PHYS 3446, Fall 2006

1
PHYS 3446 Lecture 14
Wednesday, Oct. 25, 2006 Dr. Jae Yu

• Particle Accelerators
• Electro-static Accelerators
• Cyclotron Accelerators
• Synchrotron Accelerators
• 2. Elementary Particle Properties
• Forces and their relative magnitudes
• Elementary particles
• Quantum Numbers
• Gell-Mann-Nishijima Relations
• Production and Decay of Resonances

2
Announcements

• Quiz in class next Wednesday, Nov. 1

3
Principles of Calorimeters
Total absorption calorimeter See the entire
shower energy
Sampling calorimeter See only some fraction of
shower energy
For EM
Absorber plates
For HAD
4
Example Hadronic Shower (20GeV)
5
Particle Accelerators

• How can one obtain high energy particles?
• Cosmic ray ? Sometimes we observe 1000TeV cosmic
  rays
• Low flux and cannot control energies too well
• Need to look into small distances to probe the
  fundamental constituents with full control of
  particle energies and fluxes
• Particle accelerators
• Accelerators need not only to accelerate
  particles but also to
• Track them
• Maneuver them
• Constrain their motions to the order of 1mm
• Why?
• Must correct particle paths and momenta to
  increase fluxes and control momenta

6
Particle Accelerators

• 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
• 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, SppS
  at CERN
• Proton-Proton Large Hadron Collider at CERN
  (late 2007)
• 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

7
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 q then get accelerated through
  series of electrodes, gaining kinetic energy of
  TqV 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).

8
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,
  increasing HV

9
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

10
Resonance Accelerators Cyclotron

• Fixed voltage machines have intrinsic limitations
  in their energy due to 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

11
Resonance Accelerators Cyclotron

• While the Ds 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 Ds
• 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

12
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
• In a constant angular speed, wv/r. The
  frequency of the motion is
• Thus, to continue accelerate the particle the
  electric field should alternate in this
  frequency, cyclotron resonance frequency
• The maximum kinetic energy achievable for an
  cyclotron with radius R is

13
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
  light particles to very high energies

14
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
• For v c, the resonance frequency becomes
• Thus for high energies, either B or n should
  increase
• Machines with constant B but variable n are
  called synchro-cyclotrons
• Machines with variable B independent of the
  change of n is called synchrotrons

15
Synchroton Accelerators

• Electron synchrotrons, B varies while n is held
  constant
• Proton synchrotrons, both B and n varies
• For v c, the frequency of motion can be
  expressed
• For an electron
• For magnetic field strength of 2Tesla, one needs
  radius of 50m to accelerate an electron to
  30GeV/c.

16
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

17
Forewords

• What are elementary particles?
• Particles that make up matter in the universe
• What are the requirements for elementary
  particles?
• Cannot be broken into smaller pieces
• Cannot have sizes
• The notion of elementary particles have changed
  from 1930s through present
• In the past, people thought protons, neutrons,
  pions, kaons, r-mesons, etc, as elementary
  particles
• Why?
• Due to the increasing energies of accelerators
  that allows us to probe smaller distance scales
• What is the energy needed to probe 0.1fm?
• From de Broglie Wavelength, we obtain

18
Forces and Their Relative Strengths

• Classical forces
• Gravitational every particle is subject to this
  force, including massless ones
• How do you know?
• Electromagnetic only those with electrical
  charges
• What are the ranges of these forces?
• Infinite!!
• What does this tell you?
• Their force carriers are massless!!
• What are the force carriers of these forces?
• Gravity graviton (not seen but just a concept)
• Electromagnetism Photons

19
Forces and Their Relative Strengths

• What other forces?
• Strong force
• Where did we learn this force?
• From nuclear phenomena
• The interactions are far stronger and extremely
  short ranged
• Weak force
• How did we learn about this force?
• From nuclear beta decay
• What are their ranges?
• Very short
• What does this tell you?
• Their force carriers are massive!
• Not really for strong forces
• All four forces can act at the same time!!!

