Synchrotron Radiation for Materials Science Applicationsattwood/srms/2007/Intro2007.pdf · David Attwood Lecture 1 Intro to Sychrotron Radiation, EE290F, 16 Jan 2007 Synchrotron Radiation

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: [email protected]• 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



• 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


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


—

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


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


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


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


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


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


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


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)


An Undulator Up Close

Undulator_Close_Jan07.ai

ALS U5 undulator, beamline 7.0, N = 89, λu = 50 mm


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


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


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


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)


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


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


MAX II

Pcen (W)

Power in the Central Radiation ConeFor Three Soft X-Ray Undulators


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


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


Coherence at Short Wavelengths


Spatial and Spectral Filtering to ProduceCoherent Radiation

Courtesy of A. Schawlow, Stanford


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

)


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

)


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


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


StanfordWiggler.ai

Stanford Permanent Magnet Wiggler

LBNL/EXXON/SSRL (1982), SSRL Beamline VI55 pole (N = 27.5), λw = 7 cm


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


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••


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.)


Sample

Translatingexit slit

Translatingentrance

slit

Sphericalgrating

Horizontialdeflection/focusing

mirror

Verticalfocusing

mirrorVerticalfocusing

mirror

Horizontalfocusing

mirror

EllipticallyPolarizingUndulator

meVresBL.ai

High Spectral Resolution (meV) Beamline


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)



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

Documents

Synchrotron Radiation for Materials Science Applicationsattwood/srms/2007/Intro2007.pdf · David Attwood Lecture 1 Intro to Sychrotron Radiation, EE290F, 16 Jan 2007 Synchrotron Radiation