Lecture 11 – Accelerators
Principles
Examples
Introduction to Particle Physics - Max Klein – Lecture
31.3.14
11 - Liverpool University
M.Klein 31.3.2014 L11
References
• M. Conte & W. MacKay, “An introduction to the physics of
particle accelerators”, World Scientific, Singapore, 1991.
• H. Wiedemann, “Particle accelerator physics, 1 : basic
principles and linear beam dynamics”- 2nd ed. , Springer,
Berlin 1999.
• A. Sessler & E. Wilson, “Engines of Discovery : A Century of
Particle Accelerators,” World Scientific, Singapore, 2007.
• S.Y. Lee, “Accelerator Physics” - 2nd ed. / Lee, World
Scientific, Singapore, 2004.
• J.B. Rosenzweig, “Fundamentals of Beam Physics,” Oxford
Univ. Press, 2003.
• A.W. Chao, M. Tigner, “Handbook of accelerator physics and
engineering”, World Scientific, Singapore,1999 From F. Zimmermann
Course Overview
24.2. Introduction and Basics
3.3. Quantum Numbers and Quarks, Gluons
10.3. Leptons,Photons, QED and Neutrinos,Weak Interactions
17.3. Detectors, Tracking and Calorimeters [here already due to travel]
24.3. Quark Mixing and Densities and Heavy Quarks
31.3. Accelerators and Recollection
Easter Break
28.4. Higgs and HEP Outlook
Tutorials: 7.3., 20.3., next 3.4., + one more
M.Klein 31.3.2014 L11
Electrostatic
Accelerator
Braun cathode ray tube (1897)
Karl Ferdinand Braun
m 2 p2
qV = v =
2
2m
p = 2mqV
Rutherford 1930
Momentum of particle of charge
q and mass m after passage of
a voltage difference. Limited by V.
Van de Graaf
Cockcroft Walton
Tandem
Oscillographs, CRT TV sets..
Tazzari, Cern Acc School 2006
M.Klein 31.3.2014 L11
High Frequency Linear Accelerator
m 2 p2
qNV = v =
2
2m
p = 2mqNV
Passage through N times
a voltage difference V
Multiple acceleration
cf Laurence Nobel lecture:
1920
V : v1 = 2qV / m
Dt =
L1 T 1
= =
v1 2 2 f
f1 =
v1
1
=
2qV / m
2L1 2L1
2V : v2 = 2 × 2qV / m = 2 ×v1
f2 =
Rolf Wideroe, 1902-1996
1927 (PhD)
[2 sections, 25kV, 50Hz]
v2
v 2
= 1
2L2 2L2
L2 = 2 ×L1
f2 = f1 = f
Lk = k ×L1, k = 1...N
[note: V=u for RW!]
Resonance condition:
Frequency = velocity/2L
at each gap. As frequency
is constant, length has to
grow like √k.
For large v=c, frequency has
to be very high to keep L small
M.Klein 31.3.2014 L11
mv2
= qvB
r
q
v = rB
m
mv
r=
qB
pr pm T 1
t=
=
= =
v qB 2 2 f
v
f=
2p r
qB
f=
2p m
Cyclotron
[B=const, f=const, r varies]
Lawrence invents the cyclotron 1931 based on Wideroes
linac. Strong magnetic field to bend particles on a circle.
Alternating electric field (potential between two halves):
Each turn an energy qV is gained. The time per turn is
independent of the radius as r and v increase like √k with
the frequency resonance condition analogous to
Wideroe’s.
m 2 q2
Ekin = v =
(rB) 2
2
2m
Large radius and high mag field
to achieve large energy. Needs
constant mass, i.e. non
relativistic
conditions (Bethe Ep < 20
MeV..?)
V
M.Klein 31.3.2014 L11
mv2
= qvB
r
q
v = rB
m
mv
r=
qB
pr pm T 1
t=
=
= =
v qB 2 2 f
v
f=
2p r
qB
f=
2p m
Cyclotron
[B=const, f=const, r varies]
Lawrence invents the cyclotron 1931 based on Wideroes
linac. Strong magnetic field to bend particles on a circle.
Alternating electric field (potential between two halves):
Each turn an energy qV is gained. The time per turn is
independent of the radius as r and v increase like √k with
the frequency resonance condition analogous to
Wideroe’s.
m 2 q2
Ekin = v =
(rB) 2
2
2m
Large radius and high mag field
to achieve large energy. Needs
constant mass, i.e. non
relativistic
conditions (Bethe Ep < 20
MeV..?)
M.Klein 31.3.2014 L11
Cyclotron
184”
4’’
11’’, 27’’ (1932)
60” - 8 MeV p - 220t magnet – 1938
[isotopes, plutonium during WWII..]
Phase stability: McMillan, Veksler 1945
“Fast: early arrival: less push
slow: late arrival: more push” (Koeth)
Tazzari, Cern Acc School 2006
M.Klein 31.3.2014 L11
Betatron
[B varies, f=const, r=const]
Cyclotron: radius increases during acceleration ~√k
Betatron: radius constant but magnetic field increases with time [Kerst]
r=
mv
qB
rotE = V=
dB
dt
d
ò E ds= ò rotE × dF = - dt ò BdF
s
V = p r02
F
F
d B
dt
p = q ò E dt = q ò
p = q× r0 × B / 2
V
dt
2p r0
Variable magnetic field induces
electric field. This causes an
accelerator voltage V. Particles
are accelerated without an extra
external voltage applied. The
accelerator voltage V is proportional
to the radius of the accelerator
squared and the mean field.
The generated momentum p is
given as the product of r and B.
Stability requires that the mean field
divided by 2 is equal to the field at
r0 (Wideroe stability criterion).
M.Klein 31.3.2014 L11
Synchrotron
mv
qB
p = qrB = 0.3Br
r=
high field, large radius
LHC : 7TeV = 0.3* 5.6T * 4.1km
m0
m=
,b = v/c
2
1- b
f=
The synchrotron cures deficits of cyclotron
and betatron by adjusting the magnetic field to
compensate for the relativistic rise of mass
and the frequency to keep the radius constant.
B(v) =
mv v
m0
=
qr0 qr0 1- b 2
v(B) =
v
2p r
Cyclotron: radius changes with
v,
frequency is constant (for small
)
and B is constant. Must fail in
relativistic velocity range.
Betatron: keep radius constant
and vary B field, but again fails
in
relativistic region.
fk =
1
1
m0 2
+
(
)
c2 qr0 B
v k
2p r0
fk (B) =
k - accelerator elements * turns
k
2p
×
1
2
æ r0 ö æ m0 ö
ç ÷ +ç
÷
è c ø è qr0 B ø
2
Orbit stabilisation required
“phase stability” Veksler, McMillan (1945)
Bunched beam:
only particles at right moment are accelerated.
CERN: SPS: 400GeV, 4600 bunches, revolution
frequency is 200 MHz from 2MW rf. 105 turns in 2s
M.Klein 31.3.2014 L11
[B varies, f varies, r=const]
Accelerator Elements
Dipole: keep beam on orbit
Cavity: rf structure to
develop large oscillating
field. up to tens of MV/m.
“ride on crest of a wave”
Quadrupole: focus/defocus
beam alternating in x/y plane
“strong focussing” principle
FODO lattice concept
M.Billing, Cornell 07
[Christofilos 1950; Courant, Snyder
1952]
M.Klein 31.3.2014 L11
Beam Optics
Linear optics described by Hills equation
x ' ' K ( s ) x  0
Solution expressed in terms of “beta-function”
xs   A0
 s ds '

