Production of
synchrotron radiation
Sverker Werin
MAX IV laboratory,
Lund university
Light to investigate the world
Wavelength
1 nm
Sverker Werin – MAX IV laboratory, Lund University
1 um
1 mm
1m
1 km
-2-
First discovery of SR 1947
"On April 24, Langmuir and I were
running the machine … we asked the
technician to observe with a mirror
around the protective concrete wall. ”
(Herb Pollock)
General Electric Research Laboratory,
Schenectady, NY, US
-3-
Light sources – electric field
www.nature.com
Light sources – electric field
www.nature.com

Near field
Far field
Dipole radiation (antenna)
Dipole radiation (relativistic)
Dipole radiation (relativistic)
Sverker Werin – MAX IV laboratory, Lund University
-9-
Dipole radiation (relativistic)
1/g=1/energy
What is the wavelength of this signal?
15
30
45
60
Radiation
~1/energy
time
Light and waves
Light wave
Wavelenght=> colour
Which colour/wavelength?
Fouriertransform
4R
c  3 m
3g
Wavelength
X
Energy
Filter
Filter the light
?
Filter the light
When did the light get colour?
… and in ”fancy”
language
Heisenberg’s
uncertainty relation
Fourier transform
Radiation 2D by T. Shintake
http://www.shintakelab.com/en/enEducationalSoft.htm
In the synchrotron
Bending magnet radiation
Wavelength
Energy
- 19 -
Bending magnet
Example (MAX II)
Energy
1.5 MeV (g3000)
R
3.5 m
critical
Ecritical
0.54 nm
2.3 KeV
4R
 c  3 m
3g
Energy lost by one e- over one turn
𝐸 4 𝐺𝑒𝑉
∆𝐸 𝑘𝑒𝑉 = 88.5
𝜌𝑚
- 20 -
Liénard-Weichert fields
𝑒
𝑛−𝛽
𝐸 𝑟, 𝑡 =
4𝜋𝜀0 𝛾 2 𝑅2 1 − 𝛽𝑛
near
3
+
𝑛×
𝑛 − 𝛽 × 𝛽′
𝑐𝑅 1 − 𝛽𝑛
3
𝑟𝑒𝑡
far
𝑛
𝛽′
𝛽
- 21 -
Polarisation
E field in direction of
acceleration  polarisation
Changes with observation plane
d
 dt gmo v   q E  v  B 

 d gm c 2  q v  E
o
 dt


a q E
- 23 -
Time structure
RF system
Storage ring
100-300 ps
500 MHz
MAX IV SPF
100 fs
100 MHz
Slicing
50 fs
Free Electron Laser
20 fs
Multi bunch
Single bunch
Uneven fill patterns
- 24 -
By: Goscinny.
Idea: PSI.
- 25 -
Flux and brilliance
photons
Flux 
s  0.1% BW  A
Flux
Brilliance 
4 2  x  x ' y  y '
 x   x2   r2
 x'    
2
x'
2
r'
Emittance   x x '
Peak brilliance
What counts
To compare
Light
Electrons
Bending magnet spectrum
0.1%BW
0.1
1,00E+13
100
During the peak of a
bunch
Forever or during a
macro pulse from
the accelerator
1,00E+12
Flux
Average brilliance
E0
1,00E+11
1,00E+10
1,00E+09
100
1000
E0
10000
100000
Energy (eV)
- 26 -
Think of a gaussian light beam…
𝜆
𝜎𝜑 =
= 𝜎𝑟′
2𝜋𝑤0
f
w0
w(z)
𝑤0 = 𝜎𝑟
Define a
quality factor:
𝜎𝑟 𝜎𝑟′ =
𝜆
2𝜋
Fundamental feature of
light!
(=nothing to do about it ;-)
E-field or intensity?
Spherical or cartesian?
(factors of 2 and 2)
…and then of an electron beam.
𝜎𝑥
𝜎𝑥′
x’
x
𝜎𝑥 𝜎𝑥′ = 𝜀
DIFFRACTION LIMIT
PHOTON ENERGY (keV)
100
Emittance
10
The goal for the accelerator designer is to
make the electron beam ”smaller” than
the light diffraction:
1
0,1
0
0,25
0,5
0,75
EMITTANCE (nm)
1
𝜎𝑟 𝜎𝑟′ =
𝜆
> 𝜀 = 𝜎𝑥 𝜎𝑥′
2𝜋
But, increasingly difficult for
shorter and shorter wavelengths.
Flux and brilliance
photons
Flux 
s  0.1% BW  A
Flux
Brilliance 
4 2  x  x ' y  y '
 x   x2   r2
 x'    
2
x'
2
r'
Emittance   x x '
Peak brilliance
What counts
To compare
Light
Electrons
Bending magnet spectrum
0.1%BW
0.1
1,00E+13
100
During the peak of a
bunch
Forever or during a
macro pulse from
the accelerator
1,00E+12
Flux
Average brilliance
E0
1,00E+11
1,00E+10
1,00E+09
100
1000
E0
10000
100000
Energy (eV)
- 29 -
In the synchrotron (revisited)
- 30 -
In the synchrotron (revisited)
Insertion devices
Undulator/ Wiggler
Periodic magnetic
structures
- 31 -
Insertion devices
Superconducting multi pole wiggler in MAX II
Undulator in MAX II
- 32 -
A wiggler
• Shorter wavelength / higher photon
energy
• 3 or many strong magnets
• Flux is the sum (no interference)
Bending magnet spectrum
1,00E+13
1,00E+12
Flux
4R
m
c 
3
3g
mv
m
R
qB
1,00E+11
1,00E+10
1,00E+09
100
1000
10000
100000
Energy (eV)
- 33 -
Undulator
light
undulator

