accelerator and colliders -...
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Accelerator and Colliders
Suyong Choi
2/14/2011 1 Winter School on Collider Physics
Contents • Accelerators
o Components
o Existing and future accelerators
• Cross section and luminosity o Cross section
o Instantaneous and integrated luminosity
• Homework
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Particle Experiment • Probe with compton wavelength ~ size of target
• Beam
• Target
• Detector
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Probing small things • To probe 1 micrometer
p =ℎ
𝜆= 2𝜋
ℏ𝑐
𝜆𝑐= 2𝜋
200𝑀𝑒𝑉 𝑓𝑚
109𝑓𝑚 𝑐= 4𝜋 ×
0.1𝑒𝑉
𝑐≈ 1𝑒𝑉/𝑐
• To probe 1 fm
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Large Hadron Collider (LHC)
• 27 km circumference
• Design energy: 7 TeV + 7 TeV
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Reach of Accelerator Technologies
• New accelerator
technologies needed
to reach x10~100 in
energy
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Cyclotron • 27inch accelerator
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• 1931 Lawrence and Livingston at Berkeley
• Accelerate with fixed RF frequency and constant B-field
Limitations of Cyclotrons • Ratio between velocity and radius of curvature
𝑣
𝑟=𝑞𝐵
𝛾𝑚
• Revolution time in cyclotron
𝑇 =2𝜋𝑟
𝑣=2𝜋𝛾𝑚
𝑞𝐵
• For relativistic case, acceleration cannot occur with constant frequency. Cyclotrons are impractical for high-energies
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Accelerators • Systematic approach
to answer questions in
particle physics
• Factor x10 in 15 years
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General Structure of Accelerators
• Beam source o Electron
o Ion
• Electrostatic accelerator o Cockroft-Walton
• Linear accelerator o Uses RF field
• Storage ring o RF field
o Dipole and quadrupole magnets produce B field for bending and
focussing
o RF field and B field strength must change as particle accelerates
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Electron Beam Source • Principle – photoemission
o Ga-As (Gallium-Arsenide)
• Higher energy beam early on with RF photoinjector o Space charge effect becomes smaller by 1/p2
• Look in backup on how other beams are produced
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RF Acceleration • In a uniform wave guide, 𝑣𝑝ℎ𝑎𝑠𝑒 > 𝑐, RF field quickly
becomes out of phase with particles
• We need a disk-loaded wave guide
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Accelerator Structure • Focussing
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Synchrotron Accelerator
• Magnetic field for bending magnet should be
increased as E increases
• RF accelerating field should be synchronized with
beam
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Bending Charged Particles
• Dipole magnetic field is used to bend in x-dir.
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Charged Particle Motion in Constant Magnetic Field
• Motion of charged particle perpendicular to 𝐵
𝛾𝑚𝑣2
𝑟= 𝑞𝑣𝐵 ⇒ 𝛾𝑚𝑣 = 𝑝𝑇 = 𝑞𝐵𝑟
• Practical equation: 𝑝𝑇𝐺𝑒𝑉
𝑐= 0.3 × 𝐵 𝑇 × 𝑟[𝑚]
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LHC Dipole Magnet • 1232 15 meter dipole
magnets in LHC tunnel
• 11000 ampere current
max
• 8.5 T max. B field
• 1.9K operating
temperature
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Focusing Charged Particles
• Quadrupole focuses in y and defocusses in x for +q
beam going through page
• Array of quadrupoles rotated 90 degrees
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Fixed Target vs Collider • Colliding beam experiment
o First proposed in 1956 by Kerst
o Oppositely directed beam with same energy colliding
