Light Sources IITakashi TANAKARIKEN SPring-8 Center

Outline• Introduction• Fundamentals of Light and SR• Overview of SR Light Source• Characteristics of SR (1)• Characteristics of SR (2)• Practical Knowledge on SR

What is SR Light Source?
Magnets to deflect the electronbeam and generate SR.
Bending Magnet (BM)
S

N

N

S

S

N

N

S

S

N

N

S

S

N

N

S

S

N

N

S

S

N

N

S

N

S

N
Insertion Device (ID)S3

Bending Magnet• One of the accelerator components inthe storage ring.
• Generate uniform field to guide theelectron beam into a circular orbit.
• EMs combined with highly-stable power
supplies are adopted in most BMs tosatisfy the stringent requirement on field
quality and stability.
• Superconducting magnets are used in a
few facilities in pursuit of harder x rays.
4

Insertion Device• Installed (inserted) into the straightsection of the storage ring between
two adjacent BMs.
• Generate a periodic magnetic field to
let the injected electron beam movealong a periodic trajectory.
• Most IDs are composed of PMs, while
EMs are used for special use such as
helicity switching.
• Two types: wiggler and undulator
5Magnetic Circuit of IDs
ygx
λuz

Halbach typepole piece
Hybrid typeIn each type, a sinusoidal
magnetic field is obtained:
6

Example of ID Magnets
Halbach-type Magnet Array for
SPring-8 Standard Undulators

e- Beam

NdFeB Magnet

cooling channel
7

Example of SR Image
BL41XU@SP-8, first image of SR
with a fluorescent screen (<0.1mA)
SR from Downstream BM
SR from Undulator

SR from Upstream BM

g = 50 mm

g = 20 mm
8Comparison of SR Light Sources
Photon Flux Density(photons/sec/mrad2/0.1%b.w.)

1019
1018

Undulator (BL09XU)

1017
1016

Wiggler (BL08W)

1015
1014

Bending Magnet

1013
1012 110102103
104
Photon Energy (eV)

105

106
9Outline• Introduction• Fundamentals of Light and SR• Overview of SR Light Source• Characteristics of SR (1)– Radiation from Bending Magnets• Characteristics of SR (2)• Practical Knowledge on SR

Directionality of BM Radiation
e-e-

𝛾 −1

Directional(V-plane)
Isotropic(H-plane)

BM radiation is similar
to a beacon lamp Sheet beam 2D directionality

11

Pulse Structure of BM Radiation
𝛾 −112

Intensity

Pulse Structure of BM Radiation∆τTime13

What’s the Pulse Duration?

𝟐𝝆𝜸−𝟏
𝝆𝟐𝜸−𝟏𝛾 −1
Pulse duration for e-Δ𝑡 = 2𝜌𝛾 −1 /𝑐Time Squeezing
Pulse duration for observerΔ𝑡𝜌Δ𝜏 = 2 = 32𝛾𝛾 𝑐

14

Spectrum of BM Radiation𝐸� (𝜔)𝐸(𝑡)Fourier
Transform

Δ𝜏𝑡Δ𝜔

 BM radiation has a white spectrum
reaching the frequency of Δ𝜔~1/Δ𝜏~𝛾 3 𝑐/𝜌 𝜔𝑐 =32Δ𝜏

=3𝛾3 𝑐2𝜌𝜔(“critical frequency”) givesa criterion for BM spectrum.
 In practical units,ℏ𝜔𝑐 (keV) = 0.665𝐸 2 GeV 2 𝐵(T)15

Example of Spectrum
Photon Flux (photons/sec/0.1% B.W.)

1013∆θx=0.1mrad

Larger aperture collects
photons with lower energies

1012

1011

∆θy=10mrad∆θy=0.1mrad

1010

109 010101

Critical
Energy102
103
104
Photon Energy (eV)

105

106
16

Angular Profile of BM Radiation
Noramlized Density (arb.unit)

1.2
1.0

ω/ωc=10-2ω/ωc=10.8

γ-10.6ω/ωc=10-1

0.4
0.2

ω/ωc=10Power Profile

0.00.00

0.05

0.10
0.15
0.20
θy(mrad)Empirical formulafor angularof profileBM radiation
 power divergenceprofile ~ fluxat ωc−1𝜎=0.6𝛾
𝜔/𝜔 larger angularfor
𝑦𝑦 divergence𝑐 lower energy

17Outline• Introduction• Fundamentals of Light and SR• Overview of SR Light Source• Characteristics of SR (1)• Characteristics of SR (2)– Electron Trajectory in IDs– Wiggler Radiation– Undulator Radiation• Practical Knowledge on SR

Coordinate Systems𝑦𝑥
𝜃𝑦 ~𝑌/𝑍

𝜃𝑥 ~𝑋/𝑍𝒓(𝑡) = (𝑥𝑒 𝑡 , 𝑦𝑒 𝑡 , 𝑧𝑒 𝑡 )𝑹 = (𝑋, 𝑌,𝑍)𝑧Assuming 𝒓 ≪ 𝑍 (farfield approximation), theradiation pattern depends
only on 𝚯 = (𝜃𝑥 , 𝜃𝑦 )19

