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Intro to Sychrotron Radiation, EE290F, 16 Jan 2007David Attwood Lecture 1
Synchrotron Radiation forMaterials Science Applications
David AttwoodUniversity of California, Berkeley
andCenter for X-Ray Optics
Lawrence Berkeley National Laboratory
(http://www.coe.berkeley.edu/AST/srms)
Synchrotron Radiation for Materials Science Applications(www.coe.berkeley.edu/AST/srms)
Soft X-Rays andExtreme Ultraviolet Radiation:Principles and ApplicationsCambridge University Press or
• Table of contents• Errata
Intro_Webpage2007
• Instructor: Prof. David T. Attwood Email: attwood@berkeley.edu• Co-listed at UC Berkeley as EE290F and AST290S• Spring semester, January 16 to May 8, 2007, Tu & Th 2:10–3:30 PM 2007 Class Schedule Starting 1/16/2007, this class will be broadcast live over the Internet (Berkeley Webcast) and electronically archived for later viewing• New paperback textbook:
If not yet available through Cambridge University Press (Feb. 1, 2007), a smaller paperback version can be obtained through the UC Berkeley ASUC bookstore website, http://ucberkeley.bkstr.com Click on: Find your textbooks and follow prompts to book required for EE290F. • Lecture material used in class: 1. Intro. to Synchrotron Radiation• Homework problems: Chapter 1 Etc.
or ASUC bookstore
•
Spring 2007 Class Schedule for Synchrotron Radiation for Materials Science Applications
SpringClassSchedule.aiSynchrotron Radiation for Materials Science ApplicationsProfessor David AttwoodUniv. California, Berkeley
1. Introduction to Synchrotron Radiation (16 Jan 2007) 2. X-Ray Interaction with Matter: Absorption, Scattering, Refraction (18 Jan 2007) 3. Probing Matter: Diffraction, Spectroscopy, Photoemission; given by Prof. Anders Nilsson, Stanford University (23 Jan 2007) 4. Radiation by an Accelerated Charge: Scattering by Free and Bound Electrons (25 Jan 2007) 5. Multi-Electron Atom, Atomic Scattering Factors: Wave Propagation and Refractive Index (30 Jan 2007) 6. Refraction and Reflection, Total Internal Reflection, Brewster's Angle, Kramers-Kronig (1 Feb 2007) 7. Multilayer Interference Coatings, Scattering, Diffraction, Reflectivity and Applications (6 Feb 2007) 8. Introduction to Synchrotron Radiation, Bending Magnet Radiation (8 Feb 2007) 9. Bending Magnet Critical Photon Energy; Undulator Central Radiation Cone (13 Feb 2007) 10. Undulator Equation and Radiated Power (15 Feb 2007) 11. Spectral Brightness of Undulator Radiation, Harmonics, Wiggler Radiation (20 Feb 2007) 12. Spatial and Temporal Coherence; Coherent Undulator Radiation (22 Feb 2007) 13. Applications of Coherent Undulator Radiation (27 Feb 2007) 14. Visit the Advanced Light Source, Berkeley (ALS) (1 March 2007)
15. Advanced Spectroscopy for Atomic and Molecular Physics; given by Prof. Anders Nilsson, Stanford University (6 March 2007)16. X-Ray Absorption Spectroscopy: XAFS, NEXAFS, XANES, EXAFS; given by Dr. Tony VanBuuren, LLNL/UC Merced (8 March 2007) 17. X-Ray Diffraction for Materials Analysis; given by Dr. Simon Clark, ALS/LBNL (13 March 2007) 18. Photoemission and Photoemission Spectroscopy; given by Dr. Zahid Hussain, ALS/LBNL (20 March 2007) 19. Angle Resolved Photoemission and Nano-ARPES; given by Dr. Eli Rotenberg, ALS/LBNL (22 March 2007)20. Photo-Emission Electron Microscopy (PEEM); given by Dr. Andreas Scholl, ALS/LBNL (3 April 2007)21. X-Rays and Magnetism; given by Prof. Jochim Stöhr, Stanford University (5 April 2007)22. XMCD; Out-of-Plane Bending Magnetic Radiation; given by Brooke Mesler, UC Berkeley (10 April 2007) 23. Zone Plate Microscopy and Applications (12 April 2007)24. Nanoscale Magnetic Imaging; given by Dr. Peter Fisher, CXRO/LBNL (17 April 2007) 25. Nanotomography for the Life Sciences; given by Prof. Carolyn Larabell, UCSF, and Dr. Mark LeGros, LBNL (19 April 2007) 26. X-Ray Microtomography for Material Studies; given by Dr. Alastair MacDowell, ALS/LBNL (24 April 2007) 27. Coherent Soft X-Ray Scattering for Studying Nanoscale Materials; given by Prof. Stephen Kevan, U. Oregon, Eugene (26 April 2007) 28. Student Projects (oral reports on related material)
1 µm 100 nm 10 nm 1 nm 0.1 nm = 1Å
10 keV
CuK
2a0
SiK OK CK SiL
1 keV Photon energy
Wavelength
100 eV 10 eV 1 eV
IR VUV
Hard X-raysUV Extreme Ultraviolet
Soft X-rays
• See smaller features• Write smaller patterns• Elemental and chemical sensitivity
CuKα
The Short Wavelength Regionof the Electromagnetic Spectrum
Ch01_F01VG.aiProfessor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
+Ze
Photoelectron
Photon(ω)
KL
M
e–
Characteristic Absorption Edges forAlmost All Elements in this Spectral Region
Ch01_F02a_F10_Tb1.ai
n = ∞ n = 4n = 3
n = 2
n = 1
N0
M
L
K
Bin
ding
ene
rgy
(neg
ativ
e)K
inet
ic e
nerg
y(p
ositi
ve)
EK, abs
Ekinetic = – EK, abs
EL, abs
Kβ
Kα
Lα Lβ
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
n
N
M
L
K
44...4
NVII 4f7/2..NIV 4d3/2..NI 4s
MV 3d5/2MIV 3d3/2MIII 3p3/2MII 3p1/2MI 3s
LIII 2p3/2LII 2p1/2LI 2s
K 1s
33...0
7/25/2...1/2
33333
22110
5/23/23/21/21/2
222
110
3/21/21/2
1 0 1/2
j
Kα1
Cu Kα1 = 8,048 eV (1.541Å) Cu Lα1
= 930 eVCu Kα2
= 8,028 eV (1.544Å) Cu Lα2 = 930 eV
Cu Kβ1 = 8,905 eV Cu Lβ1
= 950 eV
Absorption edgesfor copper (Z = 29):
EN1, abs = 7.7 eV
.
