Fundamental Concepts of Particle Accelerators
Koji TAKATA
KEK
koji.takata@kek.jp
http://research.kek.jp/people/takata/home.html
Accelerator Course, Sokendai,
Second Term, JFY2010
Oct. 28, 2010
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Contents
I
I
I
I
The Dawn of Particle Accelerator Technology
I DC high voltage generators
I Use of magnetic induction: betatron
I Drift tube linac and cyclotron
I Great progress just after world war II
Basic Concepts
I Principle of RF phase stability
I Strong focusing
I Synchrotron radiation (SR)
I Collider
I Technical issues
Accelerators in Future
I ERL (Energy Recovery Linac) : SR source of new type
I LC : Linear Collider
I µ-µ Collider and/or µ-Factory
I Laser-plasma acceleration
Livingston Chart
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
The Dawn of Particle Accelerator Technology
I
Artificial disintegration of atomic nuclei
I
First Accelerators
I
from DC Acceleration to RF Acceleration
I
Problems in RF Acceleration
I
Rapid Development of Electronics around
World War II (1941 - 1945) or after
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
First artificial disintegration of atomic nuclei (1)
I
Ernest Rutherford’s discovery of nuclear disintegration
(1917 - 1919)
I
He confirmed that protons were produced in a nitrogen-gas
filled container in which a radioactive source emitting alpha
particles was placed.
α + 147 N → p + 168 O
I
This provoked strong demand for artificially generate high
energy beams to study the nuclear disintegration phenomena
in more detail.
I
Thus started the race for developing high energy accelerators,
and Rutherford himself was a great advocator.
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
First artificial disintegration of atomic nuclei (2)
I
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 from a DC voltage-multiplier.
p + 73 Li → α + α
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
DC HV Accelerators
I
I
DC Generators：two major methods
I
Cockcroft & Walton’s 800 kV voltage-multiplier circuit with
capacitors and rectifier tubes
I
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.
I
analysis of the ratio
archaeology
14
C/12 C : an important tool for
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Cockcroft & Walton’s voltage-multiplier circuit
V(3+cos ωt)
V(1+cos ωt)
V cos ωt
V(5+cos ωt)
AC
0
2V
4V
6V
0
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Cockcroft around 1932
See the picture in From X-rays to Quarks, page 227 by Segrè, E.
(W. H. Freeman and Company, 1980) .
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Glass Tube with Beam Acceleration Gaps
Visit the home page :
http://www.daviddarling.info/encyclopedia/C/Cockcroft.html
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
750 keV Cockcroft-Walton Accelerator Used at KEK
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Van de Graaff’s 1.5 MV Belt-charged Generator
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Limitations in Electrostatic Accelerators
I
DC acceleration is limited by high-voltage breakdown (BD).
I
typical BD voltages for a 1cm gap of parallel metal plates
Ambience
air (1 atm)
SF6 (1 atm)
SF6 (7 atm)
transformer oil
UHV
I
Typical BD Voltages
≈ 30 kV
≈ 80 kV
≈ 360 kV
≈ 150 kV
≈ 220 kV
no drastic increase in BD limits for much larger plate gaps.
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
High Voltage Breakdown of a Van de Graaff generator
A demonstration of BD to housing walls.
Search for the key word ”van der graaf generator” at
http://en.wikipedia.org/wiki/
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Intermediate stage towards RF Acceleration
Use of Faraday’s law of induction
I
Irrotational electric field due to magnetic flux change,
a prelude to RF acceleration [Donald W. Kerst’s betatron
(1940)]:
∇×E=−
∂B
,
∂t
then
I
Es ds = −
C
∂
∂t
∫∫
B · n dxdy = −
S
∂
Φ
∂t
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Kerst’s Betatron
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Start of Real RF Accelerators
Linear and/or Circular
I Linear accelerator (linac) :
I
I
I
Gustaf Ising’s proposal (1925)
Rolf Wideröe made a prototype of the Ising linac (1928)
Multiple RF acceleration in a magnetic field
I
Ernest Lawrence’s cyclotron (1931)：
I
the first circular accelerator
repeated acceleration at the cyclotron frequency ：
ωc = eB⊥ /m
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
The first linac by Wideröe
I
I
25 kV per gap ×2 with the drift tube
he convinced the scheme can be repeated indefinitely many
times to reach higher beam energies
RF
Ion
So urce
Beam
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
First Cyclotrons
See the picture in From X-rays to
Quarks, page 229 by Segrè, E.
