W.S. Graves July, 2011
W.S. GravesJuly, 2011
MIT
Tools of Particle Physics IAccelerators
W.S. Graves July, 2011
1.Introduction to Accelerator Physics
2.Three Big Machines
•• Large Large HadronHadron Collider (LHC)Collider (LHC)
•• International Linear Collider (ILC)International Linear Collider (ILC)
•• MuonMuon ColliderCollider
3.Future Laser/Plasma Accelerators
Outline
Courtesy of C. Prior, RAL
Motion in Electric and Magnetic Fields Governed by Lorentz force
Acceleration along a uniform electric field (B=0)
BvEqdtpd
EpE
qcBvEpE
qcdtdE
dtpdpc
dtdEE
cmcpE
22
2
420
222
cvtmeEx
vtz
for path parabolic
22
0
A magnetic field does not alter a particle’s energy. Only an electric field can do this.
Courtesy of C. Prior, RAL
0
0
20
)(
)(
mqBvb
qBvma
Bvqvm
Behaviour under constant B-field, E=0 Motion in a uniform, constant magnetic field Constant energy with spiralling along a uniform magnetic
field
qBp
vE
qBc
2
Courtesy of C. Prior, RAL
Methods of Acceleration: Linear Simplest example is a vacuum chamber
with one or more DC accelerating structures with the E-field aligned in the direction of motion. Limited to a few MeV
To achieve energies higher than the highest voltage in the system, the E-fields are alternating at RF cavities. Avoids expensive magnets
No loss of energy from synchrotron radiation
But requires many structures
Large energy increase requires a long accelerator
SLAC linear accelerator
SNS Linac, Oak Ridge
Courtesy of C. Prior, RAL
Methods of Acceleration: Circular Synchrotron Principle of frequency modulation but in addition variation in
time of B-field to match increase in energy and keep revolution radius constant.
Magnetic field produced by several bending magnets
(dipoles), increases linearly with momentum. For q=e and
high energies:
.
Practical limitations for magnetic fields => high energies only
at large radius
e.g. LHC E = 8 TeV, B = 10 T, = 2.7 km
nf
v
EqBc
2
qBp
chargeunit per [m] [T] 0.3[GeV]so BEceE
epBρ
Courtesy of C. Prior, RAL
Ring Concepts Important concepts in rings:
Revolution period
Revolution (angular) frequency
If several bunches in a machine, introduce RF cavities in
straight sections with fields oscillating at a multiple h of the
revolution frequency. h is the harmonic number.
For synchrotrons, energy increase E when particles pass RF cavities can increase energy only so far as can increase B-field in dipoles to keep constant .
cL
vR
2
Lc
12
Lhchrf
2
qBp
qpB
Courtesy of C. Prior, RAL
Effect on Particles of an RF Cavity Cavity set up so that particle at the centre of bunch,
called the synchronous particle, acquires just the right amount of energy.
Particles see voltage
In case of no acceleration, synchronous particle hass = 0 Particles arriving early see < s
Particles arriving late see > s
energy of those in advance is decreased relative to the synchronous particle and vice versa.
To accelerate, make 0 < s< so that synchronous particle gains energy
)(sin2sin 00 tVtV rf
Bunching EffectsqVE sin0
Courtesy of C. Prior, RAL
Strong Focusing: Alternating Gradient Principle
A sequence of focusing-defocusing fields provides a stronger net focusing force.
Quadrupoles focus horizontally, defocus vertically or vice versa. Forces are linearly proportional to displacement from axis.
A succession of opposed elements enable particles to follow stable trajectories, making small (betatron) oscillations about the design orbit.
Technological limits on magnets are high.
Courtesy of C. Prior, RAL
Sextupoles are used to correct longitudinal momentum errors.
Focusing Elements
SLAC quadrupole
Courtesy of C. Prior, RAL
General equation of ellipse is
, , are functions of distance (Twiss parameters), and is a constant. Area = .
RMS emittance
(statistical definition)
Transverse Phase Space Under linear forces, any particle
moves on an ellipse in phase space (x,x´).
Ellipse rotates in magnets and shears between magnets, but its area is preserved: Emittance
x
x´
x
x´
22 2 xxxx
222 xxxxrms
Courtesy of C. Prior, RAL
Electrons and Synchrotron Radiation Particles radiate when they are accelerated, so charged
particles moving in dipole magnetic fields emit radiation (due to centrifugal acceleration) in the forward direction.
After one turn of a circular accelerator, total energy lost by synchrotron radiation is
mp/me = 1836 and m/me = 207. For the same energy and radius,
4
20
18
/GeVm10034.6GeV
cmGeVEE
13 9/ 10 / 10e p eE E E E
Courtesy of C. Prior, RAL
Luminosity Measures interaction rate per unit cross section -
an important concept for colliders. Simple model: Two cylindrical bunches of area A.