20
Forces Relative Strengths

• The strengths can be obtained through potential,
  considering two protons separated by a distance
  r.
• Magnitude of Coulomb and gravitational potential
  are
• q magnitude of the momentum transfer
• What do you observe?
• The absolute values of the potential E decreases
  quadratically with increasing momentum transfer
• The relative strength is, though independent of
  momentum transfer

Fourier x-form
Fourier x-form
21
Forces Relative Strengths

• Using Yukawa potential form, the magnitudes of
  strong and weak potential can be written as
• gW and gs coupling constants or effective
  charges
• mW and mp masses of force mediators
• The values of the coupling constants can be
  estimated from experiments

Fourier x-form
Fourier x-form
22
Forces Relative Strengths

• We could think of p as the strong force mediator
  w/
• From observations of beta decays,
• However there still is an explicit dependence on
  momentum transfer
• Since we are considering two protons, we can
  replace the momentum transfer, q, with the mass
  of protons

23
Forces Relative Strengths

• The relative strength between EM and strong
  potentials is
• And that between weak and EM potentials is

24
Interaction Time

• The ranges of forces also affect interaction time
• Typical time for Strong interaction 10-24sec
• What is this?
• A time that takes light to traverse the size of a
  proton (1 fm)
• Typical time for EM force 10-20 10-16 sec
• Typical time for Weak force 10-13 10-6 sec
• In GeV ranges, the four forces are different
• These are used to classify elementary particles

25
Elementary Particles

• Before the quark concepts, all known elementary
  particles were grouped in four depending on the
  nature of their interactions

26
Elementary Particles

• How do these particles interact??
• All particles, including photons and neutrinos,
  participate in gravitational interactions
• Photons can interact electromagnetically with any
  particles with electric charge
• All charged leptons participate in both EM and
  weak interactions
• Neutral leptons do not have EM couplings
• All hadrons (Mesons and baryons) responds to the
  strong force and appears to participate in all
  the interactions

27
Elementary Particles Bosons and Fermions

• All particles can be classified as bosons or
  fermions
• Bosons follow Bose-Einstein statistics
• Quantum mechanical wave function is symmetric
  under exchange of any pair of bosons
• xi space-time coordinates and internal quantum
  numbers of particle i
• Fermions obey Fermi-Dirac statistics
• Quantum mechanical wave function is
  anti-symmetric under exchange of any pair of
  Fermions
• Pauli exclusion principle is built into the wave
  function
• For xixj,

28
Bosons, Fermions, Particles and Antiparticles

• Bosons
• All have integer spin angular momentum
• All mesons are bosons
• Fermions
• All have half integer spin angular momentum
• All leptons and baryons are fermions
• All particles have anti-particles
• What are anti-particles?
• Particles that has same mass as particles but
  with opposite quantum numbers
• What is the anti-particle of
• A p0?
• A neutron?
• A K0?
• A Neutrinos?

29
Quantum Numbers

• When can an interaction occur?
• If it is kinematically allowed
• If it does not violate any recognized
  conservation laws
• Eg. A reaction that violates charge conservation
  will not occur
• In order to deduce conservation laws, a full
  theoretical understanding of forces are necessary
• Since we do not have full theory for all the
  forces
• Many of general conservation rules for particles
  are based on experiments
• One of the clearest conservation is the lepton
  number conservation
• While photon and meson numbers are not conserved

30
Baryon Numbers

• Can the decay occur?
• Kinematically??
• Yes, proton mass is a lot larger than the sum of
  the two masses
• Electrical charge?
• Yes, it is conserved
• But this decay does not occur (lt10-40/sec)
• Why?
• Must be a conservation law that prohibits this
  decay
• What could it be?
• An additive and conserved quantum number, Baryon
  number (B)
• All baryons have B1
• Anti-baryons? (B-1)
• Photons, leptons and mesons have B0
• Since proton is the lightest baryon, it does not
  decay.

31
Assignments

1. Carry out Fourier transformation and derive
   equations 9.3 and 9.5