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Koji TAKATA
KEK
koji.takata@kek.jp
http://research.kek.jp/people/takata/home.html
Accelerator Course, Sokendai
Second Term, JFY2012
Oct. 25, 2012
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Fundamental Concepts of Particle Accelerators
I : Dawn of Particle Accelerator Technology
Contents
§1 Dawn of Particle Accelerator Technology
§2 High-Energy Beam Dynamics: (1)
§3 High-Energy Beam Dynamics: (2)
§4 RF Acceleration
§5 Future of the High Energy Accelerators
§6 References
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
2 / 20
Dawn of Particle Accelerator Technology
Contents
1
discovery of artificial nuclear disintegration（1919 - 1932）
and birth of particle accelerators
2
various types of early accelerators
3
from DC acceleration to RF acceleration
4
problems in RF acceleration
5
Great Progress Just after World War II（1941 - 1945）
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
3 / 20
Discovery of artificial nuclear disintegration（1919 - 1932）and the birth of
particle accelerators (1)
Ernest Rutherford (Cavendish Lab, Cambridge, UK）discovered
nuclear disintegration by the alpha (α) rays (1917 - 1919).
• He confirmed that protons were produced in a nitrogen-gas filled
container in which a radioactive source emitting alpha rays was placed.
α + 147 N → p + 168 O
This discovery provoked strong demands to artificially generate high
energy beams to study in more detail the nuclear disintegration
phenomena.
Thus started the race for developing high energy accelerators, and
Rutherford himself was a great advocator.
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
4 / 20
Discovery of artificial nuclear disintegration（1919 - 1932）
and birth of particle accelerators (2)
The first disintegration of atomic nuclei with accelerator beams was
achieved at the Cavendish Laboratory in 1932 by John D. Cockcroft
and Ernest T. S. Walton, who used 800 kV proton beams accelerated
by a DC voltage-multiplier.
p + 73 Li → α + α
They revised the multiplier circuit first invented by H. Greinacher
(1919).
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
5 / 20
DC HV Accelerators
DC Generators：two major methods
Cockcroft & Walton’s 800 kV voltage-multiplier circuit with
capacitors and rectifier tubes.
Van de Graaff’s 1.5 MV belt-charged generator (1931).
Electrostatic accelerators are still in use for the mass spectroscopy,
because of their fine and stable tunability of the acceleration voltage.
• analysis of the ratio
14
C/12 C : an important tool for archaeology.
• the time after a creature stopped breathing is estimated in
14
C’s half
decay time 5, 730 years.
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
6 / 20
Cockcroft & Walton’s voltage-multiplier circuit
V(3+cos ωt)
V(1+cos ωt)
V cos ωt
V(5+cos ωt)
AC
0
Koji Takata (KEK)
2V
4V
Fund. Conc. Part. Acc. 1
6V
0
Acc. Course, Oct. 2012
7 / 20
Cockcroft around 1932
Ref.:
E. Segrè, From X-rays to Quarks, page 227,
(W. H. Freeman and Company, 1980).
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
8 / 20
Van de Graaff’s 1.5 MV Belt-charged Generator
Insulating Belt
High Voltage for Acceleration
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
9 / 20
HV Limits in Electrostatic Accelerators
DC acceleration is limited by high-voltage breakdown (BD).
• Typical BD voltages for a 1cm gap of parallel metal plates
Ambience
Typical BD Voltages
Air (1 atm)
SF6 gas (1 atm)
SF6 gas (7 atm)
Transformer oil
Ultra High Vacuum
≈
≈
≈
≈
≈
30 kV
80 kV
360 kV
150 kV
220 kV
• Wider gaps do not make drastic improvement in BD limits.
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
10 / 20
High Voltage Breakdown Demonstration for a Van de Graaff generator
Ref. :
“van der graaf generator” in “ http://en.wikipedia.org/wiki/”
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
11 / 20
Intermediate stage towards RF Acceleration：D. W. Kerst’s betatron (1940)
Electric field due to time variation of the magnetic flux Φ.
• The AC transformers work on this principle.
• Faraday’s law in Maxwell’s equation:
∇×E=−
∂B
.
∂t
• Integrate the tangential component of the electric field E
along a closed boundary C of an area S:
I
E · dl = −
C
∂
∂t
∫∫
B · n dxdy = −
S
∂
Φ,
∂t
where dl: line element of the curve C, and
n: unit normal-vector of the area dS = dxdy.
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
12 / 20
Kerst’s First Publication of the Betatron
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
13 / 20
First Linear Accelerator (Linac) by Wideröe
Proposal by Gustaf Ising (Sweden, 1925).
Trial study by Rolf Wideröe (Norway/Germany, 1928).
VRF ∼ 25 kV (1 MHz) per gap ×2 with a drift tube.
He convinced that the scheme can be repeated any number of times
to reach ever higher beam energies.
RF
Ion
So urce
Drift Tube
Beam
This is the prototype of the present-day drift tube linacs (DTL).
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
14 / 20
Ernest Lawrence’s Cyclotron (1931)
Trial study of the multiple RF acceleration of charged particles
moving on a circular orbit in a magnetic field.
• The first circular accelerator.
• Multiple acceleration at the cyclotron frequency
ωc = eB⊥ /m.
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
15 / 20
Early Cyclotrons
Lawrence with the first cyclotron
Ref. :
Segrè, E. From X-rays to Quarks,
page 229 (W. H. Freeman and
Company, 1980)
A cyclotron at RIKEN, Japan, accelerated
protons to 9 MeV and
deuterons to 14 MeV (1939).
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
16 / 20
Circular Motion of Particles in the Cyclotron
RF Generator
dee
dee
rn
rn+1(> rn)
Circular orbit of particles with charge e
and mass m in magnetic field B
（assuming β = v/c ≪ 1).
• orbit radius: r =
mvc
|e|B .
• revolution frequency: fc =
|e|B
2πm .
• f depends only on B and neither on
Magnetic Field
Electric Field
beam
dee
Koji Takata (KEK)
r nor on v.
• cyclotron frequency: ωc = 2πfc .
dee
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
17 / 20
Demonstration of the Circular Orbit of Electron Beams in a Magnetic Field
Ref. :
“http://en.wikipedia.org/wiki/Cyclotron”
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
18 / 20
Problems in RF Acceleration
1
Linacs：
• poor RF power sources: electron tube technology was not yet matured.
2
Cyclotrons：
• relativistic increase of particle mass:
→ decrease of ωc ,
→ asynchronism with RF.
3
Betatrons：
• It was very difficult to inject and trap electron beams correctly on the
circular orbit in the donut.
• Indispensable was the analysis of the transverse oscillations of particles.
• It led to the present-day theory of the betatron oscillations.
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
19 / 20
Great Progress Just after World War II
1
Discovery of the phase stability principle in RF acceleration.
• Vladimir Veksler (1944) and Edwin M. McMillan (1945).
• Cyclotrons.
→ synchrocyclotron, and eventually
→ synchrotron.
2
Strong focusing: new idea for the transverse beam focusing.
• Christofilos (1950) and Courant-Livingston-Snyder (1952).
3
Radars in practical use quickened the development of high power
microwave tubes.
• magnetrons and klystrons.
Koji Takata (KEK)
Fund. Conc. Part. Acc. 1
Acc. Course, Oct. 2012
20 / 20