2g2
• Many weak magnets
• Interference peaks
• Harmonics
• Helical polarisation exists

K2
2 2
1 
 g  
2


K = undulator parameter,
typically between 1 and 4
1,00E+14
Flux (Ph/s*A*0.1%BW)
undulator = period length for
magnets, typically 2-3 cm
1,00E+15
1,00E+13
1,00E+12
1,00E+11
1,00E+10
0
5
10
15
20
25
30
35
40
45
50
Wavelength (Å)
- 34 -
Interference in the undulator
- 35 -
Interference in the undulator
- 36 -
Interference in the undulator
1 st
harmonic
3 rd
harmonic
1,00E+15
Flux (Ph/s*A*0.1%BW)
1,00E+14
1,00E+13
1,00E+12
1,00E+11
1,00E+10
0
5
10
15
20
25
30
35
40
45
50
Wavelength (Å)
- 37 -
Undulator
light
undulator

2g2
• Many weak magnets
• Interference peaks
• Harmonics
• Helical polarisation exists

K2
2 2
1 
 g  
2


K = undulator parameter,
typically between 1 and 4
1,00E+14
Flux (Ph/s*A*0.1%BW)
undulator = period length for
magnets, typically 2-3 cm
1,00E+15
1,00E+13
1,00E+12
1,00E+11
1,00E+10
0
5
10
15
20
25
30
35
40
45
50
Wavelength (Å)
- 38 -
Linewidth, energy and angular spread

w  K 2
2 2
  2 1 
 g  
2g 
2

1

 Natural iN

  
  
  
  
 


 ...
 




