Lec 01Intro2007

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Intro to Sychrotron Radiation, EE290F, 16 Jan 2007David Attwood Lecture 1

Synchrotron Radiation forMaterials Science Applications

David Attwood

University of California, Berkeley

and

Center for X-Ray Optics

Lawrence Berkeley National Laboratory

(http://www.coe.berkeley.edu/AST/srms)

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Synchrotron Radiation for Materials Science Applications(www.coe.berkeley.edu/AST/srms)

Soft X-Rays and

Extreme Ultraviolet Radiation:Principles and Applications

Cambridge 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 2:103:30 PM2007 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 versioncan 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.

orASUC bookstore

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Spring 2007 Class Schedule for Synchrotron

Radiation for Materials Science Applications

SpringClassSchedule.aiSynchrotron Radiation for Materials Science Applications

Professor David Attwood

Univ. 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 Sthr,

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)

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1 m 100 nm 10 nm 1 nm 0.1 nm = 1

10 keV

CuK

2a0

SiKOKCKSiL

1 keV

Photon energy

Wavelength

100 eV10 eV1 eV

IR VUV

Hard X-raysUV Extreme Ultraviolet

Soft X-rays

See smaller features

Write smaller patterns

Elemental and chemical sensitivity

CuK

The Short Wavelength Regionof the Electromagnetic Spectrum

Ch01_F01VG.aiProfessor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007

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+Ze

Photoelectron

Photon

()

KL

M

e

Characteristic Absorption Edges forAlmost All Elements in this Spectral Region

Ch01_F02a_F10_Tb1.ai

n = n = 4

n = 3

n = 2

n = 1

N0

M

L

K

Bindingenergy

(negative)

Kineticenerg

y

(positive)

EK, abs

Ekinetic = EK, abs

EL, abs

K

K

L L


Univ. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007

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n

N

M

L

K

44...4

NVII 4f7/2..NIV 4d3/2..NI 4s

MV 3d5/2MIV 3d3/2MIII 3p3/2

MII 3p1/2MI 3s

LIII 2p3/2LII 2p1/2LI 2s

K 1s

33...0

7/25/2...1/2

333

33

221

10

5/23/23/2

1/21/2

222

110

3/21/21/2

1 0 1/2

j

K1

Cu K1 = 8,048 eV (1.541) Cu L1 = 930 eVCu K2 = 8,028 eV (1.544) Cu L2 = 930 eV

Cu K1 = 8,905 eV Cu L1 = 950 eV

Absorption edges

for 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(1.381)

K2

L1

M1

L2L2

K1 K3 K3

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

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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 Attwood


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1

HHydrogen

1.0079

1

1s1

3

LiLithium

0.534.63

6.941

1

1s22s1

4

BeBeryllium

1.8512.32.23

9.012

2

1s22s2

2

HeHelium

4.003

1

1s2

11

Na0.972.53

22.990

1

[Ne]3s1

12

Mg1.744.303.20

24.31

2

[Ne]3s2

Sodium

Potassium

13

Al2.706.022.86

26.98

3

[Ne]3s23p1

Aluminum

14

Si2.334.992.35

1.823.54

2.093.92

28.09

4

[Ne]3s23p2

15

P

30.974

3,5,4

[Ne]3s23p3

Silicon

14

Si2.334.992.35

28.09

4

[Ne]3s23p2

Silicon

Density (g/cm3)

Concentration (1022atoms/cm3)

Nearest neighbor ()

