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12-11-2015
1
Accelerator Physics:
Synchrotron radiation
Wigglers, Undulators
Monochromators
Lecture 4a
Søren Pape Møller – ISA
Synchrotron Radiation (SR)
• Acceleration of charged particles
– Emission of EM radiation
– In accelerators: Synchrotron Radiation
• Significance
– Effect on particle/accelerator
– Characterization and use of SR
• Literature
– Chap. 2 + 8 in “Wille”
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2
General Electric synchrotron accelerator built in 1946,
the origin of the discovery of synchrotron radiation from
70 MeV electrons.
The arrow indicates the evidence of “arcing”.
SR fra ASTRID
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3
Udsendelse af synkrotron
stråling
Synkrotronstråling fra ASTRID
Fotonenergi (eV)
Bølgelængde (nm)
Synkrotronstråling fra ASTRID
Sollys
Synligt lys
0.1 10 1000 100000
0.01 1 100 10000
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4
Emission of Synchrotron Radiation
• Present lecture, see “Wille” – Details, see Jackson – “Classical Electrodynamics”
– Here: Mainly key physical elements
• Acceleration of charged particles EM radiation
• Lamor: Total power v<<c
• Angular distribution (Hertz dipole)
Relativistic particles
cv
2
0m
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Linear acceleration
• Accelerator energy gain: dE/dx ≈ 15 MeV/m
– Ratio between energy lost and gain:
– h = 5 * 10-14 (for v ≈ c)
– Negligible
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Circular accelerators
• In practice: Only SR from electrons!
vv
dt
d
Energy loss per turn
[m]
[GeV]5.88
2][
4
R
E
c
RPdtPkeVE ss
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Angular distribution of synchrotron
radiation
Spectrum of SR
• Spectrum: Harmonics of frev
• Characteristic/critical frequency
• Divide power in ½
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8
Synkrotronstråling
GeVT
864.1nm GeVT665.0keV
2
2
EBEB cc
0.01 0.1 1 101E10
1E11
1E12
1E13
c
=358 eV
ved 580 MeV
og 1.6 T
Universelt
synkrotronstrålings
spektrum
ph
oto
ns/s
/mra
d/0
.1%
BW
/Ge
V
Energy/c
ASTRID og synkrotronstråling
Fotonenergi (eV)
Bølgelængde (nm)
Inte
nsi
tet
Synkrotronstrålingfra ASTRID
Sollys
Synligtlys
0.1101000100000
0.01 1 100 10000
c
𝜀𝑐[𝑒𝑉] = 665𝐸2 𝐺𝑒𝑉 𝐵[𝑇]
𝜃 ≈ 1/𝛾 ≈ 1𝑚𝑟𝑎𝑑
𝛾 = 1/ 1 − 𝛽2
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E.g. ASTRID (580 MeV)
Vertical angular distribution
Polarization
_____ og -----
GeVT665.0keV 2EBc
Spectral Brightness
1E+11
1E+12
1E+13
1E+14
1E+15
1E+16
1E+17
0.001 0.01 0.1 1 10Photon Energy (keV)
Ph
/s*m
m^
2*m
rad
^2
*0.1
BW
Undulator, ASTRID2
Undulator
2T 12 pol wiggler, ASTRID2
Bend, ASTRID1
Bend ASTRID2
ASTRID2
• Horizontal
emittance [nm]
– ASTRID2:12.1
– ASTRID: 140
• Diffraction limit:
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10
ASTRID/2 beamstørrelse
2mm
0.1mm
ASTRID (140 nm)
0.2mm
0.01mm
ASTRID2 (10 nm)
Diffraktionsbegrænset i V og delvist i H
4' RR
Synkrotron stråling : Effekt
Energitab/omgang : U[keV] = 88.5*E4[GeV4]/r[m]
Udstrålet effekt: P[kW] = U[keV]*I[A]
E [GeV] B [T] c [keV] U [keV] P [kW]
ASTRID 0.100 0.276 0.002 0.007 0.001
ASTRID 0.580 1.6 0.36 8.3 1.7
ESRF 6 0.86 20.7 4922 1000
LEP 100 0.1 665 2950000 29000
I praksis, max 100 GeV for elektron synkrotron -> linear accelerator
200 mA
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11
Light sources in Europe Name Country Website
Institute for Storage Ring Facilities Denmark http://www.isa.au.dk/
European Synchrotron Radiation
Facility France http://www.esrf.eu
SOLEIL France http://www.synchrotron-soleil.fr/
Angstromquelle Karlsruhe - ANKA Germany http://anka.kit.edu
BESSY II - Helmholtz-Zentrum Berlin Germany http://www.helmholtz-berlin.de/
Dortmund Electron Storage Ring
Facility Germany http://www.delta.tu-dortmund.de/
ELSA - Electron Stretcher Accelerator Germany http://www-elsa.physik.uni-
bonn.de/elsa-facility_en.html
Metrology Light Source Germany http://www.ptb.de/mls/
PETRA III at DESY Germany http://photon-science.desy.de
DAFNE Italy http://web.infn.it/Dafne_Light/
Elettra Synchrotron Light Laboratory Italy http://www.elettra.eu
Dubna Electron Synchrotron Russia http://wwwinfo.jinr.ru/delsy/
Kurchatov Synchrotron Radiation
Source Russia http://www.nrcki.ru/e/engl.html
TNK Russia http://www.niifp.ru/page/sinhrotron
ALBA Spain http://www.cells.es/
MAX IV Laboratory Sweden http://www.maxlab.lu.se/
Swiss Light Source Switzerland http://www.psi.ch/sls/
Diamond Light Source United Kingdom http://www.diamond.ac.uk/
ESRF – MAX IV
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Storage rings for SR
• SR – unique broad spectrum!
