Wednesday, Oct. 25, 2006PHYS 3446, Fall 2006 Jae Yu 1 PHYS 3446 – Lecture #14 Wednesday, Oct. 25, 2006 Dr. Jae Yu 1.Particle Accelerators Electro-static

Wednesday, Oct. 25, 2006 PHYS 3446, Fall 2006Jae Yu

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PHYS 3446 – Lecture #14Wednesday, Oct. 25, 2006

Dr. Jae Yu1. Particle Accelerators• Electro-static Accelerators• Cyclotron Accelerators• Synchrotron Accelerators2. Elementary Particle Properties• Forces and their relative magnitudes• Elementary particles• Quantum Numbers• Gell-Mann-Nishijima Relations• Production and Decay of Resonances


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• Quiz in class next Wednesday, Nov. 1

Announcements


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Principles of Calorimeters

Total absorption calorimeter: See the entire shower energy

Sampling calorimeter: See only some fraction of shower energy

For EM

Absorber plates

visE fE

For HAD visE fE

0

0 0

vis

visabs vis

XE

X X

0

0 0

vis

visabs vis E


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Example Hadronic Shower (20GeV)


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• 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 1m

• Why?– Must correct particle paths and momenta to increase fluxes and control

momenta

Particle Accelerators


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• 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

Particle Accelerators


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• 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 T=qV through every set of electrodes

Electrostatic Accelerators: Cockcroft-Walton

• 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).


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• 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

Electrostatic Accelerators: Van de Graaff


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• 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

Electrostatic Accelerators: Van de Graaff


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• 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

Resonance Accelerators: Cyclotron


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• 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



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• 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, =v/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


2vmr

v qB

r mc

2f

2

2 2 2max max 2

1 1

2 2

qBRT mv m R

mc

vBqc

2

qB

mc 1

2

q B

m c


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• 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

Resonance Accelerators: Linear Accelerator


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• 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 should increase• Machines with constant B but variable are called synchro-

cyclotrons• Machines with variable B independent of the change of is

called synchrotrons

Synchroton Accelerators

dv v Bm m v q

dt c

2

1 1

2

q B

m c


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• Electron synchrotrons, B varies while is held constant

• Proton synchrotrons, both B and 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.


1

2 2

v cf

R R

/( )

0.3 )

p GeV cpcR m

qB B Tesla


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• 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



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• 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 1930’s through present– In the past, people thought protons, neutrons, pions, kaons, -

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 0.1–fm?– From de Broglie Wavelength, we obtain

Forewords

P

c

c

2000 /MeV c197fm

0.1fm

MeV

c


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• 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

Forces and Their Relative Strengths


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• 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!!!

Forces and Their Relative Strengths


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• 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

Forces’ Relative Strengths

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EM

eV r

r

2

Ng

G mV r

r

2

2EM

eV r

q

2

2N

g

G mV r

q

Fourier x-form

Fourier x-form

EM

g

V

V

2

2N

e

G m

2 5

22

1

N

e c

c Gmc

39 236

2

1 1 10~ 10

137 6.71

GeV

GeV


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• 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 m: masses of force mediators

• The values of the coupling constants can be estimated from experiments


SV r Fourier x-form

Fourier x-form

2

15Sg

c

SV r

WV r WV r

2

0.004Wg

c

2Sg

r

2m c r

ce

2Sg

2 2 2q m c2Wg

r

2Wm c r

ce

2Wg

2 2 2Wq m c


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• We could think of 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


m 280 /Wm GeV c

2 2 2 4 1pq c m c GeV

2140 /MeV c


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• The relative strength between EM and strong potentials is

• And that between weak and EM potentials is


S

EM

V

V

EM

W

V

V

315 137 1 2 10

2 41 180 1.2 10

137 0.004

2 2

2 2 2 2Sg c q

c e q m c

2 42

2 2 4 2 2pS

p

m cg c

c e m c m c

2 2 22

2 2W

W

q m ce c

c g q

2 4 2 22

2 2 4p W

W p

m c m ce c

c g m c


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• 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

Interaction Time


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

Elementary Particles


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• 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

Elementary Particles


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• 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 xi=xj,

Elementary Particles: Bosons and Fermions

1 2 3, , ,... ...B i nx x x x x

1 2 3, , ,... ...F i nx x x x x

F

1 32 , ,... ., ..B i nx xx x x

1 32 , ,... ., ..F i nx xx x x

F


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• 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 0?• A neutron?• A K0?• A Neutrinos?

Bosons, Fermions, Particles and Antiparticles


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• 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

Quantum Numbers


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• 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 (<10-40/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 B=1• Anti-baryons? (B=-1)• Photons, leptons and mesons have B=0

• Since proton is the lightest baryon, it does not decay.

Baryon Numbers0p e


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Assignments1. Carry out Fourier transformation and derive

equations 9.3 and 9.5

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Wednesday, Oct. 25, 2006PHYS 3446, Fall 2006 Jae Yu 1 PHYS 3446 – Lecture #14 Wednesday, Oct. 25, 2006 Dr. Jae Yu 1.Particle Accelerators Electro-static