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

16

S

32.066

2,4,6

[Ne]3s23p4

Sulfur

17

Cl

35.453

1,3,5,7

[Ne]3s23p5

Chlorine

18

Ar

39.948

1,3,5,7

[Ne]3s23p6

ArgonMagnesium

19

K0.861.33

39.098

1

[Ar]4s1

20

Ca1.532.303.95

40.08

2

[Ar]4s2

Calcium

21

Sc2.994.013.25

44.96

3

[Ar]3d14s2

Scandium

22

Ti4.515.672.89

47.88

4,3

[Ar]3d24s2

Titanium

23

V6.097.202.62

50.94

5,4,3,2

[Ar]3d34s2

Vanadium

24

Cr7.198.332.50

52.00

6,3,2

[Ar]3d54s1

Chromium

25

Mn7.478.19

54.94

7,6,4,2,3

[Ar]3d54s2

Manganese

26

Fe7.878.492.48

55.85

2,3

[Ar]3d64s2

Iron

27

Co8.829.012.50

58.93

2,3

[Ar]3d74s2

Cobalt

28

Ni8.919.142.49

58.69

2,3

[Ar]3d84s2

Nickel

29

Cu8.938.472.56

63.55

2,1

[Ar]3d104s1

Copper

30

Zn7.136.572.67

65.39

2

[Ar]3d104s2

Zinc

31

Ga5.915.102.44

69.72

3

[Ar]3d104s24p1

Gallium

32

Ge5.324.422.45

72.61

4

[Ar]3d104s24p2

Germanium

33

As5.784.642.51

74.92

3,5

[Ar]3d104s24p3

Arsenic

34

Se4.813.672.32

78.96

2,4,6

[Ar]3d104s24p4

Selenium

35

Br3.122.35

79.904

1,5

[Ar]3d104s24p5

Bromine

36

Kr

83.80

[Ar]3d104s24p6

Krypton

Rubidium

37

Rb1.531.08

85.47

1

[Kr]5s1

38

Sr2.581.784.30

87.62

2

[Kr]5s2

Strontium

39

Y4.483.033.55

88.91

3

[Kr]4d15s2

Yttrium

40

Zr6.514.303.18

91.22

4

[Kr]4d25s2

Zirconium

41

Nb8.585.562.86

92.91

5,3

[Kr]4d45s1

Niobium

42

Mo Tc10.26.422.73

95.94

6,3,2

[Kr]4d55s1

Molybdenum

4311.57.072.70

(98)

7

[Kr]4d55s2

Technetium

44

Ru12.47.362.65

101.1

2,3,4,6,8

[Kr]4d75s1

Ruthenium

45

Rh12.47.272.69

102.91

2,3,4

[Kr]4d85s1

Rhodium

46

Pd12.06.792.75

106.4

2,4

[Kr]4d10

Palladium

47

Ag10.55.862.89

107.87

1

[Kr]4d105s1

Silver

48

Cd8.654.632.98

112.41

2

[Kr]4d105s2

Cadmium

49

In7.293.823.25

114.82

3

[Kr]4d105s25p1

Indium

50

Sn7.293.703.02

118.71

4,2

[Kr]4d105s25p2

Tin

51

Sb6.693.312.90

121.76

3,5

[Kr]4d105s25p3

Antimony

52

Te6.252.952.86

127.60

2,4,6

[Kr]4d105s25p4

Tellurium

53

I4.952.35

126.90

1,5,7

[Kr]4d105s25p5

Iodine

54

Xe

131.29

[Kr]4d105s25p6

Xenon

Cesium

55

Cs1.900.86

132.91

1

[Xe]6s1

56

Ba3.591.584.35

137.33

2

[Xe]6s2

Barium

57

La6.172.683.73

138.91

3

[Xe]5d16s2

Lanthanum

72

Hf13.34.483.13

178.49

4

[Xe]4f145d26s2

Hafnium

73

Ta16.75.552.86

180.95

5

[Xe]4f145d36s2

Tantalum

74

W19.36.312.74

183.85

6,5,4,3,2

[Xe]4f145d46s2

Tungsten

Francium

87 Fr

(223)

1

[Rn]7s1

88 Ra

(226)

