Light Sources I
Takashi TANAKARIKEN SPring-8 Center

Cheiron 2014, Light Source I1

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

Lecture I?

Lecture II?

2

Outline• Introduction• Fundamentals of Light and SR• Overview of SR Light Source• Characteristics of SR (1)• Characteristics of SR (2)• Practical Knowledge on SR3

Overview of SR Facility
SR Light Source(Undulator)

Accelerators

ExperimentalHallCheiron 2014, Light Source I4

Whatʼs the Advantage of SR?
Brilliance vs. wavelengthfor various light sources
LightSourceSun
X-ray Tube
Light Bulb
SRTotal Power(W)
1026
103
102
103~104

Radiation power
Comprehensive understandingofforvarious light sources
SR (and light source)
is required
for efficient experiments.
Cheiron 2014, Light Source I

5

Topics in This Lecture (1)• Fundamentals of Light and SR– General description of light– Why we need SR?
– Physical quantity of light– Uncertainty of light: Fourier anddiffraction limits– SR: Light from a moving electron• Overview of SR Light Source– Types of light sources– Magnet configuration
Cheiron 2014, Light Source I6

Topics in This Lecture (2)• Characteristics of SR– Radiation from bending magnets– Electron Trajectory in insertion devices– Radiation from insertion devices• Practical Knowledge on SR– Finite emittance and energy spread– Heat load and photon flux
– Evaluation of optical properties of SR– Definition of undulators and wigglers– Numerical examples
Cheiron 2014, Light Source I7

Outline• Introduction• Fundamentals of Light and SR– General description of light– Why we need SR?
– Physical quantity of light– Uncertainty of light: Fourier anddiffraction limits– SR: Light from a moving electron

8What is Light?
What is light? It is a kind of wave, but…
Surf
Water

VariousWaves

RippleWater

String Phone
StringSoundAir

What propagates the light wave?
Electric and Magnetic Field

Cheiron 2014, Light Source I

9Electric Field+++++++e--

The E-field is generated byelectric charges, and gives aforce on a charged particle.
Cheiron 2014, Light Source I

10Magnetic Field

e-The M-field is generated by moving
electric charges, and give a force ona moving charged particle.

Cheiron 2014, Light Source I11

Electro- and Magnetostatic Phenomena
Thunder(charge in cloud)Van de Graaff
Generator

Motions of electrons (charges)
Electrostaticare stationary or steady.
We do not observe any
Electromagnet
radiation in such a steady state.
Permanent
MagnetCheiron 2014, Light Source I

Magnetostatic 12

Non-Steady State: Thought Experiment3x108me-Electric Field Linee+e+e+

Does e+ moves simultaneously? If so,
the information on e- propagateswith an infinite speed!
Cheiron 2014, Light Source I13

Non-Steady State: Thought Experiment3x108me-e+e+e+

Information on e- (Efield) propagates withthe speed of light!
Cheiron 2014, Light Source I

14

E-Field Line Is Not “Rigid”

e-e+e+e+

Electric field line canpropagate as a wave
Source of Light
Cheiron 2014, Light Source I

15

Light as an Electromagnetic Wave
(magnetic vector)(electric vector)(wavelength)

Electric and magnetic
fields can propagate
as a transverse wave
Cheiron 2014, Light Source I

Analysis of, gives all
the information on light.
(axis of propagation)
16

Light as a Photon
Light is not only an electromagnetic
wave but also a particle, or a photon.
EM wave with awavelength of 0.1nm
0.1nm (1 )Photons with anenergy of 12.4 keV
Cheiron 2014, Light Source I

17

Wave? Photon?
PhotonPhotoelectric Effect

EM Wave

Interference/Evaluation of SR
characteristics(brilliance, flux, …)
Cheiron 2014, Light Source I

Polarization

Formulation of SR withclassical electrodynamics(field amplitude)18

Outline• Introduction• Fundamentals of Light and SR– General description of light– Why we need SR?
– Physical quantity of light– Uncertainty of light: Fourier anddiffraction limits– SR: Light from a moving electron

19

Observation with Light
Light Source(Bulb)

ComputerSRAnalyzer(Brain)

High-quality light source foran accurate observation!
Reflection

Diffraction

Object(flower)

Detector(eye)Protein Crystal

ＣＣＤ Camera

Cheiron 2014, Light Source I

20

Which Quality is Better?
Specs of SPring-8- E = 8GeV
- I = 100mA- L = 1500m

1mW Laser (pointer)