Field Integrals

Equation of motion of an electron
moving in a magnetic field B

𝐼1 , 𝐼2 : 1st and 2nd field integrals of the ID
20

Trajectory in an Ideal ID

Magnetic Field

Velocity

Position K Value Deflection Parameter

E=8GeV,K=1,λu=5cm：βxmax=64µrad, xmax=0.5µm

21Effects due to the ID Magnetic Field
transverse
velocity
Oscillating Term

longitudinalvelocity
Original value

Average Value 𝜷𝒛

ID field induces: transverse (x) oscillation
 longitudinal (z) oscillation
 effective deceleration (Δ𝛽𝑧 = 𝐾 2 /4𝛾 2 )22General Form of Time Squeezing

Time squeezing takes place most significantly
when the electron is moving in the directionof observation (𝜷 = 𝜽).

23

Outline• Introduction• Fundamentals of Light and SR• Overview of SR Light Source• Characteristics of SR (1)• Characteristics of SR (2)– Electron Trajectory in IDs– Wiggler Radiation– Undulator Radiation• Practical Knowledge on SR

Wiggler Radiation• Wiggler radiation (WR) is regarded
as incoherent sum of SR emitted
at each position of wiggler.
– Summation as photons in theframework of geometrical optics.

𝐹𝑤 ~2𝑁𝐹𝐵𝐵
Flux :
Emittance : 𝜎𝑥𝑥,𝑦𝑦 × 𝜎𝑥,𝑦 ≫ 𝜆/4𝜋
Brilliance :𝐵𝑤 ≪ 2𝑁𝐵𝐵𝐵

25

Photon Distribution in Phase Space
phase ellipse ofx’,y’ lightx’,y’
diffraction-limited
x,yx’,y’x,yx’,y’x,y𝜎𝑥,𝑦x’,y’𝜎𝑥𝑥,𝑦𝑦 x,yx,yBeam Waist Position• Larger N results in larger area ofphoton distribution in the phasespace, i.e., larger emittance.
• B does not linearly depend on N

26

Comparison with BM Radiation
BM (εc=29keV),

1017

Wiggler (εc=38keV), N=37

Flux Density, Brilliance

Flux Density

Brilliance

1016

1015

1014

1013

103

104

105

Photon Energy (eV)

106

103

104

105

106

Photon Energy (eV)27

Outline• Introduction• Fundamentals of Light and SR• Overview of SR Light Source• Characteristics of SR (1)• Characteristics of SR (2)– Electron Trajectory in IDs– Wiggler Radiation– Undulator Radiation• Practical Knowledge on SR

Fundamental Wavelength of UR
λuzperiod of electron motion= period of emitted lightTimeSequeezingθ

period of observed lightFundamental Wavelength λ1H. Kitamura et al.,J. Appl. Phys. 21 (1982) 1728

29

UR with Infinite Periods• If the undulator length is infinite, the pulse
duration is infinitely long, and thus theradiation is completely monochromatic withline spectrum.
• In practice, the undulator length is finite,
so the line spectrum is broadened.
infinite
periodsfω1

finiteperiods

f
ω

ω1

ω
30

Effects due to Finite Periods
λ1/cElectric Field at Observert

T=Nλ1/c

Fourier Transform

Square of “sinc” function dominates UR31

Brief Note on UR Formulae• In the previous derivations of UR
spectral function, no knowledge onelectrodynamics is required.
• In practice, E0 is a complicatedfunction of θ and K, and needs to be
calculated by Fourier transforming
the electric field derived from theLienard-Wiecherd potential.
• However, the simple derivation gives
us a clear understanding on URproperties.

32

Normalized Flux Density

Energy Spectrum of UR

1.0

𝜃=00.8
0.6
0.4

N=5
N=10
N=100

0.2
0.0-0.4-0.2
0.00.20.4
Normalized Photon Energy (ω-ω1)/ω133Angular Profile of UR𝜔 = 0.9𝜔1 (0)𝜔 = 𝜔1 (0)𝜔 = 1.1𝜔1 (0)34Angular Divergence of UR
UR is not a Gaussian Beam
Angular Profile at ω=ω1(0)Gaussian Profile with σr’“Natural” Angular
Divergence of UR(𝐿 = 𝑁𝜆𝑢 )35Source Size of UR“Natural” Angular
Divergence of UR(𝐿 = 𝑁𝜆𝑢 ) Unlike WR, UR is spatiallycoherent, i.e., diffraction limited.
 This means that 𝜎𝑟 𝜎𝑟′ = 𝜆/4𝜋
“Natural” Source
size of UR

Longer device results in smaller angulardivergence & larger source size, but theemittance does not change.