2

[Rn]7s2

Radium

Cerium

58

Lanthanide series

Actinide series

Ce6.772.913.65

140.12

3,4

[Xe]4f15d16s2

59

Pr6.782.903.64

140.91

3,4

[Xe]4f36s2

Praseodymium

60

Nd Pm7.002.923.63

7.543.023.59

144.24

3

[Xe]4f46s2

Neodymium

61 (145)3

[Xe]4f56s2

Promethium

62

Sm

150.36

3,2

[Xe]4f66s2

Samarium

5.252.083.97

63

Eu

152.0

3,2

[Xe]4f76s2

Europium

7.873.013.58

64

Gd

157.25

3

[Xe]4f75d16s2

Gadolinium

8.273.133.53

65

Tb

158.93

3,4

[Xe]4f96s2

Terbium

8.533.163.51

66

Dy

162.50

3

[Xe]4f106s2

Dysprosium

8.803.213.49

67

Ho

164.93

3

[Xe]4f116s2

Holmium

9.043.263.47

68

Er

167.26

3

[Xe]4f126s2

Erbium

9.333.323.45

69

Tm

168.93

3,2

[Xe]4f136s2

Thulium

6.972.423.88

70

Yb

173.04

3,2

[Xe]4f146s2

Ytterbium

9.843.393.43

71

Lu

174.97

3

[Xe]4f145d16s2

Lutetium

Thorium

90

Th11.73.043.60

232.05

4

[Rn]6d27s2

91

Pa15.44.013.21

231.04

5,4

[Rn]5f26d17s2

Protactinium

92

U Np Pu Am Cm Bk Cf Es Fm Md No Lr 19.14.822.75

19.84.89

238.03

6,5,4,3

[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

89 Ac Sg Bh Hs MtRf Db10.12.673.76

(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

75

Re21.06.802.74

186.21

7,6,4,2,1

[Xe]4f145d56s2

Rhenium

76

Os22.67.152.68

190.2

2,3,4,6,8

[Xe]4f145d66s2

Osmium

77

Ir22.67.072.71

192.2

2,3,4,6

[Xe]4f145d76s2

Iridium

78

Pt21.46.622.78

195.08

2,4

[Xe]4f145d96s1

Platinum

79

Au19.35.892.88

197.0

3,1

[Xe]4f145d106s1

Gold

80

Hg

200.59

2,1

[Xe]4f145d106s2

Mercury

81

Tl11.93.503.41

204.38

3,1

[Xe]4f145d106s26p1

Thallium

82

Pb11.33.303.50

207.2

4,2

[Xe]4f145d106s26p2

Lead

83

Bi9.802.823.11

208.98

3,5

[Xe]4f145d106s26p3

Bismuth

84

Po9.272.673.35

(209)

114(287)

4,2

[Xe]4f145d106s26p4

Polonium

85

At

(210)

1,3,5,7

[Xe]4f145d106s26p5

Astatine

86

Rn

(222)

110(271)

111(272)

112(283)

[Xe]4f145d106s26p6

Radon

5

BBoron

2.4713.71.78

10.81

3

1s22s22p1

6

CCarbon

2.2711.41.42

12.011

4,2

1s22s22p2

7

NNitrogen

14.007

3,5,4,2

1s22s22p3

8

OOxygen

16

2

1s22s22p4

9

FFluorine

19.00

1

1s22s22p5

10

NeNeon

20.180

1s22s22p6

Group

IA

IIA

IIIA IVA VA VIA VIIA VIIIA IB IIB

IIIB IVB VB VIB VIIB

VIII

Solid

Gas

Liquid

Syntheticallyprepared

Periodic_Tb_clr_May2007.ai

Broadly Tunable Radiation is Needed to Probe

the Primary Resonances of the Elements

Professor David AttwoodUniv. California, Berkeley Intro to Synchrotron Radiation, EE290F, 16 Jan 2007

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9/47


Surface science

Magnetic materials

Materials chemistry

Environmental sciences

Protein crystallogrphy

Biomicroscopy

Chemical dynamics

Typical Applications of Synchrotron Radiation

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BrightPowrfulXRs.ai

Bright and Powerful X-Rays

from Relativistic Electrons

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



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Ch05_F09VG_Jan07.ai

Synchrotron Radiation from Relativistic Electrons

xv

Note: Angle-dependent doppler shift

v

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Ch05_F11VG.ai

Synchrotron Radiation in a Narrow Forward Cone

a sin2

1

2

~

(5.1)

(5.2)

Frame moving with electron Laboratory frame of reference



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Ch05_F11modif_VG.ai

Relativistic Electrons Radiate

in a Narrow Forward Cone

a sin2

k k

k = 2/

Lorentztransformationk

k

1

2

kxkz

k

2ktan

21

2

Dipole radiation

Frame of reference

moving with electrons

Laboratory frame of reference

x

z

kx = k

kz = 2k (Relativistic Doppler shift)z

x

z=

x



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Ch05_UsefulFormulas.ai

Some Useful Formulas for Synchrotron Radiation

= 1239.842 eV nm

Ee = mc2, p = mv

= = 1957 Ee(GeV)

= = ; = ; (1 )

where

Undulator: ;

Bending Magnet: ,

Ee

mc2

1

22

1

1

v

cv2

c2

1

1 2



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e

1

F

e

1 N

F

e

1

>>

F

Ch05_F01_03.ai

Bending magnetradiation

Wiggler radiation

Undulator radiation

Three Forms of Synchrotron Radiation



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3rdGenFacilities_Jan06.ai

Third Generation Facilities, Like Electtra,Have Many Straight Sections and a SmallElectron Beam

e

Photons

X-ray Many straight

sections containingperiodic magneticstructures

Tightly controlledelectron beam

UV

Modern Synchrotron

Radiation 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



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Third Generation Synchrotron Facilities