.EM3, abs = 75 eV.EM1, abs = 123 eV
EL3, abs = 933 eVEL2, abs = 952 eVEL1, abs = 1,097 eV
EK, abs = 8,979 eV (1.381Å)
Kα2
Lα1
Mα1
Lβ2Lα2
Kβ1Kβ3
Kγ3
Energy Levels, Quantum Numbers, andAllowed Transitions for the Copper Atom
Ch01_F11VG_rev.6.05.aiProfessor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
ApxB_1_47_Jan07.ai
Electron Binding Energies, in Electron Volts(eV), for the elements in their Natural Forms
www.cxro.LBL.gov
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
1H
Hydrogen
1.00791
1s1
3Li
Lithium
0.534.63
6.9411
1s2 2s1
4Be
Beryllium
1.8512.32.23
9.0122
1s2 2s2
2He
Helium
4.0031
1s2
11Na0.97
2.53
22.9901
[Ne]3s1
12Mg1.74
4.303.20
24.312
[Ne]3s2
Sodium
Potassium
13Al2.70
6.022.86
26.983
[Ne]3s23p1
Aluminum
14Si2.33
4.992.35
1.823.54
2.093.92
28.094
[Ne]3s23p2
15P
30.9743,5,4
[Ne]3s23p3
Silicon
14Si2.33
4.992.35
28.094
[Ne]3s23p2
Silicon
Density (g/cm3)
Concentration (1022atoms/cm3)
Nearest neighbor (Å)
Atomic number Atomic weight
References: International Tables for X-ray Crystallography (Reidel, London, 1983) (Ref. 44) and J.R. De Laeter and K.G. Heumann (Ref. 46, 1991).
Key
Symbol
ElectronconfigurationName
Oxidation states(Bold most stable)
Phosphorus
16S
32.0662,4,6
[Ne]3s23p4
Sulfur
17Cl35.4531,3,5,7
[Ne]3s23p5
Chlorine
18Ar39.9481,3,5,7
[Ne]3s23p6
ArgonMagnesium
19K0.86
1.33
39.0981
[Ar]4s1
20Ca1.53
2.303.95
40.082
[Ar]4s2
Calcium
21Sc2.99
4.013.25
44.963
[Ar]3d14s2
Scandium
22Ti4.51
5.672.89
47.884,3
[Ar]3d24s2
Titanium
23V6.09
7.202.62
50.945,4,3,2
[Ar]3d34s2
Vanadium
24Cr7.19
8.332.50
52.006,3,2
[Ar]3d54s1
Chromium
25Mn7.47
8.19
54.947,6,4,2,3
[Ar]3d54s2
Manganese
26Fe7.87
8.492.48
55.852,3
[Ar]3d64s2
Iron
27Co8.82
9.012.50
58.932,3
[Ar]3d74s2
Cobalt
28Ni8.91
9.142.49
58.692,3
[Ar]3d84s2
Nickel
29Cu8.93
8.472.56
63.552,1
[Ar]3d104s1
Copper
30Zn7.13
6.572.67
65.392
[Ar]3d104s2
Zinc
31Ga5.91
5.102.44
69.723
[Ar]3d104s24p1
Gallium
32Ge5.32
4.422.45
72.614
[Ar]3d104s24p2
Germanium
33As5.78
4.642.51
74.923,5
[Ar]3d104s24p3
Arsenic
34Se4.81
3.672.32
78.96–2,4,6
[Ar]3d104s24p4
Selenium
35Br3.12
2.35
79.9041,5
[Ar]3d104s24p5
Bromine
36Kr
83.80
[Ar]3d104s24p6
Krypton
Rubidium
37Rb1.53
1.08
85.471
[Kr]5s1
38Sr2.58
1.784.30
87.622
[Kr]5s2
Strontium
39Y4.48
3.033.55
88.913
[Kr]4d15s2
Yttrium
40Zr6.51
4.303.18
91.224
[Kr]4d25s2
Zirconium
41Nb8.58
5.562.86
92.915,3
[Kr]4d45s1
Niobium
42Mo Tc10.2
6.422.73
95.946,3,2
[Kr]4d55s1
Molybdenum
4311.5 7.072.70
(98)7
[Kr]4d55s2
Technetium
44Ru12.4
7.362.65
101.12,3,4,6,8
[Kr]4d75s1
Ruthenium
45Rh12.4
7.272.69
102.912,3,4
[Kr]4d85s1
Rhodium
46Pd12.0
6.792.75
106.42,4
[Kr]4d10
Palladium
47Ag10.5
5.862.89
107.871
[Kr]4d105s1
Silver
48Cd8.65
4.632.98
112.412
[Kr]4d105s2
Cadmium
49In7.29
3.823.25
114.823
[Kr]4d105s25p1
Indium
50Sn7.29
3.703.02
118.714,2
[Kr]4d105s25p2
Tin
51Sb6.69
3.312.90
121.763,5
[Kr]4d105s25p3
Antimony
52Te6.25
2.952.86
127.60–2,4,6
[Kr]4d105s25p4
Tellurium
53I4.95
2.35
126.901,5,7
[Kr]4d105s25p5
Iodine
54Xe131.29
[Kr]4d105s25p6
Xenon
Cesium
55Cs1.90
0.86
132.911
[Xe]6s1
56Ba3.59
1.584.35
137.332
[Xe]6s2
Barium
57La6.17
2.683.73
138.913
[Xe]5d16s2
Lanthanum
