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Lenny Rivkin
Ecole Polythechnique Federale de Lausanne (EPFL)
and Paul Scherrer Institute (PSI), Switzerland
SYNCHROTRON RADIATION
CERN Accelerator School: Introduction to Accelerator Physics
November 5, 2012, Granada, Spain
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Useful books and references
A. Hofmann, The Physics of Synchrotron Radiation Cambridge University Press 2004
H. Wiedemann, Synchrotron Radiation Springer-Verlag Berlin Heidelberg 2003
H. Wiedemann, Particle Accelerator Physics I and II Springer Study Edition, 2003
A. W. Chao, M. Tigner, Handbook of Accelerator Physics and Engineering, World Scientific 1999
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Synchrotron Radiation and Free Electron Lasers
Grenoble, France, 22 - 27 April 1996 (A. Hofmann’s lectures on synchrotron radiation) CERN Yellow Report 98-04
Brunnen, Switzerland, 2 – 9 July 2003 CERN Yellow Report 2005-012
http://cas.web.cern.ch/cas/Proceedings.html
CERN Accelerator School Proceedings
GENERATION OF
SYNCHROTRON RADIATION
Swiss Light Source, Paul Scherrer Institute, Switzerland
Curved orbit of electrons in magnet field
Accelerated charge Electromagnetic radiation
Crab Nebula
6000 light years away
First light observed
1054 AD
First light observed
1947
GE Synchrotron
New York State
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Synchrotron radiation: some dates
1873 Maxwell’s equations
1887 Hertz: electromagnetic waves
1898 Liénard: retarded potentials
1900 Wiechert: retarded potentials
1908 Schott: Adams Prize Essay
... waiting for accelerators …
1940: 2.3 MeV betatron,Kerst, Serber
Maxwell equations (poetry)
War es ein Gott, der diese Zeichen schrieb
Die mit geheimnisvoll verborg’nem Trieb
Die Kräfte der Natur um mich enthüllen
Und mir das Herz mit stiller Freude füllen. Ludwig Boltzman
Was it a God whose inspiration
Led him to write these fine equations
Nature’s fields to me he shows
And so my heart with pleasure glows. translated by John P. Blewett
THEORETICAL UNDERSTANDING
1873 Maxwell’s equations
made evident that changing charge densities would
result in electric fields that would radiate outward
1887 Heinrich Hertz demonstrated such waves:
….. this is of no use whatsoever !
1898 Liénard:
ELECTRIC AND
MAGNETIC FIELDS
PRODUCED BY A POINT
CHARGE MOVING ON AN
ARBITRARY PATH
(by means of retarded potentials … proposed first by Ludwig Lorenz in 1867)
1912 Schott:
COMPLETE THEORY OF
SYNCHROTRON RADIATION
IN ALL THE GORY DETAILS
(327 pages long)
… to be forgotten for 30 years
(on the usefulness of prizes)
Donald Kerst: first betatron (1940)
"Ausserordentlichhochgeschwindigkeitelektronen
entwickelndenschwerarbeitsbeigollitron"
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Synchrotron radiation: some dates
1946 Blewett observes energy loss
due to synchrotron radiation
100 MeV betatron
1947 First visual observation of SR
70 MeV synchrotron, GE Lab
1949 Schwinger PhysRev paper
…
1976 Madey: first demonstration of
Free Electron laser
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
A larger view
Crab Nebula
6000 light years away
First light observed
1054 AD
First light observed
1947
GE Synchrotron
New York State
Storage ring based
synchrotron light source
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Charge at rest: Coulomb field, no radiation
Uniformly moving charge
does not radiate
Accelerated charge
Why do they radiate?
v = const.
But! Cerenkov!
