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Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Electron dynamicswith
Synchrotron Radiation
Lenny Rivkin
Paul Scherrer Institute (PSI)
and
Swiss Federal Institute of Technology Lausanne (EPFL)
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Click to edit Master title styleUseful books and references
H. Wiedemann, Synchrotron RadiationSpringer-Verlag Berlin Heidelberg 2003
H. Wiedemann, Particle Accelerator Physics I and IISpringer Study Edition, 2003
A.Hofmann, The Physics of Synchrotron RadiationCambridge University Press 2004
A. W. Chao, M. Tigner, Handbook of Accelerator Physics and Engineering, World Scientific 1999
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Click to edit Master title style
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 2003CERN Yellow Report 2005-012
Previous CAS Schools Proceedings
CERN Accelerator School Proceedings
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Curved orbit of electrons in magnet field
Accelerated charge Electromagnetic radiation
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Electromagnetic waves
Crab Nebula
6000 light years away
First light observed
1054 AD
First light observed
1947
GE Synchrotron
New York State
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
60‘000 SR users world-wide
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Why do they radiate?
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Synchrotron Radiation isnot as simple as it seems
… I will try to showthat it is much simpler
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Charge at restCoulomb field, no radiation
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Uniformly moving charge does not radiate
v = constant
But! Cerenkov!
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Click to edit Master title styleFree isolated electron cannot emit a photon
Easy proof using 4-vectors and relativity
momentum conservation if a photon is emitted
square both sides
in the rest frame of the electron
this means that the photon energy must be zero.
𝑷𝑖 = 𝑷𝑓 + 𝑷𝛾
𝑷𝛾 = (𝐸𝛾 , 𝑝𝛾)
𝑚2 = 𝑚2 + 2𝑷𝑓 ∙ 𝑷𝛾+ 0 ⇒ 𝑷𝑓 ∙ 𝑷𝛾 = 0
𝑷𝑓 = (𝑚, 0)
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
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Synchrotron RadiationBasic Properties
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Click to edit Master title styleTime compression
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
n
1 – =
1 – 2
1 + 1
22
obs = 1
22
emit
emitobs TT )1( βn
emitobs )cos1(
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
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
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
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
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
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
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
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
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Spectrum of synchrotron radiation
• Synchrotron light comes in a series of flashesevery T0 (revolution period)
• the spectrum consists ofharmonics 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
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Wavelength continuously tunable !
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 = 665E
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
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
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 Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Synchrotron light polarization
An electron in a storage ring
TOP VIEW
Polarization:
Linear in the plane of the ring
the electric field vector
SIDE VIEW
TILTED VIEW
elliptical out of the plane
E
E
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Synchrotron light basedelectron beam diagnostics
Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest
Seeing the electron beam (SLS)
visible light, vertically polarisedX rays
mx 55~
Seeing the electron beam (SLS)
Making an image of the electron beam using the verticallypolarised synchrotron light