(W. H. Freeman and Company,
1980) .
A Riken cyclotron accelerated
protons to 9 MeV and deuterons to
14 MeV (1939)
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Circular Orbit of Charged Particles in Magnetic Field
Search for the key word ”Cyclotron” in
http://en.wikipedia.org/wiki/
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Principle of Cyclotron Operation
RF Generator
dee
dee
rn
Magnetic Field
rn+1(> rn)
Electric Field
beam
dee
dee
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Problems in RF Acceleration
I
Linacs：
I
I
Cyclotrons：
I
I
poor RF sources; electron tube technology was yet in its
infancy.
relativistic increase of particle mass
→ decrease of ωc
→ asynchronism with RF
Betatrons：
I
I
intensity of trapped beam depends critically on the injected
beam’s positions and angles.
analysis of transverse oscillations of particles led to the theory
of betatron oscillations of today.
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
DC high voltage generators
Use of magnetic induction: betatron
Drift tube linac and cyclotron
Great progress just after world war II
Advances during World War II (1941 - 1945)
I
High power microwave tubes for the radars were put to
practical use
I
I
magnetrons and klystrons
Discovery of the phase stability principle in RF acceleration
I
Vladimir Veksler (1944) and Edwin M. McMillan (1945)
I
cyclotron → synchrocyclotron → synchrotron
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
The Principle of Phase Stability
I
Particles of different energies have
I
I
I
I
I
I
differences in velocity and in orbit length;
then, particles may be asynchronous with the RF frequency.
The RF field, however, may have a restoring force at a certain
phase, around which asynchronous particles be captured, that
is to say bunched.
This enables a stable, continuous acceleration of the whole
particles in a bunch to high energies.
Circular accelerators based on this principle are called
“synchrotron.”
This principle is also applicable to linacs, particularly in low
energy range, to bunch continuous beams emitted from a
source and to lead bunches to downstream accelerator
sections.
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Synchrotron Oscillation (1)
I
Assume a sinusoidal RF electric field in an RF cavity gap:
V = V0 sin ωt
.
I
Assume a synchronous particle pass the gap center at
ωt = 0, 2π, 4π, . . .
and its acceleration voltage be Va (< V0 ).
I
Then in one RF period, there are there are two ϕ’s which
satisfy
Va = V0 sin ϕ.
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Sinusoidal RF Wave
V0
Va
0
π/2
π
φ
-V0
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Synchrotron Oscillation (2)
I
Only one of the two ϕ’s can capture particles, which make
oscillations around the phase.
I
These oscillations are called synchrotron oscillation and the
phase is the synchronous phase ϕs .
I
Which one is the ϕs depends on that the revolution time is
longer or shorter for a energy deviation ∆E(> 0) from the
synchronous energy.
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Synchrotron Oscillation in an RF Bucket (1)
For the case of ϕs = 30◦
abscissa : ∆ϕ = ϕbeam − ϕs , ordinate : ∆E = Ebeam − Es
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Synchrotron Oscillation in an RF Bucket (2)
For the case of ϕs = 0◦
abscissa : ∆ϕ = ϕbeam − ϕs , ordinate : ∆E = Ebeam − Es
2
1
3
2
-3
-2
-1
1
2
3
1
-1
-3
-2
-1
1
2
3
-2
-1
-2
-3
time sequence of motion of
particles initially on the abscissa
(particles of a larger ∆ϕ move
slower or have a smaller ωs )
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Advances in Beam Focusing Technique
I
Magnetic, not electric, focusing for high energy particles
I
Weak focusing in early cyclotrons and betatrons
I
Strong focusing
I
Nicholas C. Christofilos (1950)
I
Ernest D. Courant, M. Stanley Livingston,
and Hartland S. Snyder (1952)
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Equation of Motion
I
In electric field E and magnetic field B, the equation motion
of a particle is
dp
= e (E + v × B)
dt
where
p = mv = γm0 v
with
m0 : rest mass
√
γ = 1/ 1 − β 2 : Lorentz factor
β = |v| /c = v/c
Fundamental Concepts of Particle Accelerators
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Coordinate System
I
I
In the analysis of beam focusing, it is usually important to
describe the equation of motion of particles only for small
deviations x and y along the path s of the reference orbit of a
synchronous particle
Thus, a Frenet-Serret frame with respect to the reference
orbit is preferred:
I
I
I
unit vector tangent to the curve,
unit vector in the direction of curvature,
and the cross product of the them.