72Hf13.3
4.483.13
178.494
[Xe]4f145d26s2
Hafnium
73Ta16.7
5.552.86
180.955
[Xe]4f145d36s2
Tantalum
74W19.3
6.312.74
183.856,5,4,3,2
[Xe]4f145d46s2
Tungsten
Francium
87Fr
(223)1
[Rn]7s1
88Ra
(226)2
[Rn]7s2
Radium
Cerium
58Lanthanide series
Actinide series
Ce6.772.913.65
140.123,4
[Xe]4f15d16s2
59Pr6.78
2.903.64
140.913,4
[Xe]4f36s2
Praseodymium
60Nd Pm7.00
2.923.63
7.543.023.59
144.243
[Xe]4f46s2
Neodymium
61 (145)3
[Xe]4f56s2
Promethium
62Sm
150.363,2
[Xe]4f66s2
Samarium
5.252.083.97
63Eu
152.03,2
[Xe]4f76s2
Europium
7.873.013.58
64Gd
157.253
[Xe]4f75d16s2
Gadolinium
8.273.133.53
65Tb158.93
3,4
[Xe]4f96s2
Terbium
8.533.163.51
66Dy
162.503
[Xe]4f106s2
Dysprosium
8.803.213.49
67Ho
164.933
[Xe]4f116s2
Holmium
9.043.263.47
68Er167.26
3
[Xe]4f126s2
Erbium
9.333.323.45
69Tm
168.933,2
[Xe]4f136s2
Thulium
6.972.423.88
70Yb
173.043,2
[Xe]4f146s2
Ytterbium
9.843.393.43
71Lu174.97
3
[Xe]4f145d16s2
Lutetium
Thorium
90Th11.7
3.043.60
232.054
[Rn]6d27s2
91Pa15.4
4.013.21
231.045,4
[Rn]5f26d17s2
Protactinium
92U Np Pu Am Cm Bk Cf Es Fm Md No Lr19.1
4.822.75
19.84.89
238.036,5,4,3
[Rn]5f36d17s2
Uranium
9320.55.20
(237)6,5,4,3
[Rn]5f46d17s2
Neptunium
94 (244)6,5,4,3
[Rn]5f67s2
Plutonium
11.92.943.61
95 (243)6,5,4,3
[Rn]5f77s2
Americium
96 (247)3
[Rn]5f76d17s2
Curium
97 (247)4,3
[Rn]5f97s2
Berkelium
98 (251)3
[Rn]5f107s2
Californium
99 (252)
[Rn]5f117s2
Einsteinium
100 (257)
[Rn]5f127s2
Fermium
101 (258)
[Rn]5f137s2
Mendelevium
102 (259)
[Rn]5f147s2
Nobelium
103 (262)
[Rn]5f146d17s2
Lawrencium
89Ac Sg Bh Hs MtRf Db10.1
2.673.76
(227)3
[Rn]6d17s2
Actinium
104 (261)
[Rn]5f146d27s2
Rutherfordium
105 (262)
[Rn]5f146d37s2
Dubnium
106 (266)
[Rn]5f146d47s2 [Rn]5f146d57s2 [Rn]5f146d67s2 [Rn]5f146d77s2
Seaborgium
107 (264)
Bohrium
108 (277)
Hassium
109 (268)
Meitnerium
75Re21.0
6.802.74
186.217,6,4,2,–1
[Xe]4f145d56s2
Rhenium
76Os22.6
7.152.68
190.22,3,4,6,8
[Xe]4f145d66s2
Osmium
77Ir22.6
7.072.71
192.22,3,4,6
[Xe]4f145d76s2
Iridium
78Pt21.4
6.622.78
195.082,4
[Xe]4f145d96s1
Platinum
79Au19.3
5.892.88
197.03,1
[Xe]4f145d106s1
Gold
80Hg
200.592,1
[Xe]4f145d106s2
Mercury
81Tl11.9
3.503.41
204.383,1
[Xe]4f145d106s26p1
Thallium
82Pb11.3
3.303.50
207.24,2
[Xe]4f145d106s26p2
Lead
83Bi9.80
2.823.11
208.983,5
[Xe]4f145d106s26p3
Bismuth
84Po9.27
2.673.35
(209)
114 (287)
4,2
[Xe]4f145d106s26p4
Polonium
85At
(210)1,3,5,7
[Xe]4f145d106s26p5
Astatine
86Rn
(222)
110 (271) 111 (272) 112 (283)
[Xe]4f145d106s26p6
Radon
5B
Boron
2.4713.71.78
10.813
1s2 2s2 2p1
6C
Carbon
2.2711.41.42
12.0114,2
1s2 2s2 2p2
7N
Nitrogen
14.0073,5,4,2
1s2 2s2 2p3
8O
Oxygen
16–2
1s2 2s2 2p4
9F
Fluorine
19.00–1
1s2 2s2 2p5
10Ne
Neon
20.180
1s2 2s2 2p6
GroupIA
IIA
IIIA IVA VA VIA VIIA VIIIA IB IIB
IIIB IVB VB VIB VIIB
VIII
Solid
Gas
Liquid
Synthetically prepared
Periodic_Tb_clr_May2007.ai
Broadly Tunable Radiation is Needed to Probethe Primary Resonances of the Elements
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Intro to Sychrotron Radiation, EE290F, 16 Jan 2007David Attwood Lecture 1
• Surface science
• Magnetic materials
• Materials chemistry
• Environmental sciences
• Protein crystallogrphy