3rdGenSynchFacil_Jan07.aiIntro to Synchrotron Radiation, EE290F, 16 Jan 2007

ESRF 6 GeV France

ALS 1.9 GeV USA

APS 7 GeV USABESSY II 1.7 GeV Germany

ELETTRA 2.0 GeV Italy

SPring-8 8 GeV Japan

MAX II 1.5 GeV Sweden

SLS 2.4 GeV Switzerland

PLS 2 GeV Korea

SRRC 1.4 GeV Taiwan

SSRL 3 GeV USA

CLS 2.9 GeV Canada

Soleil 2.5 GeV France

Diamond 3 GeV UKFacilities Under Construction

Australian 3 GeV AustraliaLight Source

Courtesy of Herman Winick, SSRL, Stanford

www-ssrl.slac.stanford.edu/SR_SOURCES.HTML

Others are in the design stage or planning an upgrade to third generation.



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Synchrotron Radiation

e

Photons

X-ray

Many straightsections containing

periodic magnetic

structures

Tightly controlledelectron beam

UV

(5.80)

(5.82)

(5.85)

Ch05_F00VG_Jan06.ai

Undulator

radiation

N

S

N

S

S

N

S

N

e

u

t

2 ns

70 psNe



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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 10 100

Photon energy (keV)

Photon

flux(ph/sec)

Ec

50%

Ee = 1.9 GeV = 400 mAB = 1.27 Tc = 3.05 keV

(5.7a)

(5.7b)

(5.8)

e

= 1mrad/ = 0.1%

Advantages: covers broad spectral range

least expensive

most accessable

Disadvantages: limited coverage ofhard x-rays

not as bright as undulator

4Ec

50%

ALS



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Ch05_F08_Jan07.ai

Undulator Radiation from a Small Electron BeamRadiating into a Narrow Forward Cone is Very Bright

Magnetic undulator

(N periods)

Relativistic

electron beam,

Ee = mc2

2

u u22

1

N

~

cen1

N

cen=

~

Brightness =

Spectral Brightness =

photon flux

(A) ()

photon flux

(A) () (/)



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An Undulator Up Close

Undulator_Close_Jan07.ai

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



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22/47

Undulator Radiation

eN

S S

N

N N

S S

u

E = mc2

=1

1 v2

c2

N = # periods

esin2 ~

1

2 cen

e radiates at the

Lorentz contracted

wavelength:

Doppler shortened

wavelength on axis:

Laboratory Frameof Reference

Frame ofMoving e

Frame ofObserver

FollowingMonochromator

For 1N

cen1

N

cen 40 rad

=u

Bandwidth:

N

= (1 cos)

= (1 + 22)

Accounting for transverse

motion due to the periodic

magnetic field:

u

22

u

22= (1 + + 22)K

2

2

where K = eB0u /2mc

Ch05_LG186.ai

~

~

~~

typically



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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 observedradiation wavelength is not quite so short. The force equation for an electron is

where p = mv 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 cos2zu

y

z

x

v

e

= e(E + vB)dp

dt

e(vB)dp

dt



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Calculating Power in the Central Radiation Cone: Usingthe well known dipole radiation formula by transformingto the frame of reference moving with the electrons

Ch05_T4_topVG.ai

e

*e

z

N periods

x

z

Lorentz transformation

Lorentztransformation

sin2

= N

u

u

x

z= N

cen =

1

* N

=u*

Determinex, z, tmotion:

x, z, tlaboratory 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 + vB)

m = e B0 cos

vx(t); ax(t) = . . .

vz(t);

az(

t) =

. . .

dp

dt

dvx

dt

dz

dt

2zu

dP

d

e2

a2 sin2

1620c3

= (1sin2 cos2 ) cos2utdP

d

e2

c2

40u

K2

(1 +K2/2)22



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Power in the Central Cone

Ch05_LG189_Jan06.ai

Pcen =

cen=

e2I

0u K2

2

eB0u2m0c

1

N

1

N

= / 1+ K2

2

x = (1 + + 22)u22

K2

2

K =

cen =

N periods

1

1N

cen =

e

u

Photon energy (eV)