y
particle
ρ
x
s
tangent at s
reference orbit
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Typical Weak-Focusing Magnetic Field
Cylindrically symmetric magnet poles and magnetic fields of the
early cyclotrons
z
0
r
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Betatron Oscillations : Weak Focusing
I
First order approximation of the field pattern of the previous
page
(
)
(
)
x
y
By = B0 1 − n + . . .
and Bx = B0 −n + . . . ,
ρ
ρ
where n =
I
dBy dρ
By / ρ
: the n value
Equation of motion
d2 x 1 − n
+
x=0
ds2
ρ2
I
I
and
d2 y
n
+ 2y = 0
2
ds
ρ
Focusing both horizontally and vertically → 0 < n < 1
Betatron wavelength
√
λβ,x = 2πρ/ 1 − n
√
λβ,y = 2πρ/ n
Fundamental Concepts of Particle Accelerators
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Quadrupole Magnetic Fields for Stronger Focusing
I
I
I
No limitations for the n value.
Focusing in one direction, defocusing in the other.
Later we will see the focusing is superior to the defocusing
y
2
1
-2
-1
1
2
x
-1
-2
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Q magnets and B magnets of JPARC RCS synchrotron (1)
http://j-parc.jp/Acc/en/index.html
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Q magnets and B magnets of JPARC RCS synchrotron (2)
http://j-parc.jp/Acc/en/index.html
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Q magnets and B magnets of JPARC Main Ring (1)
http://j-parc.jp/Acc/en/index.html
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Q magnets and B magnets of JPARC Main Ring (2)
Sextupole magnets are sometimes used.
http://j-parc.jp/Acc/en/index.html
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Optical Lens Equivalent of a Quadrupole Magnet
convex lens in one direction and concave lens in the perpendicular
direction
beam
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Strong Focusing with a Standard FODO Array
F : focusing Q, D : defocusing Q, O : drift section vspace3mm
I
In the following figure, convex lenses are for horizontal
focusing and concave lenses for vertical focusing.
I
The red curves are beam envelopes for a unit emittance.
1
0.5
0.5
1
1.5
2
2.5
3
-0.5
-1
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Emittance Ellipse for a periodic sequence of Q magnets
x! /k
ag replacements
#0
#1
#2
#3
0
-1
x/x0
1
0.5
0.5
#4
#5
#6
x′2
x2 + 2 = x20
k
√
where
1
k=
L
L
f
(
L
1−
4f
)
Concepts focusing
of Particle Accelerators
f : focal length, L : length betweenFundamental
neighboring
Q’s
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Betatron Oscillations : Strong Focusing (1)
I
Use quadrupole magnets with |n| ≫ 1, but with changing the
sign of n alternatively
I
Equation of motion
d2 x
+ Kx (s) x = 0
ds2
d2 y
+ Ky (s) y = 0
ds2
I
Focusing/Defocusing forces Kx (s) and Ky (s) are periodic
functions for the ring circumference L.
I
They are Mathieu-Hill type functions
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Betatron Oscillations : Strong Focusing (2)
I
General solution：x = Ax
for y)
I
I
I
I
√
β(s) cos (ψ(s) − ψ0 ) (similar too
Ax and Ay are constants proper to each particles and are
independent of the position s on the orbit
4 + β ′2 2
A2x =
x − β ′ βxx′ + βx′2
4β
measure a particular particle’s (x, x′ ) or (y, y ′ ) for many turns
at a position s, the points trace an ellipse on the
corresponding phase space.
ellipse’s direction and eccentricity are functions of s,
but area= πA2x (y) is conserved
the largest area is, roughly speaking, called the emittance of
the bunch
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Betatron Oscillations : Strong Focusing (3)
I
Beta function βx (y) (s) is defined as the betatron amplitude
for Ax (y) = 1 :
2ββ ′′ − β ′2 + 4β 2 K (s) = 4.
