Tools of Particle Physics I
Accelerators
W.S. Graves
July, 2011
MIT
W.S. Graves July, 2011
Outline
1.Introduction to Accelerator Physics
2.Three Big Machines
• Large Hadron Collider (LHC)
• International Linear Collider (ILC)
• Muon Collider
3.Future Laser/Plasma Accelerators
W.S. Graves July, 2011
Motion in Electric and Magnetic Fields


  
dp
 q EvB
dt

Governed by Lorentz force
2 2
E  p c  m02 c 4
2

dE 2  dp
 E
c p 
dt
dt
dE qc 2     qc 2  


p E v  B 
pE
dt
E
E



Acceleration along a uniform electric field (B=0)
z  vt 
eE 2  parabolic path for v  c
x
t
2m0 
Courtesy of C. Prior, RAL

A magnetic field does not
alter a particle’s energy.
Only an electric field can
do this.
Behaviour under constant B-field, E=0

Motion in a uniform, constant magnetic field
 Constant energy with spiralling along a uniform magnetic
field
m0 v 2

 qv B 
m0 v

(a)
qB
v
qB
(b)   
 m0
p
 
qB
Courtesy of C. Prior, RAL
qBc 2
v


E

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
SLAC linear accelerator
radiation
 But requires many structures
 Large energy increase requires a long
accelerator
SNS Linac,
Oak Ridge
Courtesy of C. Prior, RAL
Methods of Acceleration: Circular

Synchrotron

p

qB
f  n
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:
p E
Bρ

 so E [GeV]  0.3 B [T]  [m] per unit charge
qBc 2 v .
e ce


E
  Practical limitations for magnetic fields => high energies only
at large radius
e.g. LHC
Courtesy of C. Prior, RAL
E = 8 TeV, B = 10 T,  = 2.7 km
Ring Concepts
2 R L


v
c
 1 c
 
2  L

 Revolution period 
 Revolution (angular) frequency 

revolution frequency.
 h is the harmonic number.

Courtesy of C. Prior, RAL
If several bunches in a machine, introduce RF cavities in
straight sections with fields oscillating at a multiple h of the
2hc
rf  h 
L
p

qB
Important concepts in rings:
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 .
p
B 
q
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 has
s = 0



Bunching Effect
Courtesy of C. Prior, RAL

V0 sin 2rf t  V0 sin  (t )
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
E  qV0 sin  s
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
Focusing Elements
SLAC quadrupole
Sextupoles are used to
correct longitudinal
momentum errors.
Courtesy of C. Prior, RAL
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

General equation of ellipse is
 x2  2 x x   x 2  

, ,  are functions of distance
(Twiss parameters), and  is a
constant. Area = .

RMS emittance
 rms 
x2
x2  xx 
(statistical definition)
Courtesy of C. Prior, RAL
2
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
6 .034  10
 E GeV  
 m 

18
 E GeV 

2
m
GeV
/
c
 0





4
mp/me = 1836 and m/me = 207. For the same energy and
radius,
Ee / E p  1013
Courtesy of C. Prior, RAL
Ee / E  109
Luminosity
Area, A
Courtesy of C. Prior, RAL

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
N2
L f
A

Luminosity

CERN and Fermilab p-pbar colliders have L ~ 1030
cm-2s-1. SSC was aiming for L ~ 1033 cm-2s-1
Decision Tree for Future HEP Facilities
0.5 TeV e+e3 TeV e+e-
Pierre Oddone
W.S. Graves July, 2011
3-4 TeV +-
HEP Facility Sizes
W.S. Graves July, 2011
LHC accelerator complex
≥ 7 seconds from
source to LHC
14.06.2011
LHC performance in 2011 - LAL/Orsay
Beam 1
Beam 2
TI8
TI2
LHC proton path
The LHC needs most of the CERN accelerators...
16
14.06.2011
LHC performance in 2011 - LAL/Orsay
LHC layout and parameters

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
RF
Nominal LHC parameters
Beam energy (TeV)
7.0
No. of particles per bunch
1.15x1011
No. of bunches per beam
2808
Stored beam energy (MJ)
362
Transverse emittance (μm)
3.75
Bunch length (cm)
7.6
- β* = 0.55 m (beam size =17 μm)
- Crossing angle = 285 μrad
- L = 1034 cm-2 s-1
17
The LHC Arcs
8.33 T
nominal field
11850 A
nominal
current
W.S. Graves July, 2011
Incident of Sept. 19th 2008
The final circuit commissioning was performed in the week following
the startup with beam.
14.06.2011
LHC performance in 2011 - LAL/Orsay

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).
21
Magnet Interconnection
LHC performance in 2011 - LAL/Orsay
Melted by arc
14.06.2011
Dipole busbar
22
Collateral damage
LHC performance in 2011 - LAL/Orsay
Quadrupole-dipole
interconnection
Sooth clad beam
vacuum chamber
Main damage area covers ~ 700 metres.


14.06.2011
Quadrupole support
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).
23
International Linear Collider
e- e+ damping rings
e+ production
e+ pre-acceleration
target
e- transport line
e- source +
preacceleration
e+ transport line
undulator
2-stage
bunch
compression
e+ main linac
e- main linac
W.S. Graves July, 2011
e+ beam dump
IP and 2
moveable
detectors
e- beam dump
2-stage
bunch
compression
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
W.S. Graves July, 2011
Cavity Fabrication
ILC RF unit at Fermilab
W.S. Graves July, 2011
Muon Collider
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
Courtesy of S. Geer, FNAL
W.S. Graves July, 2011
√s = 3 TeV
Circumference = 4.5km
L = 3×1034 cm-2s-1
/bunch = 2x1012
(p)/p = 0.1%
* = 5mm
Rep Rate = 12Hz
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 = 2s)
- 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
Palmer
 MC designs require the
muon beam to be cooled by
~ O(106) in 6D
Ionization cooling reduces
transverse (4D) phase
space.
Courtesy of S. Geer, FNAL
W.S. Graves July, 2011
liq
H
 This can be accomplished
with solenoid coils
arranged in a helix, or with
solenoid coils tilted.
s
 To also cool longitudinal
phase space (6D) must mix
degrees of freedom as the
cooling proceeds
Alexhin & Fernow
Laser/Plasma Accelerators
Courtesy of W. Leemans, LBL
W.S. Graves July, 2011
Courtesy of W. Leemans, LBL
W.S. Graves July, 2011
Thank you!
Questions?
W.S. Graves July, 2011