Any particle in one bunch sees a fraction N /A of the other bunch. (=interaction cross section). Number of interactions between the two bunches is N2 /A. Interaction rate is R = f N2 /A, and
Luminosity
CERN and Fermilab p-pbar colliders have L ~ 1030
cm-2s-1. SSC was aiming for L ~ 1033 cm-2s-1
Area, A
ANfL
2
W.S. Graves July, 2011
Pierre Oddone
0.5 TeV e+e-
3 TeV e+e-
3-4 TeV +-
Decision Tree for Future HEP Facilities
W.S. Graves July, 2011
HEP Facility Sizes
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LHC accelerator complex
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Beam 1
TI2
Beam 2TI8
LHC proton path
The LHC needs most of the CERN accelerators...
≥ 7 seconds from source to LHC
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14.0
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LHC layout and parameters
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8 arcs (sectors), ~3 km each 8 long straight sections (700 m each) beams cross in 4 points 2-in-1 magnet design with separate
vacuum chambers → p-p collisions
-- β* = 0.55 m (beam size =17 μm)- Crossing angle = 285 μrad- L = 1034 cm-2 s-1
RF
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Nominal LHC parametersBeam energy (TeV) 7.0No. of particles per bunch 1.15x1011
No. of bunches per beam 2808Stored beam energy (MJ) 362Transverse emittance (μm) 3.75Bunch length (cm) 7.6
The LHC ArcsThe LHC Arcs
8.33 Tnominal field
11850 A nominalcurrent
W.S. Graves July, 2011
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Incident of Sept. 19th 200814
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The final circuit commissioning was performed in the week following the startup with beam.
During the last commissioning step of the last main dipole circuit an electrical fault developed at ~5.2 TeV (8.7 kA) in the dipole bus bar (cable) at the interconnection between a quadrupole and a dipole magnet.
Later correlated to quench due to a local R ~220 n – nominal 0.35 n
An electrical arc developed and punctured the helium enclosure.Around 400 MJ from a total of 600 MJ stored in the circuit were dissipated in the cold-mass and in electrical arcs.
Large amounts of Helium were released into the insulating vacuum.The pressure wave due to Helium flow was the cause of most of the damage (collateral damage).
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Magnet Interconnection14
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Dipole busbar
Melted by arcMelted by arc
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Collateral damage14
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Quadrupole-dipole interconnection
Quadrupole support
Main damage area covers ~ 700 metres. 39 out of 154 main dipoles, 14 out of 47 main quadrupoles
from the sector had to be moved to the surface for repair (16) or replacement (37).
Sooth clad beam vacuum chamber
W.S. Graves July, 2011
International Linear ColliderInternational Linear Collider
e- main linac
IP and 2 moveable detectors
e+ main linac
e+ beam dump e- beam dump
e- e+ damping rings
e- source + pre-acceleration
e+ pre-acceleration
e+ production
undulator
target
e+ transport line
e- transport line
2-stage bunch compression
2-stage bunch compression
e- main linac
IP and 2 moveable detectors
e+ main linac
e+ beam dump e- beam dump
e- e+ damping rings
e- source + pre-acceleration
e+ pre-acceleration
e+ production
undulator
target
e+ transport line
e- transport line
2-stage bunch compression
2-stage bunch compression
W.S. Graves July, 2011
Why Superconducting RF Cavities?SC cavities offer
– a surface resistance six orders of magnitude lower than normal conductors
– high efficiency even when cooling is included– low frequency, large aperture for smaller wake-field effects
Relations for the surface fields to acclerating gradient:
Epeak/Eacc = 2 -minimize this to reduce field emission
Bpeak/Eacc = 4 mT/(MV/m) -minimize to avoid quenches
Cavity FabricationCavity Fabrication
W.S. Graves July, 2011
ILC RF unit at Fermilab
W.S. Graves July, 2011
MuonMuon ColliderCollider
W.S. Graves July, 2011
Muon Collider Schematic
Proton source: Upgraded PROJECT X (4 MW, 2±1 ns long bunches)
1021 muons per year that fit within the acceptance of an accelerator
√s = 3 TeVCircumference = 4.5kmL = 3×1034 cm-2s-1
/bunch = 2x1012
(p)/p = 0.1%* = 5mmRep Rate = 12Hz
Courtesy of S. Geer, FNAL
W.S. Graves July, 2011
Challenges
● Muons are born within a large phase space ( → )
- To obtain luminosities O(1034) cm-2s-1, need to reduce initial phase space by O(106)
● Muons Decay (0 = 2s) - Everything must be done fast
→ need ionization cooling- Must deal with decay electrons- Above ~3 TeV, must be careful about decay
neutrinos !
Courtesy of S. Geer, FNAL
W.S. Graves July, 2011
6D Cooling
liqHs
MC designs require the muon beam to be cooled by ~ O(106) in 6D
Ionization cooling reduces transverse (4D) phase space.
To also cool longitudinal phase space (6D) must mix degrees of freedom as the cooling proceeds
This can be accomplished with solenoid coils arranged in a helix, or with solenoid coils tilted.
Palmer
Alexhin & Fernow
Courtesy of S. Geer, FNAL
W.S. Graves July, 2011Courtesy of W. Leemans, LBL
Laser/Plasma AcceleratorsLaser/Plasma Accelerators
W.S. Graves July, 2011Courtesy of W. Leemans, LBL
W.S. Graves July, 2011
Thank you!Thank you!
Questions?Questions?