I
Phase ψ of betatron oscillation :
∫ s
ψ=
ds/β.
I
Wavelength λβ of the betatron oscillation : the length
corresponding the phase advance ∆ψ = 2π.
I
Betatron tune νβ ≡ L/λβ .
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Colliders (1)
I
In order to observe the high energy particle reactions : targets
in laboratory frame were solely used (fixed target experiment).
I
The reaction, however, depends not on the laboratory energy
of the projectile from an accelerator, but on the center of
mass energy of the projectile and target.
I
Touschek’ idea to use colliding beams (1960)
I
The first collider：AdA (Frascati, 1961)
200 MeV e− ⇒⇐ 200 MeV e+
I
The collider has become a paradigm of high energy
accelerators of today.
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Colliders (2) : ECM
I
Consider collision of particles of the same rest mass m0 .
I
In a fixed target case with the projectile accelerated to γm0 c2
I
I
the total energy: ET /m0 c2 = (γ + 1)
I
the total momentum: pT /m0 c = βγ =
I
since E 2 − c2 p2 is a Lorentz invariant,
√
√
ECM /m0 c2 = 2γ + 2 ≈ 2γ
√
γ2 − 1
In a collision of two particles of the same energy γm0 c2
ECM /m0 c2 = ET /m0 c2 = 2γ
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Colliders (3) : Luminosity
I
For reaction cross section σ and beam cross section at the
collision point S, the probability of reaction for a pair of
particles is,
σ
S
I
Hence the probability for N+ and N− particles at a rate of
f times per second
σ
f × N + × N− ×
S
I
Coefficient of σ is the luminosity L
N+ × N −
L=f×
S
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Synchrotron Radiation (1)
I
The synchrotro radiation, SR, is an electric dipole radiation
from a charged particle in acceleration v̇
I
Radiation power in the rest frame is given by Larmour’s
formula
( )
( )2
2re me dv 2
2re
dp
P =
=
3c
dt
3me c dt
where re ≡ e2 /(4πε0 me c2 ) = 2.82 × 10−15 m is the electron’s
classical radius.
Fundamental Concepts of Particle Accelerators
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
PSfrag replacements
Electric Dipole Radiation : Electric Field Pattern
#0
#1
#2
#3
Radiation pattern (cylindrically
symmetric) of
#4
#5
an electric dipole at rest#6
x/xz/λ
0
xe /x0
x! /k 4
η (m)
s=0
s = 0 + nL
2
s = L2
s = L4
s = 0+ + nL
r/λ
s = 0+ 0
s = 0+
s = L + nL = 0 + (n + 1)L
−
−
s/L-2
s (m)
f = 1.6L
ρ = 50 m
-4
L=2m
0
1
2
3
4
5
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Synchrotron Radiation (2)
I
Since P is the ratio of radiated energy to elapsed time, both
of which transform in the same manner under Lorentz
transformations, P must be an invariant.
I
Then ( )2 in the right hand side of the equation should have
the following invariant form
(dp/ds)2 − (dE/ds)2 /c2
where ds is the differential of proper time
√
ds = dt2 − (dx2 + dy 2 + dz 2 ) /c2 = dt/γ.
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Synchrotron Radiation (3)
I
Hence in laboratory frame the radiated power is
{[
]
[
] }
d (γc) 2
2re me 2
d (γv) 2
γ
−
P =
3c
dt
dt
I
The radiated energy per turn ∆E for a ring with radius ρ
∆E
4π re 3 4
=
β γ
2
me c
3 ρ
I
A practical formula for ∆E(keV), E(GeV) and ρ(m)
∆E(keV) ≈ 88.5 [E(GeV)]4 /ρ(m).
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Synchrotron Radiation (4)
I
I
I
Pattern of electric dipole radiation in electron’s rest frame
（x′ , y ′ , z ′ , ct′ ）
dP/dΩ ∝ sin2 θ
where Ω being the solid angle and θ the angle from z ′ axis.
Transformation to laboratory frame
x′ = x, y ′ = y, z ′ = γ (z − vt) ,
ct′ = γ (ct − vz/c) .