   Nat    Angle    Energy   U errors

2
2
d d
2g 2
2



 Angle d  1  K 2
2
2
2

d dg 2g


 Energy dg 
g
Why wiggler, why undulator?
MAX II SC MPW
(Super Conducting Multi Pole Wiggler)
Flux from a SC multipole wiggler at MAX II
(as wiggler and undulator)
Period = 0.06 m
1,00E+15
K = 20
1,00E+14
B = 3.5 T
R = 1.4 m
 undulator = 670 nm (1.8 eV)
Flux(ph/s/0,1%
critical = 0.22 nm ( 5.6 KeV)
1,00E+13
1,00E+12
1,00E+11
1,00E+10
1,00E+09
1
10
100
1000
Photon energy (eV)
10000
100000
Why wiggler, why undulator? (p 2)
MAX II undulator
Period = 0.06 m
Flux from an undulator on MAX II
(as wiggler and undulator)
K=4
1E+15
B = 0.7 T
critical = 1.1 nm ( 1.1 KeV)
 undulator = 30 nm (41 eV)
Flux(ph/s/0,1%
R = 7.2 m
1E+14
1E+13
1
10
100
Photon energy (eV)
1000
10000
Software
http://ftp.esrf.eu/pub/scisoft/xop2.3/
http://radiant.harima.riken.go.jp/spectra/
- 42 -
A beam line
Inuti ringbyggnaden
Photo electrons
Photo electrons
Absorption
?
Scattering
Rhodium
Geometry and chemicals bonds with the help of photon spectroscopy
Clean rhodium
crystal surface
With a small amount
of oxygen
The Ribosome structure and function
2009 years Nobelprice in Chemistry
Venkatraman Ramakrishnan, Thomas A. Steitz och Ada E. Yonath
Solar cells and batteries
Grätzel type solar cell
Bonding of dye molecules
J. Schnadt et al.
Probing charge transfer times
< 2.5 fs
Rechargeable Li batteries
Forgery – and new discoveries…
STANFORD SCIENTISTS USE X-RAYS TO SEE
2,000-YEAR-OLD DOCUMENT
Archimedes’ original text
Archimedes used ink which
contained large amount of
iron.
By using X-rays at different
wavelengths (close to the Fe
Ka edge) one could see
where the iron was.
Petrified embryo of animals
... the greatest invention since sliced bread!!!
X-ray image
Hologram, 3D image
Let us start
dreaming…
What happens if
we combine
them?
See atoms and molecules
http://www.mnh.si.edu
http://eartholographics.blogspot.se
Movie of moving objects
http://www.netanimations.net
http://dev.nsta.org
Synchrotron light
• Incoherent
• ”Long” pulses (100 ps)
• High average power
Free electron laser
• Coherent
• Short pulses (10 fs)
• High peak power (GW)
• Ring
• Electrons
• Undulators
• Linear accelerator
• Electrons
• Undulators
In principle it is fairly simple!
25 - 100 m
Make the electron beam slightly better:
• Reduce the emittance 50 times
• Reduce the pulse lengdth 1000 times
• Accelerate a little more
• Fix a little higher stability and filter
• …
Emission of light and coherence
A bunch of electrons
E= cos(wt+f1) + cos(wt+f2) + ….
I=E2 = cos2(wt+f1) + cos2(wt+f2) + ….
…+ cos(wt+f1)cos(wt+f2) +… =
= Nelectrons cos2(wt+f1)
Nelectrons = 108
Emission of light and coherence
A single electron in an undulator
E= cos(wt+f1) + cos(wt+f1+2) + ….
I=E2 = cos2(wt+f1) + cos2(wt+f1+2) + ….
…+ cos(wt+f1)cos(wt+f1+2) +… =
= N2magnets cos2(wt+f1)
Nmagnets = 100
Emission of light and coherence
A bunch of electrons in an undulator
E= cos(wt+f1) + cos(wt+f1+2) + ….
I=E2 = cos2(wt+f1) + cos2(wt+f1+2) + ….
…+ cos(wt+f1)cos(wt+f1+2) +… =
= N2magnets Nelectrons cos2(wt+f1)
Nmagnets, undulator = 100
Nelectrons = 108
Emission of light and coherence
A micro bunched beam in an undulator
Brilliance
1E34
1E30
Peak brilliance
1E26
FELs
Micro
bunching
E= cos(wt+f1) + cos(wt+f1+2) + ….
I=E2 = cos2(wt+f1) + cos2(wt+f1+2) + ….
1E22
Synchrotron
…+ cos(wt+f1)cos(wt+f1+2)
It can’t be +… =
1E18
1E14
X-ray
tubes
= N2magnets N2electronstrue!
cos2(wt+f1)
1E10
1E06
1870
1920
1970
Year
Nmagnets,
2020
undulator = 100
Nelectrons = 108
x1020
In principle it is fairly simple!
25 - 100 m
Make the electron beam slightly better:
• Reduce the emittanse 50 times
• Reduce the pulse lengdth 1000 times
• Accelerate a little more
• Fix a little higher stability and filter
• …
How to make the bunching?
• Make an energy modulation
• Transform it into a density modulation
Energy
modulation
Density
modulation
10 um
Coherent
radiation in
harmonics
1 km
1Å
1 cm
Light interacting with an
electron beam
d
 dt mv   qE  v  B 

d
2

mc  qE v
 dt
 
Undulator
Energy exchange
E-field
evx
g
Some e- gain energy
Some e- loose energy
=0
Bunching
-E
Detour & lower v
+E
Shortcut & higher v
e-
g
Bunched e- with
distance of light
wavelength
Saturation
vx
g
Overbunching
Amplification
E-field
vx
Phase shift
(Frequency
slightly off
resonance)
g
• All e- loose energy
• E-field gains energy
• ≠0
SASE
(Self Amplified Stimulated Emission)
• From noice
P
• No mirrors ( X-rays)
• Tunable
L
• ”Spiky” (t and )
Noise in SASE
Resonator FEL
• IR 5-250 mm
• UV  200 nm
• Tunable: magnet /
e- energy
• Mirrors limit
• Storage ring: high
rep. Rate, ”stable”
• Linac: high peak
power, ”unstable”
SEEDING
laser
• Remove instabilities
• CHG with gain HGHG
Monochromator
LCLS, Stanford
1.5 Å
SASE
Thanks for listening!