• Biomicroscopy
• Chemical dynamics
Typical Applications of Synchrotron Radiation
BrightPowrfulXRs.ai
Bright and Powerful X-Raysfrom Relativistic Electrons
ψ
θ
e–
Undulator radiationSynchrotron radiation
e–
• 1010 brighter than the most powerful (compact) laboratory source
• An x-ray “light bulb” in that it radiates all “colors” (wavelengths, photons energies)
• Lasers exist for the IR, visible, UV, VUV, and EUV
• Undulator radiation is quasi- monochromatic and highly directional, approximating many of the desired properties of an x-ray laser
N
NN
N
S
S
S
S
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Ch05_F09VG_Jan07.ai
Synchrotron Radiation from Relativistic Electrons
λ′
λ′ λxv
Note: Angle-dependent doppler shift
v << c v c~<
λ = λ′ (1 – cosθ) λ = λ′ γ (1 – cosθ) ~ (1 + γ2θ2)
γ =
vc
v2
c2
λ′2γ
1
1 –
vc
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
—
Ch05_F11VG.ai
Synchrotron Radiation in a Narrow Forward Cone
a′ sin2Θ′Θ′
θ – 12γ~
(5.1)
(5.2)
Frame moving with electron Laboratory frame of reference
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Ch05_F11modif_VG.ai
Relativistic Electrons Radiatein a Narrow Forward Cone
a′ sin2Θ′
k′ k
k′ = 2π/λ′
Lorentztransformationk′
k′
Θ′θ
θθ′
12γ
kxkz
k′2γk′
tanθ′2γ
12γθ
Dipole radiation
Frame of referencemoving with electrons
Laboratory frame of reference
x
z
kx = k′
kz = 2γk′ (Relativistic Doppler shift)z
xz
=
x
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Ch05_UsefulFormulas.ai
Some Useful Formulas for Synchrotron Radiation
ω λ = 1239.842 eV nm
Ee = γmc2, p = γmv
γ = = 1957 Ee(GeV)
γ = = ; β = ; (1 – β)
where
Undulator: ;
Bending Magnet: ,
Eemc2
12γ2
1
1 –
vcv2
c2
1
1 – β2
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
e–
λ
1γ
F
ω
e–
λ
1γ N
F
ω
e–
1γ
λ
>>
ω
F
Ch05_F01_03.ai
Bending magnetradiation
Wiggler radiation
Undulator radiation
Three Forms of Synchrotron Radiation
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
3rdGenFacilities_Jan06.ai
Third Generation Facilities, Like Electtra,Have Many Straight Sections and a SmallElectron Beam
e–
Photons
X-ray• Many straight sections containing periodic magnetic structures
• Tightly controlled electron beam
UV
Modern SynchrotronRadiation Facility
• Many straight sections for undulators and wigglers
• Brighter radiation for spatially resolved studies (smaller beam more suitable for microscopies)
• Interesting coherence properties at very short wavelengths
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Third Generation Synchrotron Facilities
3rdGenSynchFacil_Jan07.aiIntro to Synchrotron Radiation, EE290F, 16 Jan 2007
ESRF 6 GeV FranceALS 1.9 GeV USAAPS 7 GeV USABESSY II 1.7 GeV GermanyELETTRA 2.0 GeV ItalySPring-8 8 GeV JapanMAX II 1.5 GeV SwedenSLS 2.4 GeV SwitzerlandPLS 2 GeV KoreaSRRC 1.4 GeV TaiwanSSRL 3 GeV USACLS 2.9 GeV CanadaSoleil 2.5 GeV FranceDiamond 3 GeV UK
Facilities Under ConstructionAustralian 3 GeV AustraliaLight Source
Courtesy of Herman Winick, SSRL, Stanfordwww-ssrl.slac.stanford.edu/SR_SOURCES.HTML
Others are in the design stage or planning an upgrade to third generation.