• Center of mass energy is 2𝐸 whereas in fixed target
it is 2𝑚𝐸 o 1 TeV=1000 GeV energy beam, in a fixed target can only produce 44 GeV
of useful energy
o In collider, it is 2000 GeV
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Collider and Storage Rings
• Collider and Storage ring o Probability of interaction is low at high energies
o Only a small fraction of particles interact
o Need to recycle the beams
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𝑒+𝑒− and Hadron Colliders • Electron collider
o Clean
o Precision measurement
o Due to synchrotron radiation, difficult to get to high energies
• Hadron collider o easier to accelerate to high energies
o Proton breakup produces many particles
o Better for search for heavy particles – continuous range of E
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Tevatron • Proton on antiproton at 1.96 TeV
• Discovered top quark in 1995
• Ending this year – 20 years of running
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KEKB
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• Started 1998.12 Ended 2010. 6
• Total integrated luminosity: 1052 fb-1
• Asymmetric collider
𝐸𝑒− = 8 𝐺𝑒𝑉 𝐸𝑒+ = 3.5 𝐺𝑒𝑉
• CKM Matrix and b-quark sector probed to unprecendted degree
International Linear Collider
• Beam energy: 500(?) GeV 𝑒− + 500(?) GeV 𝑒+
• 5 nm thick beam bunch
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Different Sizes of Accelerators
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Cross Section and Luminosities
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• Cross section for inelastic collision is 0.1 barn at 1 TeV CM Energy (1 barn=10-24 cm2)
• If two protons are separated by distance less than b, then they collide and break up the proton
• Cross section: 𝜎 = 𝜋𝑏2 = 10−25𝑐𝑚2
Cross Section
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b
Collision Cross Section of Fundamental Particles
• If beam energy is the only scale in the system, then
𝜎 ∝1
𝐸2~1
𝑠
o From dimensional analysis
o If other scale present, then this is not valid
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Mandelstam Variables • Assume process
• In scattering between two particles, one can define
3 variables
𝑠 = 𝑝𝐴 + 𝑝𝐵2 = 𝑝𝐶 + 𝑝𝐷
2
𝑡 = 𝑝𝐶 − 𝑝𝐴2 = 𝑝𝐵 − 𝑝𝐷
2
𝑢 = 𝑝𝐴 − 𝑝𝐷2 = 𝑝𝐶 − 𝑝𝐵
2
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pD
pC
pB pA
𝑝𝐴 + 𝑝𝐵 = 𝑝𝐶 + 𝑝𝐷
Cross Section and Luminosity
• If a certain process has 1 fb=10-15 barn, then
probability for this process to occur is 10-14 times
smaller than that to break up the proton o You have to approach closer to by factor of 10-7
• In accelerators, you have a “bunch” of particles
colliding o N particles in transverse beam radius of r
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Luminosity • Probability for interaction?
o Assume N1 particles are uniformly distributed
𝑁1𝜎
𝜋𝑟2
• By making the beam size r smaller, one can
increase chances for interaction in one crossing
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r
Instantaneous Luminosity • Two bunches colliding
𝑃 =𝑁1𝑁2𝜎
𝜋𝑟2
• Rate of interaction o In an accelerator bunches cross at a fixed frequency
𝑅 = 𝑓𝑁1𝑁2𝜎
𝜋𝑟2= ℒ𝜎
• Unit of instantaneous luminosity is usually in 𝑐𝑚−2𝑠−1
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N1 N2
May 13 2008 34
Collisions at the LHC
Integrated Luminosity • 𝐿 = ℒ𝑑𝑡
o Unit of integrated luminosity: cm-2
o 𝜎 ℒ𝑑𝑡 : Expected number of events for certain process
• It is more convenient to use larger units
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1 b-1 1024 cm-2
1 mb-1 = 103 b-1 1027 cm-2
1 b-1 = 103 mb-1 1031 cm-2
1 nb-1 = 103 b-1 1034 cm-2
1 pb-1 ?
1 fb-1 ?
Example • If ℒ = 1032𝑐𝑚−2𝑠−1 at LHC, what is the rate of
inelastic collisions?