Pcen

(W)

Tuning

curve

= N

ALS, 1.9 GeV

400 mA

u = 8 cmN = 55

K = 0.5-4.0

0 100 200 300 4000

0.50

1.00

1.50

2.00

(1 + )2

K2f(K)



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0 500 1000 1500 20000

0.5

1

1.5

2

2.5

cen =

1

* Nn = 1

n = 3

Pcen (W)

= 3720u = 50 mmN = 89

= 400 mAcen = 35 r

ALS

1

N

1

3N

=

1

=

3

= 89

= 270

= 3330u = 49 mmN = 84

= 200 mA

cen = 35 r

n = 1

n = 30.2

0.4

0.6

0.8

1.0

= 84

BESSY II

= 250

Pcen (W)

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

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cen =

1

* N

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

1

N

1

3N

=

1

=

3

0

5

10

15

n = 1

APS

n = 3

0 5 10 15 20 25

15

10

5

0

n = 1

n = 3

Pcen

(W)

= 11,800u = 42 mmN = 38

= 200 mAcen = 17 r

= 13,700u = 33 mmN = 72

= 100 mA

cen= 11 r

ESRF

Pcen (W)

= 38

= 120

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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 perfect

optical systems, and thus is useful in designingbeamlines and synchrotron radiation experiments

which involve focusing to small areas.

Spectral brightness is that portion of the brightness lying within a relative spectral bandwidth /:

B

Asds Ai

Perfect optical system:

As s= Ai i ; = 100%

s

s i

i



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Ch05_F24VG_Feb04.aiProfessor David Attwood

Univ. California Berkeley

Spectral Brightness is Useful for Experiments

that Involve Spatially Resolved Studies

Brightness is conserved(in lossless optical systems)

Starting with many photons in asmall source area and solid angle,permits high photon flux in aneven smaller area

opticsource

dsource

dsourcesource = dfocusoptic

dfocus

Smaller

after focus

Large in a

focusing optic

1-2 GeV

Undulators

6-8 GeV

Undulators

Wigglers

Bending

magnets

10 eV 100 eV 1 keV 10 keV 100 keV

Photon energy

Spectralbright

ness

12 nm 1.2 nm 0.12 nm1020

1019

1018

1017

1016

1015

1014

Intro to Synchrotron Radiation, EE290F, 16 Jan 2007

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d

Ch08_F00_Jan07.ai

e

lcoh = 2

/2{temporal (longitudinal) coherence}

d = /2 {spatial (transverse) coherence}

or d 2FWHM = 0.44

(8.3)

(8.5)

(8.5*)

Pcoh,/= 1 (K)

(8.6)

(8.9)

(/2)2

(dxx)(dyy)

0

euI(/)N2

80dxdy

Pcoh,N= Pcen

u



Coherence at Short Wavelengths

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Spatial and Spectral Filtering to ProduceCoherent Radiation

Courtesy of A. Schawlow, Stanford

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Spatially Coherent Undulator Radiation

= 13.4 nm

1 mD pinhole

25 mm wide CCD at 410 mm

Courtesy of Patrick Naulleau, LBNL / Kris Rosfjord, UCB and LBNL

d ? =

2

= 2.5 nm

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Coherent Power at the ALS

Ch09_U5cohPwrALS_Feb06.ai

1.9 GeV, 400 mA

u = 50 mm, N = 89

0.5 K 4.0

x = 260 m, x = 23 r

y = 16 m, y = 3.9 r

euv = 10%, sxr= 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)

Pcoh,

N(m

W)

Pcoh,

/(

W)

Pcen

(W)

= 89

= 103

= 103Pcoh,n=3(W)



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Ch08_BESSYII_Feb06.ai

1.7 GeV, 200 mA

u = 49 mm, N = 84

0 K 2.5

x = 314 m, x = 18 r

y = 24 m, y = 2 r

euv = 10% ; sxr= 2%0 500 1000 1500 2000

102 1030

50

100

150 30

20

10

0

Photon Energy (eV)

Pcoh,

/

(W)

Pcen

(W)

n = 1

n = 3

n = 1

n = 3

= 103

= 103

0

0.2

0.4

0.6

0.8

1.0

0

5

10

15

102 103

Photon Energy (eV)

Photon Energy (eV)

Pcoh,N

(mW)

n = 1

n = 3

= 84

Coherent Power at BESSY II

Pcoh,n=

3(W)