100W Bulb

Lighting equipment in a room: Bulb
Pointer during a presentation: Laser

Depends on the Object!
Cheiron 2014, Light Source I21

How to Define the Quality of Light?(1)ObjectLight Source Quality:
Light Source
How efficiently these
conditions are satisfied?
Detector

Illumination& Interaction

Detection &Analysis

Cheiron 2014, Light Source I22

How to Define the Quality of Light?(2)Important Features of the Light Source
Item

ObjectFlower Protein

Radiation Power◎○Source Size×△△◎◎◎

Directivity
Monochromaticity

Cheiron 2014, Light Source IWhy?
# Emitted
Photons
IlluminatedArea
Accuracy ofAnalysis

Brilliance23

What is Brilliance ?
Brilliance(photons/sec/mm2/mrad2/0.1%B.W.)
Total Power~Source Size x Angular Divergence x Band Width• Brilliance specifies the quality of lightfor observation of microscopic objects.
• The brilliance of a light source with ahigh total power is not necessarily
high.
Cheiron 2014, Light Source I24

Example of Brilliance Estimation
ItemBulb

Laser Pointer

Total Power (W)

100

10-3

Angular Div. (mrad2) 4x106 1
Source Size: (mm2)1021Bandwidth: (%)

1000.01

Brilliance(photons/sec/....)~108~1016

Laser is the best light source toobserve the microscopic object!
Cheiron 2014, Light Source I

25

X ray as a Probe• Definition (not unique)– Electromagnetic wave (= light) with l of
10 nm(10-8 m) ~ 0.1Å(10-11 m)• Properties– High Energy/Photon– High Penetration (Roentgen etc..)• Application to Microscopic Objects– X-ray Diffraction– Fluorescent X-ray Analysis• No Practical Lasers!! (until recently)
Cheiron 2014, Light Source I

Synchrotron Radation (SR)26

Outline• Introduction• Fundamentals of Light and SR– General description of light– Why we need SR?
– Physical quantity of light– Uncertainty of light: Fourier anddiffraction limits– SR: Light from a moving electron27Phase Space Representation-x'1

zx'1x'x'1

x1x'1x2

x-x'1
Real Space

Cheiron 2014, Light Source Ix1x2x-x'1
Phase Space28

Photon Propagation in Phase Spacezx'
Beam
Envelope
Waist

Cheiron 2014, Light Source Ixx

Liouvilleʼs Theorem:
Area of the phase ellipse(beam emittance) is constant.
29

zx'

Beam Size

Beam
Envelope
Source Size

Beam Sizex

AngularDivergence

Photon Propagation in Phase Spacex

Beam Size
Beam Size
Cheiron 2014, Light Source I

Source Size
30

Energy-Time Phase Space
E=E=

Dispersivemedium

Pulse LengthttBand
Width

Cheiron 2014, Light Source I

Pulse compression
scheme (optical laser)

31

6D Phase Space & Brilliancexʼ,yʼ,

Motion of each photon can bedescribed in a space spanned by
the 6 coordinates (phase space)
x,y,t
Photon distribution function in
the 6D phase space gives full
information on light source

Typical form of the photon distribution,, ,exp, ,′2Brilliance

Cheiron 2014, Light Source I

22Source Size

Central Freq.

′2

AngularDivergence

22PulseLengthBand
Width32

Photon Flux & Radiation Power
Photon Density in 6D Phase SpaceIntegrate overIntegrate
overAngular Flux Density

Total Flux
Integrate
overCheiron 2014, Light Source I

Integrate
overAngular Power Density

Total Power

Integrate
over33

To Be More Specific…

Cheiron 2014, Light Source I34

To Be More Specific…
AngularAngular
BrilliancePower Density
Flux Density
y'x,yx,yny'x=y=0,
=cy'nnx'x'Spectrum ofFlux (Density)
Slitx'

Profilexʼ,yʼ
Monitorxʼ,yʼ
Monochromator

Experimental Setup forLight Source Measurement

Cheiron 2014, Light Source I35

Outline• Introduction• Fundamentals of Light and SR– General description of light– Why we need SR?
– Physical quantity of light– Uncertainty of light: Fourier anddiffraction limits– SR: Light from a moving electron

36

Uncertainty of Lightxʼ,yʼ,

(xʼ2,yʼ2,2)(x1,y1,t1)(x2,y2,t2)x,y,txʼ, yʼ, (xʼ1,yʼ1,1)

x,y,t

Cheiron 2014, Light Source I

Light as a photon can be
fully described by the 6
coordinate variables.