Angles of axes x′ and y ′ with respect to z axis are ∼ 1/γ.
I
I
I
I
forward radiation power is within a cone of
a full angle of ∼ 2/γ.
electron is observable for an arc length of ∼ 2ρ/γ.
doppler effect shortens the wavelength by (1 − v/c) ∼ 1/2γ 2 .
Critical wavelength (Schwinger-Jackson’s definition)
λc ≡ 4πρ/3γ 3
Fundamental Concepts of Particle Accelerators
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Accelerating Cavity (1)
There are many types of accelerating cavity, which, however,
basically are variations of a cylindrical cavity (or pillbox cavity),
operating on the fundamental TM010 mode.
Hθ
Ez
b
r=
2b
0
arbitrary scale
I
1
Ez
0.8
Hθ
0.6
0.4
0.2
0
0.5
1
1.5
2
χ01r/b
d
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Accelerating Cavity (2)
Single-Cell Accelerating Cavity for Photon Factory Storage Ring
(fRF = 500 MHz, Vpeak = 0.7 MV )
r
R10mm
R234.69mm
Ez (r=0)
R91.375mm
R50mm
z
220mm
R130mm
300mm
Fundamental Concepts of Particle Accelerators
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Accelerating Cavity (3)
Global behavior of a resonant cavity is well described
by an equivalent circuit comprising three parameters
L, C, R.
L
R
C
Fundamental Concepts of Particle Accelerators
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Accelerating Cavity (4)
I
I
I
I
first of all, the resonant frequency and the Q value are derived
from the following two equations :
√
ω0 = 1/ LC and Q = ω0 RC.
one more independent relation is required to determine the
three parameters L, C, andR.
for this sake, we choose the peak acceleration voltage along
the beam orbit
this choice is reasonable, because it satisfies the energy
conservation of the（EM fields + beam）system.
∫∫∫
∫∫
J · EdV +
(E × H) · ndS = 0.
V
S
(J : beam current distribution, E × H : Poynting vector,
V : cavity volume, S : cavity surface)
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
High Gradient Electric Fields and Breakdown
I
Kilpatrick’s empirical rule
I
Fowler-Nordheim’s theory for field emission
I
Surface damage on an X-band copper structure
I
Weak discharge: multipacting
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Kilpatrick Criterion
W. D. Kilpatrick, Rev. Sci. Instr. 28 (1957) 824
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Fowler-Nordheim’s Law
R. H. Fowler and L. Nordheim, Proc. Roy. Soc. A 119 (1928) 173
J. W. Wang and G. A. Loew, SLAC-PUB-7684 (1997)
I
DC field emission current density jF [A/m2 ] :
(
)
−0.5
1.54 × 10−6 × 104.52ϕ E 2
6.53 × 109 ϕ1.5
exp −
jF =
ϕ
E
I
I
microscopic surface gradient E [V/m]
metal work function ϕ [eV]
I
Averaged over one RF cycle, jF is modified as:
(
)
−0.5
6.53 × 109 ϕ1.5
5.7 × 10−12 × 104.52ϕ E 2.5
exp −
jF =
ϕ1.75
E
I
Field enhancement factor β : E = βEmacro
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Surface Damage on the Iris of an X-band Linac Structure
R. E. Kirby, SLAC-PEL, 2000
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Multipacting : a weak discharge phenomenon
A. J. Hatch and H. B. Williams, Phys. Rev. 112 (1958) 581
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Superconductor and RF
I
Niobium is mostly used, which is a Type II superconductor
I
I
I
I
I
critical temperature Tc = 9.2K
critical field Hc = 2 × 103 Oe
in meissner state for H ≤ Hc1 = 1.7 × 103 Oe
in normal state for H ≥ Hc2 = 2.3 × 103 Oe
Maxwell equations + London equations
I
London’s penetration depth λL
• about 50 nm for niobium
I
coherent length ξ0
• about 40 nm for niobium
I
wall losses do still exist, although very small, which are caused
by normal electrons
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
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Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Equations for Superconducting State
I
Maxwell’s equations:
∇×E+
I
∂B
=0
∂t
and ∇ × H −
∂D
=J
∂t
London equations:
Js = −j
ns e2
ns e2
E and ∇ × Js = −
µ0 H
ωme
me
I
Field equations:
I
(
)
2
∇2 (J, E, H) = λ−2
L + jωσµ0 − ω ε0 µ0 (J, E, H)
√
London’s penetration depth: λL = me /ns e2 µ0
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
Klystron (1)
I
Also an accelerator with decelerating electric fields
I
Perveance µp
I
Child-Langumuir law for space-charge limited flow
• µp ∝ I/V 3/2
• cf. M. Reiser:
Theory and Design of Charged Particle Beams,
John Wiley & Sons, 1994.