Professor David AttwoodUniv. California, Berkeley
Synchrotron Radiation
e–
Photons
X-ray• Many straight
sections containingperiodic magneticstructures
• Tightly controlledelectron beam
UV
(5.80)
(5.82)
(5.85)
Ch05_F00VG_Jan06.ai
Undulatorradiation
NS
NS
SN
SN
e–
λu
λ
t
2 ns
70 psNe
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
Ch05_F07_revJune05.ai
Bending Magnet Radiation Covers a BroadRegion of the Spectrum, Including thePrimary Absorption Edges of Most Elements
1013
1014
1012
1011
0.01 0.1 1 10 100Photon energy (keV)
Pho
ton
flux
(ph/
sec)
Ec
50%
Ee = 1.9 GeVΙ = 400 mAB = 1.27 Tωc = 3.05 keV
(5.7a)
(5.7b)
(5.8)
ψθ
e–
∆θ = 1mrad∆ω/ω = 0.1%
Advantages: • covers broad spectral range • least expensive • most accessableDisadvantages: • limited coverage of hard x-rays • not as bright as undulator
4Ec
50%
ALS
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Ch05_F08_Jan07.ai
Undulator Radiation from a Small Electron BeamRadiating into a Narrow Forward Cone is Very Bright
Magnetic undulator(N periods)
Relativisticelectron beam,Ee = γmc2
λλ –
2θ
λu λu2γ2
∆λλ
1N
~
θcen –1
γ N
cen =
~
Brightness =
Spectral Brightness =
photon flux(∆A) (∆Ω)
photon flux(∆A) (∆Ω) (∆λ/λ)
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
An Undulator Up Close
Undulator_Close_Jan07.ai
ALS U5 undulator, beamline 7.0, N = 89, λu = 50 mm
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
Undulator Radiation
e–N
S S
N
N N
S Sλu
E = γmc2
γ = 1
1 – v2
c2
N = # periods
e–sin2Θ θ ~– 1
2γ θcen
e– radiates at theLorentz contractedwavelength:
Doppler shortenedwavelength on axis:
Laboratory Frameof Reference
Frame ofMoving e–
Frame ofObserver
FollowingMonochromator
For 1N
∆λλ
θcen1
γ N
θcen 40 rad
λ′ = λuγ
Bandwidth:
λ′ N
λ = λ′γ(1 – βcosθ)
λ = (1 + γ2θ2)
Accounting for transversemotion due to the periodicmagnetic field:
λu
2γ2
λu
2γ 2λ = (1 + + γ 2θ2)K2
2
where K = eB0λu /2πmc
Ch05_LG186.ai
~–
~–
~–~–
∆λ′
typically
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
The Equation of Motion in an Undulator
Ch05_F15_Eq16_19.top.ai
(5.16)
Magnetic fields in the periodic undulator cause the electrons to oscillate and thus radiate. These magnetic fields also slow the electrons axial (z) velocity somewhat, reducing both the Lorentz contraction and the Doppler shift, so that the observed radiation wavelength is not quite so short. The force equation for an electron is
where p = γmv is the momentum. The radiated fields are relatively weak so that
Taking to first order v vz, motion in the x-direction is
By = Bo cos 2πzλu
y
z
x
ve–
= –e(E + v × B)dpdt
–e(v × B)dpdt
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
Calculating Power in the Central Radiation Cone: Using the well known “dipole radiation” formula by transforming to the frame of reference moving with the electrons
Ch05_T4_topVG.ai
e–
γ*e–
z
N periods
x′
z′
Lorentz transformation
Lorentztransformation
Θ′θ′
sin2Θ′
= Nλ′∆λ′
λu
λu
x
z= N
θcen =
λ∆λ
1γ* N
′ =λuγ*
Determine x, z, t motion:
x, z, t laboratory frame of reference x′, z′, t′ frame of reference moving with theaverage velocity of the electron
Dipole radiation:
=
x′, z′, t′ motiona′(t′) acceleration
= –e (E + v × B)
mγ = e B0 cos
vx(t); ax(t) = . . .
vz(t); az(t) = . . .