• 0th generation: Paracitic use
• 1st generation: Dedicated rings for SR
• 2nd generation: Smaller beams – ASTRID?
• 3rd generation: Insertion devices (straight sections), small beam – ASTRID2
• 4th generation: FEL
Insertion devices
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Multi-pole wiggler (MPW)
• Insertion device in straight section of storage ring
• Shift SR spectrum towards higher energies by larger
magnetic fields
• Gain multiplied by number of periods
• W/MPW made up to 10 T
K>>1Wiggler
”wavelength shifter
Wiggler/undulator parameter
K=ΘW /(1/γ)=eBλu/(2πmec)
ASTRID2 Wiggler
ASTRID2 – MPW – 2 T
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Example (ASTRID2):
Multi-pole wiggler (MPW)
• B0 = 2.0 T
• = 11.6 cm
• Number of periods = 6
• K = 21.7
• Critical energy = 447 eV
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Undulator radiation
If K <~1 : Line-spectrum with harmonics
anglen observatio
21
2
0
2
0
22
2,
K
n
unw
Undulator/wiggler spektrum
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ASTRID Undulator
Construction a) Electromagnet; b) permanent magnets; c) hybrid
magnets
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0 50 100 150 2000.0
2.0x1014
4.0x1014
6.0x1014
8.0x1014
1.0x1015
Pho
ton
flux
Photon energy (eV)
K = 2.3 (25 mm gap) Integrated flux
2.02 mrad
2
1.02 mrad
2
0.52 mrad
2
0.252 mrad
2
Spectral Brightness
1E+11
1E+12
1E+13
1E+14
1E+15
1E+16
1E+17
0.001 0.01 0.1 1 10Photon Energy (keV)
Ph
/s*m
m^
2*m
rad
^2
*0.1
BW
Undulator, ASTRID2
Undulator
2T 12 pol wiggler, ASTRID2
Bend, ASTRID1
Bend ASTRID2
Brightness
• Horizontal
emittance [nm]
– ASTRID2: 10
– ASTRID: 140
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SR fra ASTRID2
2mm
0.1mm
ASTRID (140 nm)
0.2mm
0.01mm
ASTRID2 (10 nm)
Diffraktionsbegrænset
i V og delvist i H
4' RR
Diffraktionsgrænse
Insertion devices: Summary
• Wiggler (K > 1, > 1/) – Broad broom of radiation
– Broad spectrum
– Stronger mag. field: Wavelength shifter (higher energies!)
– Several periods: Intensity increase
• Undulator (K < 1, < 1/) – Narrow cone of radiation: Very high brightness
• Brightness ~ N2
– Peaked spectrum (adjustable) • Harmonics if not K<<1
– Ideal source!
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Optical systems for SR I
• Purpose
– Select wavelength: E/E ~ 1000 – 10000
– Focus: Spot size of 0.1∙0.1 mm2
Optical systems for SR II
• Photon energy: few eV’s to 10’s of keV
– Conventional optics cannot be used
• Always absorption
– UV, VUV, XUV (ASTRID/ASTRID2)
• Optical systems based on mirrors
– X-rays
• Crystal monochromators based on diffraction
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Mirrors & Gratings
• Curved mirrors for
focusing
• Gratings for selection
of wavelength
• Normally q ~ 80 – 90º
– Reflectivity!
Focusing by mirrors: Example
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21
Gratings
• kN = sin(a)+sin(b)
– NB: b < 0
– N < 2500 lines/mm
• Optimization
– Max eff. for k = (-)1
– Min eff. for k = 2, 3
• Typical max. eff. ≈ 0.2
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Useful equations
• Bending radius
• Critical energy
• Total power radiated by ring
• Total power radiated by wiggler
• Undulator/wiggler parameter
• Undulator radiation
• Grating equation
2
0
22
2,2
12
K
n
unw
eVnm 1240 E
[m]
[GeV]21.2
4
3]keV[
33
R
E
R
hcc