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AiryPattrn600eV.ai

Spatially Coherent Soft X-Rays With Pinhole

Spatial Filtering: Airy Patterns at 600 eV

= 2.48 nm (600 eV)

d = 2.5 mt = 200 msec

ALS beamline 12.0.2

u = 80 mm, N = 55, n = 3

Courtesy of Kristine Rosfjord, UC Berkeley and LBNLProfessor David Attwood


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S. Eisebitt, J. Lning, W.F. Schlotter, M. Lrgen, O. Hellwig, W. Eberhardt & J. Sthr / Nature, 16 Dec 2004

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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 =

= 1 + + 22

K = 4

0 1 2 3 4

Photon energy (KeV)

(Courtesy of K.-J. Kim)

(Courtesy of R.P. Walker and B. Diviacco)

Spectralbrightne

ss

Spectralbrightness

Spectralbrightness

u = 5 cm, N = 89

Undulator radiation (K < 1)~

eBou2mc

c =

u22

K2

2

1.5 GeV

400 mA

0 0

Higher photon energies

Spectral continuum

Higher photon flux (2N)

Wiggler radiation (K >> 1)

2eBom

3

2

3K

4

K2

2nc = 1 +

1/N

Frequency (f)

f1 f3 fn fn + 2

0

dP

d

Elettra

2 GeV

0.4 A

u = 6.0 cmN = 72

K = 3.7

nc = 22

1016

1015

1014

1013

101 102

Photon energy (eV)

Photonflux(photons/sec0.1%BW)

103 104



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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 K/ (eq. 5.21). Because the emission angles are large, one tends to

use larger collection angles, which tends to spectrally merge nearby harmonics. The resultis 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)

Photonflu

xperunitsolidangle

per0

.1%b

andwidth

(relativeunits)

BendingMagnet

Radiation

WigglerRadiation

2N

c



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StanfordWiggler.ai

Stanford Permanent Magnet Wiggler

LBNL/EXXON/SSRL (1982), SSRL Beamline VI

55 pole (N = 27.5),

w = 7 cmProfessor David Attwood


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Facility ALS BESSY II ESRF SP-8

Electron energy 1.90 GeV 1.70 GeV 6.04 GeV 8.00 GeV 3720 3330 11,800 15,700Current (mA) 400 200 200 100Circumference (m) 197 240 884 1440

RF 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 0.429 Bending 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 3.20 Number of periods 89 84 38 14Photon 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 Tuning range (n = 1) 230-620 eV 140-500 eV 2.6-7.3 keV 4.7-19 keV

Tuning range (n = 3) 690-1800 eV 410-1100 eV 7.7-22 keV 16-51 keVCentral cone half-angle (K= 1) 35 rad 33 rad 17 rad 6.6 radPower 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

Typical Parameters forSynchrotron Radiation

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Ch05_F01b_BLtransport.ai

Beamlines are Used to Transport Photons tothe Sample, and Take a Desired Spectral Slice

Photon

flux

Grating

or crystal

Monochromator

Exit

slitCurved

focusing

mirror

(glancing

incidence

reflection)

Focusing

lens (pair

of curved

mirrors,

zone plate

lens, etc.)

Sample

Photon

flux

e

Observe at sample:

Absorption spectra Photoelectron spectra Diffraction



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BendingMagnet

e

M1 (spherical)

M2 (spherical)

Plane VLSgratings

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.)



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Sample

Translatingexit slitTranslatingentrance

slit

Sphericalgrating

Horizontialdeflection/focusingmirror

Verticalfocusingmirror

Verticalfocusingmirror

Horizontalfocusingmirror

EllipticallyPolarizingUndulator

meVresBL.ai

High Spectral Resolution (meV) Beamline



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Beamline 7.0 at Berkeleys Advanced Light Source

BL7.0.ai



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Ch05_VariablePolar.ai

Variable Polarization Undulator Radiation

Aperture andmonochromator

Crossed planarundulators

0

y

x

z21

e

Variable phase delay(electron path length modulator)

/2

/2

(a) (b)

e e

y

z

xu

(Following S. Sasaki)

(Courtesy of Kwang-Je Kim)



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A Single Storage Ring ServesMany Scientific User Groups

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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.

I t t S h t R di ti EE290F 16 J 2007Professor David Attwood

References

Lec 01Intro2007

Documents

Transcript of Lec 01Intro2007