36

Higher Harmonics
Photons with at nω1 are observed aswell as at ω1, where n is an integer.
K=0.1

Normalized Flux Density

1.0

K=0.5

K=1

K=30.55th
3rd

1st0.0050

100 050

100 050

Photon Energy (keV)

100 05010037

K << 1 Case

Electric Field

𝐾𝛾 −1Time38

K ~ 1 Case

Electric Field

𝐾𝛾 −1Time39

K >> 1 Case

Electric Field

𝐾𝛾 −1Time40

Mechanisms of Higher Harmonics
K<<1K~1K>>1Electron Orbit

Radiation E-field

Spectrum41

Outline• Introduction• Fundamentals of Light and SR• Overview of SR Light Source• Characteristics of SR (1)• Characteristics of SR (2)• Practical Knowledge on SR

Effective Properties of SR• Properties of SR emitted from an e- beam
are different from those from a single e-.
• They are referred to as “effective” propertiesof SR, as opposed to “natural” properties.
SourceSizePulse
LengthAngularDiveergence43

Example in SPring-8: E-t Phase Space
20psec0.1%

Electron Beam

0.05psec

Undulator Radiation

Energy1%

100%

0.7fsec

BM Radiation
Time44

Example in SPring-8: (x,y) Space700µm
15µmElectron Beam
5.6µm

yUndulator Radiation
5.6µm
1.7µm

x

BM Radiation

45

Example in SPring-8: (x’,y’) Space
29µrad
2.6µradElectron Beam
7.8µrady'Undulator Radiation

60µrad1500µradBM Radiationx'

46

Convolution Between e- and Photon
x’,y’,ω

Electrondistribution

x’,y’,ω

x,y,tx’,y’,ω

x,y,tConvolution

Photon distribution
from a single e-x,y,t

Photon distribution
from e- beam

Broadening of temporal (t),spectral (ω), spatial (x,y)
and angular profiles (x’,y’).

47

Photon Flux Density (arb.unit)

Spectral Profile (UR)
Emittance (m.rad)
10-10
10-9
10-8
10-7

0.94

0.96

0.98

1.00

E-spread (%)
0.001
0.01
0.1
11.02

1.04 0.94

0.96

0.98

Relative Photon Energy(ω1)

1.00

1.02

1.0448Angular & Spatial Profile (UR)
Angular profile of UR
from a single electron

σr'

Σy'
Effective Angular Div.

Convolutionσy'Gauss approximation
Convolution theorem

Σx'
σx'

Angular profile of UR
from the e-beamAngular profile of the e-beam

Effective Source Size49

Heat Load on Optical Elements• SR is usually processed by severaloptical elements before irradiation tothe sample, such as the focusing
mirror, monochromator.
• These elements can be easily
damaged by the heat load of SR.
• In the case of UR, the heat load canbe reduced by taking advantage of thedifference in the angular profile of thephoton flux and radiation power.
50

Spatial Profile of Power and Flux (UR)22Fluxy(mm)

Power
1

100-1-1-2-2-2-10x(mm)12-2-1012x(mm)The power profile is much broader than the flux.
Extraction of SR with an appropriate slit is thus effective.
51

What’s the Optimum Aperture Size?
700

1.0

600

0.8
500
0.6

4000.4300

PowerPower (W)Photon Flux (1015)

Flux200

0.2
1000.0002

46

Slit Size (Σx,Σy)81052

Wiggler? Undulator? (1)• Wigglers are identical to undulator
from the point of view of magnetic
circuit.
• It is generally said that the K value
distinguishes between the two,
however, this is not exactly correct.
• What we should take care is thephoton energy region of interest.

53

Wiggler? Undulator? (2)undulatorwiggler

Photon Flux
(photons/sec/0.1%B.W.)

1015
1014
1013
1012

λu=12cm
K=10∆x=∆y=3mm@30m

1011
1010
101102

103

104

105

Photon Energy (eV)54

Undulator Radiation Gallery• For quantitative evaluation of SR, a
computer code “SPECTRA” is available.
• SPECTRA also offers a function to“visualize” the computation results
for further understanding of SR.
– brilliance curve & spectrum– on- and off-peak angular profiles of flux
– on- and off-axis spectra– effects of opening the slit aperture– undulator-to-wiggler transition

55

Brilliance Curve & Spectrum
Spectrum –, Peak Brilliance 1st – 3 rd – 5 th –56

Opening the Slit Aperture57

Off-Axis Spectrum
Moving the slit along – x, – y58

Flux Angular Profile
On-Axis Spectrum

Angular Profile(Finite Emittance)

Angular Profile(Zero Emittance)

59Undulator-to-Wiggler Transition

60

Angular Divergence & Source Size

𝜌 Δ𝜃2 22Δ𝜃~2𝜎𝑥𝑥~2𝜎𝑥

𝜌Δ𝜃
𝜆
𝜌Δ𝜃
𝜎𝑦𝑦 =𝜎 𝜎𝑦𝑦 =4𝜋𝜎𝑦𝑦2 𝑦𝑦

𝜎𝑦 ~ 𝜎𝑦𝑦 2 + 𝜎𝑦𝑓 2𝜎𝑦𝑦61