dpdt
dvxdt
dzdt
2πzλu
dP′dΩ′
e2 a′2 sin2 Θ′16π20c3
= (1–sin2 θ′ cos2 φ′) cos2 ω′ut′dP′dΩ′
e2 cγ2
40λu
K2
(1 + K2/2) 22
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
Power in the Central Cone
Ch05_LG189_Jan06.ai
Pcen =
cen =
πeγ 2I
0λuK2
2
eB0λu2πm0c
∆λλ
1γ ∗ N
1N
γ ∗ = γ / 1 + K2
2
λx = (1 + + γ 2θ2)λu
2γ 2K2
2
K =
θcen =
N periods
1 γ∗1
Nγ∗θcen =
e–
λu
Photon energy (eV)
Pce
n (W
)Tuningcurve
λ∆λ
= N
ALS, 1.9 GeV400 mAλu = 8 cmN = 55K = 0.5-4.0
0 100 200 300 4000
0.50
1.00
1.50
2.00
(1 + )2
K2f(K)
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
0 500 1000 1500 20000
0.5
1
1.5
2
2.5
θcen =
1γ* Nn = 1
n = 3
Pcen (W)
PwrCenRadCnALSbessyMAX.ai
γ = 3720λu = 50 mmN = 89Ι = 400 mAθcen = 35 µr
ALS
1N
13N
=∆λλ 1
=∆λλ 3
λ∆λ
= 89
λ∆λ
= 270
γ = 3330λu = 49 mmN = 84Ι = 200 mAθcen = 35 µr
0 500 1000 1500 2000
n = 1
n = 30
0.2
0.4
0.6
0.8
1.0
λ∆λ
= 84
λ∆λ
BESSY II
= 250
Photon Energy (eV)
Pcen (W)
0 200 400 600 800 10000
0.5
1
n = 1
n = 3
γ = 2940λu = 52 mmN = 49Ι = 250 mAθcen = 59 µr
MAX II
Pcen (W)
Power in the Central Radiation ConeFor Three Soft X-Ray Undulators
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
θcen =
1γ* N
Power in the Central Radiation ConeFor Three Hard X-Ray Undulators
Ch05_PwrCenRadCone3.ai
1N
13N
=∆λλ 1
=∆λλ 3
Professor David AttwoodUniv. California, Berkeley
0 10 20 30 400
5
10
15
n = 1APS
n = 3
Photon Energy (keV)
0 5 10 15 20 25
15
10
5
0
n = 1
n = 3
Pcen (W)
γ = 11,800λu = 42 mmN = 38Ι = 200 mAθcen = 17 µr
γ = 13,700λu = 33 mmN = 72Ι = 100 mAθcen = 11 µr
SPring-8γ = 15,700λu = 32 mmN = 140Ι = 100 mAθcen = 6.6 µr
ESRF
Pcen (W)
Pcen (W)
λ∆λ = 38
= 120λ∆λ
n = 1
n = 3
0 10 20 30 40 50 600
5
10
15
20
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Ch05_Eq57_58VG_Jan2006.ai
Brightness and Spectral Brightness
(5.57)
(5.58)
Brightness is defined as radiated power per unitarea and per unit solid angle at the source:
Brightness is a conserved quantity in perfectoptical systems, and thus is useful in designingbeamlines and synchrotron radiation experimentswhich involve focusing to small areas.
Spectral brightness is that portion of the brightness lying within a relative spectral bandwidth ∆ω/ω:
∆ωω
ω
B
η
∆Asds ∆Ai
Perfect optical system:∆As ∆Ωs = ∆Ai ∆Ωi ; η = 100%
∆Ωs
θs θi
∆Ωi
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
Ch05_F24VG_Feb04.aiProfessor David AttwoodUniv. California Berkeley
Spectral Brightness is Useful for Experimentsthat Involve Spatially Resolved Studies
• Brightness is conserved (in lossless optical systems)
• Starting with many photons in a small source area and solid angle, permits high photon flux in an even smaller area
θopticθsource
dsource
dsource θsource = dfocus θoptic
dfocus
Smallerafter focus
Large in afocusing optic
1-2 GeVUndulators
6-8 GeVUndulators
Wigglers
Bendingmagnets
10 eV 100 eV 1 keV 10 keV 100 keVPhoton energy
Spe
ctra
l brig
htne
ss
12 nm 1.2 nm 0.12 nm1020
1019
1018
1017
1016
1015
1014
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
d
Ch08_F00_Jan07.ai
λθ
λ
e–
lcoh = λ2/2∆λ temporal (longitudinal) coherence
d θ = λ/2π spatial (transverse) coherence
or d 2θFWHM = 0.44 λ
(8.3)
(8.5)
(8.5*)
Pcoh,λ/∆λ = 1– ƒ(K)
(8.6)
(8.9)
(λ/2π)2
(dxθx)(dyθy)
ωω0
eλuIη(∆λ/λ)N2
8π0dxdy
Pcoh,N = Pcen
λu
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Coherence at Short Wavelengths