• For 1032𝑐𝑚−2𝑠−1 and a physics process with 𝜎 = 1𝑓𝑏,
how long on average should I take data to detect 1
event? o Assume 100% efficiency
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Obtaining Higher Instantaneous Luminosities
• Put more particles per bunch o accelerator uses more power to accelerate and bend
• Make bunch size smaller – better focusing
• Increase collision rate of bunches o accelerator uses more power
• Constraint is in the design and construction of
accelerator components
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Higher Luminosity vs Higher Energy
• Higher energy allows production of more massive
particles o Cross section of production of heavy particles can increase dramatically
o 𝑡𝑡 cross section in 𝑝𝑝 2 TeV is 9 pb, in 14 TeV LHC it is 800 pb
• Higher luminosity allows for more events to be
collected in a given time
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Homework Problems 1. Derive 𝑝𝑇 = 0.3𝑞𝐵𝑟 when
o pT is in units of GeV/c
o Q is in units of electron charge
o B in Tesla, r in meter
2. VLHC accelerator is 74km in diameter. What is the expected beam energy if the current LHC dipole magnet technology is used? o LHC diameter is 8.4 km and has 7 TeV beam energy
3. What is the useful energy that can be used to make particles in KEKB where 𝐸𝑒− = 8 𝐺𝑒𝑉 𝐸𝑒+ =3.5 𝐺𝑒𝑉
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Backup
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Proton Beam Source • Plasma from discharge
of Hydrogen gas
• Strong electric field
separates
electrons from ions
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Positron Beam Source • Efficiency increases from 10-3 to 1
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Antiproton Beam Source
• One needs to sweep away other particles like pions
and Kaons using magets
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Electrostatic Accelerator • Cockroft-Walton at
Fermilab
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RF Acceleration • Set up longitudinal wave that is synchronized with
bunches
• Traveling wave
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Beam Cooling Electron cooling Stochastic cooling
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• Electron of same speed
as ion beam is brought
into contact
• Electronic steering
Ionization Cooling
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Electron Accelerators • Accelerate charged
particle to desired
energy/momentum
• Electron-positron
accelerators
• Proton accelerators
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• Livingston Plot
Cockroft-Walton Accelerator
• Voltage multiplier
made of
diodes and capacitors
• In 1932,
𝑝(700 𝑘𝑒𝑉) + 𝐿𝑖 → 𝐻𝑒, o first nuclear reaction by
particle accelerator
o 1951 Nobel prize
• Difficult to raise to very
high energies
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RF Field Accelerator • 1928 Wideroe’s Linear Accelerator
o Used AC voltage to accelerate Potassium ion
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Status of LHC • Last year it ran with 3.5 TeV + 3.5 TeV
• Each experiment collected about 35 pb-1
• It will collect 1 fb-1 this year
• 5 fb-1 by next year
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Fixed Target Experiment
• Four momentum of target (0,0,0,𝑀)
• Four momentum of beam 0,0, 𝑝, 𝑝2 +𝑚2
• After collision, the momentum conserved,
so, daughter particles move
with momentum p
• Energy available for
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Energy Available in a Fixed Target Experiment
• In Center-of-mass frame, Maximum energy available for producing new particle of mass M’ is when M’ is equal to the total energy of incoming particle
o Target 4-momentum: 0,0,−𝑝′, 𝑝′2 +𝑀2
o Target 4-momentum: 0,0, 𝑝′, 𝑝′2 +𝑚2
o Total 4- momentum in CM frame: 0,0,0, 𝑝′2 +𝑚2 + 𝑝′2 +𝑀2
o Largest Mass of new particle = 𝑝′2 +𝑚2 + 𝑝′2 +𝑀2
o This is Lorentz-invariant of total 4-momentum=Lorentz invariant of
(0,0, 𝑝, 𝑝2 +𝑚2 +𝑀)
• Center of mass energy= 𝑚2 +𝑀2 + 2𝑀 𝑝2 +𝑚2
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Muon Collider • Create, accelerate and collide 𝜇+𝜇−
• R&D stage - technical problems should be solved
first o Muon lifetime at rest is 2.2 s
o Creating, cooling, accelerating and accelerating with enough luminosity
is challenging
• What is it good for? o Higgs physics
o Neutrino physics
o Clean probe
o Doesn’t suffer from
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Cross Section from Theory
• In a given model, you can calculate the transition
amplitude
𝑇𝑓𝑖 = 𝜙𝑓∗ 𝑥 𝑉 𝑥 𝜙𝑖 𝑥 𝑑
4𝑥
𝑊𝑓𝑖 =𝑇𝑓𝑖
𝑇𝑉
2
: transition rate
• Relationship between cross section and transition rate
𝜎 =𝑊𝑓𝑖
𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑓𝑙𝑢𝑥(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑖𝑛𝑎𝑙 𝑠𝑡𝑎𝑡𝑒𝑠)
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