I
Efficiency vs. perveance
I
cf. R. B. Palmer and R. Miller: SLAC-PUB-4706, September
1988.
Fundamental Concepts of Particle Accelerators
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Klystron (2)
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KHDWHU
FDWKRGH
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FHUDPLF
ZLQGRZ
5)LQSXW
FHUDPLF
ZLQGRZ
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5)RXWSXW
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Principle of RF phase stability
Strong focusing
collider
synchrotron radiation (SR)
Technical issues
500 MHz-1 MW CW Klystron for KEKB
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Future Accelerators
I
ERL: Energy Recovery Linac
I
LC : Linear Collider
I
µ-µ Collider and/or µ-Factory
I
Laser-plasma acceleration
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
KEK-PF-ERL : A Future Plan
I
An SR source with a superconducting linac energy-recovered
by returned electron beams
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Linear Collider: schematic layout
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
µ-µ Collider
/LQDF
/L%H$EVRUEHUV
6\QFKURWURQ
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/LQDFV
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M
7DUJHW
6ROHQRLG
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/LQDF
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Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Laser Plasma Acceleration (1)
cf. C. Joshi and T. Katsouleas’s article in Physics Today, June
2003, p.47.
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Laser Plasma Acceleration (2)
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
Livingston Chart
I
Originally given by M. S. Livingston &
J. P. Blewett: ”Particle Accelerators,
p.6”, MacGraw Hill, 1962
Collider
(Equivalent Energy)
I
Proton Synchrotron
I
Energies for the colliders are equivalent
values for the fixed target system
Maximum beam energy ever achieved
17
10
16
10
15
10
1PeV
Ac ce l er at or E nerg y ( eV)
1014
13
10
12
10
1TeV
11
10
Electron Linac
I
10
10
10
9
10
8
10
7
10
6
Electron Synchrotron
Synchro-cyclotron
1GeV
I
Proton Linac
1MeV
1930
Electrostatic Accelerator
Betatron
Cyclotron
DC Generator
1940
1950
1960
1970
1980
1990
2000
2010
I
Electron Synchrotron : 2 × 100 GeV
(2000, CERN LEP)
Proton Synchrotron : 2 × 7 TeV
(2010, CERN LHC)
http://lhc.web.cern.ch/lhc/
Electron-positron linear collider
2 × 500 GeV? (2025 or later?)
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
References (1)
I
Segrè, E. : From X-rays to Quarks (W. H. Freeman and
Company, 1980).
I
I
Chao, A. W. and Tigner, M. (ed.) : Handbook of Accelerator
Physics and Engineering (World Scientific, 1999).
I
I
Compact encyclopedia of accelerator science and technology
Wiedemann, H. : Particle Accelerator Physics I, II (Springer,
1999).
I
I
Historical introduction to the evolution of high energy physics
and accelerator science
Text book on accelerator physics
Courant, E. D. and Snyder, H. S.: Annals of Physics, 3
(1958) p.1.
I
A classical paper on the theory of the strong focusing
Fundamental Concepts of Particle Accelerators
The Dawn of Particle Accelerator Technology
Basic Concepts
Accelerators in Future
Livingston Chart
References (2)
I
Schwinger, J. : Physical Review, 75 (1949) p.1912.
I
I
Gilmour, A. S. : Microwave Tubes (Artech House, 1986).
I
I
A classical paper on the theory of the synchrotron radiation
Text book on the electron tube technology
Padamsee, H., Knobloch, J. and Hays, T. :
RF Superconductivity for Accelerators (John Wiley & Sons,
1998).
I
Text book on RF superconductivity and its application to
energy accelerators
Fundamental Concepts of Particle Accelerators