Intro to Sychrotron Radiation, EE290F, 16 Jan 2007David Attwood Lecture 1
Spatial and Spectral Filtering to ProduceCoherent Radiation
Courtesy of A. Schawlow, Stanford
Intro to Sychrotron Radiation, EE290F, 16 Jan 2007David Attwood Lecture 1
Spatially Coherent Undulator Radiation
λ = 13.4 nm
1 µmD pinhole25 mm wide CCD at 410 mm
Courtesy of Patrick Naulleau, LBNL / Kris Rosfjord, UCB and LBNL
d ? θ = λ2π
λ = 2.5 nm
Coherent Power at the ALS
Ch09_U5cohPwrALS_Feb06.ai
1.9 GeV, 400 mAλu = 50 mm, N = 890.5 ≤ K ≤ 4.0σx = 260 µm, σx′ = 23 µrσy = 16 µm, σy′ = 3.9 µrηeuv = 10%, ηsxr = 2%
U5
0 500
n = 1
n = 3
n = 1
n = 3
n = 1
n = 3
1000 1500 20000
0.5
1.0
1.5
2.0
2.5
0
10
20
30
40
50
0
100
200
300
400 80
60
40
20
0102 103102 103
Photon Energy (eV)Photon Energy (eV)
Photon Energy (eV)
Pco
h, N
(mW
)
Pco
h, λ
/∆λ
(µW
)
Pce
n (W
)
λ∆λ
= 89 λ∆λ
= 103
λ∆λ
= 103 Pco
h, n
= 3
(µW
)
Intro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
Ch08_BESSYII_Feb06.ai
1.7 GeV, 200 mAλu = 49 mm, N = 840 ≤ K ≤ 2.5σx = 314 µm, σx′ = 18 µrσy = 24 µm, σy′ = 2 µrηeuv = 10% ; ηsxr = 2%
0 500 1000 1500 2000
102 1030
50
100
150 30
20
10
0
Photon Energy (eV)
Pco
h, λ
/∆λ
(µW
)
Pce
n (W
)
n = 1
n = 3
n = 1
n = 3
λ∆λ
= 103
λ∆λ
= 103
0
0.2
0.4
0.6
0.8
1.0
0
5
10
15
102 103
Photon Energy (eV)
Photon Energy (eV)
Pco
h, N
(mW
)
n = 1
n = 3
λ∆λ
= 84
Coherent Power at BESSY II
Pco
h, n
= 3
(µW
)
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
AiryPattrn600eV.ai
Spatially Coherent Soft X-Rays With PinholeSpatial Filtering: Airy Patterns at 600 eV
λ = 2.48 nm (600 eV)d = 2.5 µmt = 200 msecALS beamline 12.0.2λu = 80 mm, N = 55, n = 3
Courtesy of Kristine Rosfjord, UC Berkeley and LBNLProfessor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Intro to Sychrotron Radiation, EE290F, 16 Jan 2007David Attwood Lecture 1S. Eisebitt, J. Lüning, W.F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt & J. Stöhr / Nature, 16 Dec 2004
The Transition from Undulator Radiation (K ≤ 1)to Wiggler Radiation (K >> 1)
Ch05_F30_32VG.ai
K = 1• Narrow spectral lines• High spectral brightness• Partial coherence
K = 2K =
λ = 1 + + γ2θ2
K = 4
0 1 2 3 4Photon energy (KeV)
(Courtesy of K.-J. Kim)(Courtesy of R.P. Walker and B. Diviacco)
Spe
ctra
l brig
htne
ssS
pect
ral b
right
ness
Spe
ctra
l brig
htne
ss
λu = 5 cm, N = 89
Undulator radiation (K < 1)~
eBoλu2πmc
ωc =
λu
2γ2 K2
2
1.5 GeV400 mA → 0∆θ → 0
• Higher photon energies• Spectral continuum• Higher photon flux (2N)
Wiggler radiation (K >> 1)
γ2eBom
32
3K4
K2
2 nc = 1 +
1/N
Frequency (f)
f1 f3 fn fn + 2
α ≠ 0
…
dPdΩ
Elettra2 GeV0.4 Aλu = 6.0 cmN = 72K = 3.7nc = 22
1016
1015
1014
1013
101 102
Photon energy (eV)
Pho
ton
flux
(pho
tons
/sec
· 0.
1% B
W)
103 104
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Wiggler Radiation
Ch05_Eq82_87_F33rev3.02.ai
(5.7a & 82);
At very high K >> 1, the radiated energy appears in very high harmonics, and at rather largehorizontal angles θ ±K/γ (eq. 5.21). Because the emission angles are large, one tends to use larger collection angles, which tends to spectrally merge nearby harmonics. The result is a continuum at very high photon energies, similar to that of bending magnet radiation, but increased by 2N (the number of magnet pole pieces).
