrons
How do these do this?
Leptons do not have internal structure but hadrons do..
So whatever comes out of the interactions are due to hadron
internal structure
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Accelerators by Acceleration Techniques
• Electrostatic Accelerators
– Use potential differences to accelerate particles
• Cockcroft-Walton
• Van de Graaff
• Resonance Accelerators
– Accelerate particles using resonance principles
where electric energies are at the frequency particles
move
• Cyclotron
• Linear Accelerator
• Synchrotron
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Electrostatic Accelerators: Cockcroft-Walton
• Cockcroft-Walton Accelerator
– Pass ions through sets of aligned DC electrodes at successively
increasing fixed potentials
– Consists of ion source (hydrogen gas) and a target with the electrodes
arranged in between
– Acceleration Procedure
• Electrons are either added or striped off of an atom
• Ions of charge then get accelerated through series of electrodes, gaining kinetic
energy of T=QV through every set of electrodes
• Limited to about 1MeV acceleration due to
voltage breakdown and discharge beyond
voltage of 1MV.
• Available commercially and also used as the
first step high current injector (to ~1mA).
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Electrostatic Accelerators: Van de Graaff
• Energies of particles through DC accelerators are
proportional to the applied voltage
• Robert Van de Graaff developed a clever mechanism to
increase HV
– The charge on any conductor resides on its outermost
surface
– If a conductor carrying additional charge touches another
conductor that surrounds it, all of its charges will transfer to
the outer conductor increasing the charge on the outer
conductor, thereby increasing HV
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Electrostatic Accelerators: Van de Graaff
• Sprayer adds positive charge to
the conveyor belt at corona points
• Charge is carried on an insulating
conveyor belt
• The charges get transferred to the
dome via the collector
• The ions in the source then gets
accelerated to about 12MeV
• Tandem Van de Graff can
accelerate particles up to 25 MeV
• This acceleration normally occurs
in high pressure gas that has very
high breakdown voltage
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Resonance Accelerators: Cyclotron
• Fixed voltage machines have intrinsic
limitations in their energy due to high
voltage breakdown
• Machines using resonance principles
can accelerate particles in higher
energies
• Cyclotron developed by E. Lawrence
is the simplest one
• Accelerator consists of
– Two hallow D shaped metal chambers
connected to alternating HV source
– The entire system is placed under
strong magnetic field
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Resonance Accelerators: Cyclotron
• While the D’s are connected to HV sources,
there is no electric field inside the chamber
due to Faraday effect
• Strong electric field exists only in the gap
between the D’s
• An ion source is placed in the gap
• The path is circular due to the
perpendicular magnetic field
• Ion does not feel any acceleration inside a
D but gets bent due to magnetic field
• When the particle exits a D, the direction of
voltage can be changed and the ion gets
accelerated before entering into the D on
the other side
• If the frequency of the alternating voltage is
just right, the charged particle gets
accelerated continuously until it is extracted
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Resonance Accelerators: Cyclotron
• For non-relativistic motion, the frequency appropriate for
alternating voltage can be calculated from the fact that the
magnetic force provides centripetal acceleration for a circular
orbit
v qB
v2
vB
m
r
q
r
c

mc
w
• For a constant angular speed, w=v/r, the frequency of the
motion is

qB
1  q B
f
2

2 mc

2  m  c
• Thus, to continue accelerate the particle, the electric field
should alternate at this frequency, cyclotron resonance
frequency
• The maximum kinetic energy achievable for a cyclotron with
2
radius R is
 qBR 
1 2
1
2 2
Monday, Oct. 30, 2006
 3446,mFall
 2006
R 
Tmax  mvmaxPHYS
2
2
Jae Yu
mc 2
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Resonance Accelerators: Linear Accelerator
• Accelerates particles along a linear path using resonance principle
• A series of metal tubes are located in a vacuum vessel and connected
successively to alternating terminals of radio frequency oscillator
• The directions of the electric fields changes before the particles exits the
given tube
• The tube length needs to get longer as the particle gets accelerated to
keep up with the phase
• These accelerators are used for accelerating leptons to very high
energies
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Synchroton Accelerators
• For very energetic particles, the relativistic effect must be taken
into account
• For relativistic energies, the equation of motion of a charge q
under magnetic field B is
dv
vB
m
dt
 m v   q
c
• For a constant v ~ c, the resonance frequency becomes
12

1  q 1 B
1  q  v  B
f 


1  2 




2 2  m   c
2  m   c  c
2
• This relation must hold during acceleration
– B should decrease for fixed f or f should increase for fixed B
• Synchro-cyclotrons: machines with constant B but variable f
• Synchrotrons: machines with variable B independent of the
change of f
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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Synchroton Accelerators
• Electron synchrotrons, B varies while f is held constant
• For proton synchrotrons, both B and f varies
• For v ~ c, the frequency of motion can be expressed
f
1 v
c

2 R 2 R
• For a particle w/ charge e
pc p  GeV / c 
R(m) 

qB 0.3B Tesla 
• For a magnetic field strength of 2Tesla, one needs
radius of 50m to accelerate an electron to 30GeV/c.
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
15
Synchroton Accelerators
• Synchrotons use magnets
arranged in a ring-like
fashion.
• Multiple stages of
accelerations are needed
before reaching over GeV
ranges of energies
• RF power stations are
located through the ring to
pump electric energies into
the particles
Monday, Oct. 30, 2006
PHYS 3446, Fall 2006
Jae Yu
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