Intro to Sychrotron Radiation, EE290F, 16 Jan 2007 David Attwood Lecture 1 Synchrotron Radiation for Materials 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)
47
Embed
Synchrotron Radiation for Materials Science Applicationsattwood/srms/2007/Intro2007.pdf · David Attwood Lecture 1 Intro to Sychrotron Radiation, EE290F, 16 Jan 2007 Synchrotron Radiation
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Intro to Sychrotron Radiation, EE290F, 16 Jan 2007David Attwood Lecture 1
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
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
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:
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)
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
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