104
103
102
10
110 102 103 104
Photon energy (relative units)
Pho
ton
flux
per u
nit s
olid
ang
lepe
r 0.1
% b
andw
idth
(rel
ativ
e un
its)
BendingMagnet
Radiation
WigglerRadiation
2Nωc
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
StanfordWiggler.ai
Stanford Permanent Magnet Wiggler
LBNL/EXXON/SSRL (1982), SSRL Beamline VI55 pole (N = 27.5), λw = 7 cm
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
TypicalParametersSynchRad.ai
Facility ALS BESSY II ESRF SP-8
Electron energy 1.90 GeV 1.70 GeV 6.04 GeV 8.00 GeVγ 3720 3330 11,800 15,700Current (mA) 400 200 200 100Circumference (m) 197 240 884 1440RF frequency (MHz) 500 500 352 509Pulse duration (FWHM) (ps) 35-70 20-50 70 120
Bending Magnet Radiation:Bending magnet field (T) 1.27 1.30 0.806 0.679Critical photon energy (keV) 3.05 2.50 19.6 28.9Critical photon wavelength 0.407 nm 0.50 nm 0.634 Å 0.429 ÅBending magnet sources 24 32 32 23
Undulator Radiation:Number of straight sections 12 16 32 48Undulator period (typical) (cm) 5.00 4.90 4.20 3.20Number of periods 89 84 38 140Photon energy (K = 1, n = 1) 457 eV 373 eV 5.50 keV 12.7 keVPhoton wavelength (K = 1, n = 1) 2.71 nm 3.32 nm 0.225 nm 0.979 ÅTuning range (n = 1) 230-620 eV 140-500 eV 2.6-7.3 keV 4.7-19 keVTuning range (n = 3) 690-1800 eV 410-1100 eV 7.7-22 keV 16-51 keVCentral cone half-angle (K = 1) 35 µrad 33 µrad 17 µrad 6.6 µradPower in central cone (K = 1, n = 1) (W) 2.3 0.95 14 16Flux in central cone (photons/s) 3.1 × 1016 1.6 × 1016 1.6 × 1016 7.9 × 1015
σx, σy (µm) 260, 16 314, 24 395, 9.9 380, 6.8σx, σy (µrad) 23, 3.9 18, 12 11, 3.9 16, 1.8Brightness (K = 1, n = 1)a
[(photons/s)/mm2 mrad2 (0.1%BW)] 2.3 × 1019 4.6 × 1018 5.1 × 1018 1.8 × 1020
Total power (K = 1, all n, all θ) (W) 83 32 480 2,000Other undulator periods (cm) 3.65, 8.00, 10.0 4.1, 5.6, 12.5 2.3, 3.2, 5.2, 8.5 2.4, 10.0, 3.7, 12.0
Wiggler Radiation:Wiggler period (typical) (cm) 16.0 12.5 8.0 12.0Number of periods 19 32 20 37Magnetic field (maximum) (T) 2.1 1.15 0.81 1.0K (maximum) 32 12.8 6.0 11Critical photon energy (keV) 5.1 2.11 20 43Critical photon wavelength 0.24 nm 0.59 nm 0.62 Å 0.29 ÅTotal power (max. K) (kW) 13 1.8 4.8 18
aUsing Eq. (5.65). See comments following Eq. (5.64) for the case where σx, y θcen.
Typical Parameters for Synchrotron Radiation
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Ch05_F01b_BLtransport.ai
Beamlines are Used to Transport Photons tothe Sample, and Take a Desired Spectral Slice
Photonflux
Gratingor crystal
Monochromator
Exitslit Curved
focusingmirror
(glancingincidencereflection)
Focusinglens (pairof curvedmirrors,
zone platelens, etc.)
Sample
ω
Photonflux
ω
e–
Observe at sample:• Absorption spectra• Photoelectron spectra• Diffraction••
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
BendingMagnet
e–
M1 (spherical)
M2 (spherical)
Plane VLS gratings
G1G2
G3
Fixedexitslit
Sample
Detector
Scan
XBD9509-04496_Jan04.ai
A Typical Beamline:Monochromator Plus Focusing Opticsto Deliver Radiation to the Sample
Courtesy of James Underwood (EUV Technology Inc.)
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Sample
Translatingexit slit
Translatingentrance
slit
Sphericalgrating
Horizontialdeflection/focusing
mirror
Verticalfocusing
mirrorVerticalfocusing
mirror
Horizontalfocusing
mirror
EllipticallyPolarizingUndulator
meVresBL.ai
High Spectral Resolution (meV) Beamline
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Beamline 7.0 at Berkeley’s Advanced Light Source
BL7.0.aiProfessor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Ch05_VariablePolar.ai
Variable Polarization Undulator Radiation
Aperture andmonochromator
Crossed planarundulators
0°
yx
z21
e–
Variable phase delay(electron path length modulator)
π/2
π
–π/2
(a) (b)
e– e–
y
z
xλu
(Following S. Sasaki)
(Courtesy of Kwang-Je Kim)
Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007
Intro to Sychrotron Radiation, EE290F, 16 Jan 2007David Attwood Lecture 1
A Single Storage Ring ServesMany Scientific User Groups
1) D. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation (Cambridge, UK, 2000).2) P. Duke, Synchrotron Radiation (Oxford, UK, 2000).3) J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics (Wiley, New York, 2001).4) J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1999). Third edition.5) A. Hofmann, Synchrotron Radiation (Cambridge, UK, 2004).6) J. Samson and D. Ederer, Vacuum Ultraviolet Spectroscopy I and II (Academic Press, San Diego, 1998). Paperback available.
Ch05_References.aiIntro to Synchrotron Radiation, EE290F, 16 Jan 2007Professor David AttwoodUniv. California, Berkeley
References