Bremsstrahlung
or
“braking” radiation
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
t =
1
40
q
r 1 – n ret
A t =
q
40c
2
v
r 1 – n ret
A +
1
c2
t= 0
B = A
E = – –A
t
and the electromagnetic fields:
(Lorentz gauge)
Liénard-Wiechert potentials
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
E t =q
40
n –
1 – n 3 2
1r 2
ret
+
q
40c
n n –
1 – n 3 2
1r
ret
B t =
1
cn E
Fields of a moving charge
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Transverse acceleration
v a
Radiation field quickly separates itself from the Coulomb field
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
v
a
Radiation field cannot separate itself from the Coulomb field
Longitudinal acceleration
Moving Source of Waves
Electron with velocity emits a wave with period Temit
while the observer sees a different period Tobs because
the electron was moving towards the observer
The wavelength is shortened by the same factor
in ultra-relativistic case, looking along a tangent to the
trajectory
since
Time compression
obs = 1
22
emit
emitobs TT )1( βn
n
emitobs )cos1(
1 – =
1 – 2
1 + 1
22
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Radiation is emitted into a narrow cone
v << c vc
v ~ c
e = 1
e
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Sound waves (non-relativistic)
v
e
v
=
vsvs|| + v =
vsvs||
11 + v
vs
e 1
1 + vvs
Angular collimation
Doppler effect (moving source of sound)
s
emittedheardv
1v
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Synchrotron radiation power
P E2B2
C = 4
3re
mec2 3
= 8.858 10– 5 mGeV 3
Power emitted is proportional to:
2
4
2
EcCP
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
2
4
2
EcCP
The power is all too real!
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Synchrotron radiation power
P E2B2
C = 4
3re
mec2 3
= 8.858 10– 5 mGeV 3
U0 = C
E 4
U0 = 43hc
4
= 1
137
hc = 197 Mev fm
Power emitted is proportional to:
Energy loss per turn:
2
4
2
EcCP
2
42
3
2
cP
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Typical frequency of synchrotron light
Due to extreme collimation of light observer sees only a small portion of electron trajectory (a few mm)
l ~
2
t ~ l
c– l
c = lc
1 –
/1
Pulse length: difference in times it takes an electron and a photon to cover this distance
t ~
c
12 2
~ 1
t~ 30
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Spectrum of synchrotron radiation
• Synchrotron light comes in a series of flashes every T0 (revolution period)
• the spectrum consists of harmonics of
• flashes are extremely short: harmonics reach up to very high frequencies
• At high frequencies the individual harmonics overlap
time
T0
0
0
1
T
0
3 typ
continuous spectrum !
! Hz10~
4000 ~
MHz1~
16
typ
0
Wavelength continuously tunable !
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
0.001
0.01
0.1
1
0.001 0.01 0.1 1 10x = c
50%
~ 2.1x
13
13
~ 1.3 xe
– x
G1 x = x K5 35 3
x dxx
ceV = 665 E
2GeV B T
dP
d=
Ptot
c
S
c
c=
3
2
c3
Ptot =2
3hc
2
4
2
S x =
9 3
8x K5
35
3x dx
x
S x dx
0
= 1
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
A useful approximation
spectral Flux G1
0.001
0.01
0.1
1
0.001 0.01 0.1 1 10x
G1
Spectral flux from a dipole magnet with field B
Fluxphotons
s mrad 0.1%BW= 2.4610
13E[GeV] I[A]G1 x
Approximation: G1 ≈ A x1/3 g(x)
SN
Lx
xxg
1
])(1[()(
A = 2.11 , N = 0.848
xL = 28.17 , S = 0.0513
Werner Joho, PSI
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
109
1010
1011
1012
1013
Flu
x [p
hoto
ns/s
/mra
d/0.
1%B
W]
101
102
103
104
105
106
107
Photon energy [eV]
20 GeV
50 GeV
100 GeVLEP Dipole FluxI = 1 mA
Synchrotron radiation flux for different electron energies
Angular divergence of radiation
The rms opening angle R’
• at the critical frequency:
• well below
• well above
= c R 0.54
« c
R 1
c
13
13
0.4
13
13
independent of !
» c
R 0.6
c
12
12
Electron in a storage ring:
TOP VIEW
TILTED VIEW
SIDE VIEW
Polarisation
Synchrotron radiation observed in the plane of the particle orbit is horizontally polarized, i.e. the electric field vector is horizontal
Observed out of the horizontal plane, the radiation is elliptically polarized
E
E
Polarisation: spectral distribution
xSxSP
xSP
d
dP
c
tot
c
tot
x
SS8
7
SS8
1
3:1
Angular divergence of radiation
•at the critical frequency
•well below
•well above
c 2.0
c 2
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Seeing the electron beam (SLS)
visible light, vertically polarised X rays
mx 55~
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
Seeing the electron beam (SLS)
Making an image of the electron beam using the vertically
polarised synchrotron light
Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012
High resolution measurement
Wavelength used: 364 nm
For point-like source the
intensity on axis is zero
Peak-to-valley intensity ratio
is determined
by the beam height
Present resolution: 3.5 m
END
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