 s  cos 
 0 
 0  s ' 

px
x' 
ps
K (s)  K (s  C )
C = circumference
Tune: number of oscillations per turn
  (C ) 1
ds
Q

2
2 C  ( s )
F.Zimmermann
M.Klein 31.3.2014 L11
Tazzari, Cern Acc School 2006
Storage Rings
fixed target accelerator: s=2ME, collider: s=4E2 : gain: 2E/M
First e+e- storage ring ADA at Frascati: Bruno Touschek et al.
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Bruno Touschek (1921-1978) Sam Currant (1912-1988)
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Accelerator Development
Development up to 1990
LHeC
?
HERA
pp, ep, e+eM.Klein 31.3.2014 L11
World Accelerators
The demands of particle physics for high energies and intensities have had a major impact on modern society
Table taken from W. Scarf & W. Wiesczycka, Proc. EPAC2000
M.Klein 31.3.2014 L11
Recent colliding ring machines
to explore energy frontier physics
M.Klein 31.3.2014 L11
HERA ep: built 1985-1991
6.2 km ring accelerator(s)
Superconducting p ring
Warm magnet e ring
Data delivery: 1992-2007
Particle Physics - L11 - M.Klein 25/04/08
hera
Ee = 15..30GeV , Ep = 400..1000GeV
polarisati on : P(e) = -0.5...0... + 0.5
Lspec » 0.4...2 ×1030 cm-2 s-1mA- 2
I e = 20...50mA, I p = 60...100mA
Particle Physics - L11 - M.Klein 25/04/08
Tevatron
Fermilab
1985-2011
The Large Hadron Collider
LHC: 7000 * 7000 GeV2 pp [AA] from 2009 onwards
ATLAS
University of Liverpool engaged.
LEP e+e- 89-00
LHC pp 09-35
LHeC ep … 35+ ?
Particle Physics - L11 - M.Klein 10/03/11
LHC 2-in-1 Dipole
7TeV
• 8.33T
• 11850A
• 7MJ
Plans and projects for next energy frontier colliders
Latest Development:
FCC design study at
CERN 2014-2018
Ep = 50 TeV
Ee= 120 GeV

pp/ee/ep
e+e-: ILC, CLIC, CPEC; ep: LHeC …
M.Klein 31.3.2014 L11
LHC tunnel 2002
10 years from here to the Higgs boson …
M.Klein 31.3.2014 L11