Because of the wave nature,they have some uncertainty
characterized by the so-called
Fourier transform.
37

Monochromatic & Plane Wave

Monochromatic & Plane Wave
 Purely sinusoidal
 Constant amplitudex'Cheiron 2014, Light Source I

Electric-field wave

38

In Reality…
• A monochromatic and plane wave isan (ideal) form of a wave.
• In practice, a wave is composed ofmany ideal waves having different and xʼ.
• Fourier Transform is a mathematicaloperation to decompose an arbitrary
wave into a number ofmonochromatic and plane waves.
Cheiron 2014, Light Source I

39

Composition of Monochromatic Waves
E(t)

=0

=0

=20

=30

=40tE(t)tCheiron 2014, Light Source I40

ご連絡ありがとうございました。それでは人事公募の内容が確定次第 原稿を作成し、お送りします。遅くとも月末までには準備できると思 います。

Time & Frequency Domains
1.00.5

Fourier
Transform
0.5E(t)Amplitude

1.00.0Inv. Fourier
Transform

-0.5

0.0
-0.4

-0.2

0.0

t/T0

0.4
0 1 2 3 4 5 6 7 8 9 10
Fourier
Transform Pair Frequency/00.2

Time Domain: waveform asa function of t
Cheiron 2014, Light Source I

Frequency Domain: wave
amplitude as a function of  41

How Does the Waveform Changes?
1.0

1.0113570000 190400-0.5When  increases, t decreases,and vice versa
0.0E(t)0.0

Amplitude

0.5

t-0.4

-0.2

0.0

t/T0
Cheiron 2014, Light Source I

0.2

0.4

0.5

01020304050

Frequency/042

Uncertainty Relation• t and  are regarded as uncertainty
of a photon– t: longitudinal position (pulse width)– : photon energy (bandwidth)
1.0

1.0

Amplitude

0.5

E(t)

t Uncertainty relation:

0.0

0.5

0.0

-0.5
-0.4

-0.2

0.0

Cheiron 2014, Light Source I

t/T0

0.2

0.40102030

Frequency/0405043

Composition of Plane Waves
xxz

f0

E(x)

xcosx'

Cheiron 2014, Light Source I/ ′2E(x)Wavenumber
Vector44

Composition of Plane Waves
xx
E(x)

E(x)

kx=0
kx=k0
kx=2k0kx=3k0kx=4k0Cheiron 2014, Light Source I45

Spatial & Angular Domains
1.00.5

Fourier
TransformE(x)Amplitude

1.00.5Inv. Fourier
Transform

0.0

Fourier
0.2
0.40 1 2 3 4 5 6 7 8 9 10Transform
Pair0.0-0.5-0.4-0.2

0.0x

Spatial Domain: waveform
as a function of x
Cheiron 2014, Light Source I

k/k0

Angular Domain: wave
amplitude as a function of k 46

Fourier Transform Examples
Fourier TransformBoxcar Function
Product of “widths”“Sinc” Function
sin Δ /2
≡ sinc Δ /2
transform1⁄∆ of; Fourier∆ /2
Δ /20;∆ /2

pair ( and ) is aconstanttGaussian Function
12

exp

2

t
Cheiron 2014, Light Source I

=2/tGaussian Functionexp

2

=1/t47

Coherent Gaussian Beam

2.35tIn an ideal case,andreach minimum values defined
Diffraction
by the Fourier transform theory.
Coherent Gaussian Beam

2.35xʼ

2.35xSpectralDecomposition
2.35
Cheiron 2014, Light Source I48

Fourier and Diffraction LimitsFourierLimitConditiona) temporal
12Diffraction b) spatial
Limit

Extreme Cases
0 White (or Pulse)∞ Light∞ Monochromatic
0 Light∞ Parallel Light
0~
Minimum Focal~ 1 Size• If equality a) holds, the light is:– Temporally Coherent or Fourier Limited• If equality b) holds, the light is:– Spatially Coherent or Diffraction Limited 49

Cheiron 2014, Light Source IOutline• Introduction• Fundamentals of Light and SR– General description of light– Why we need SR?
– Physical quantity of light– Uncertainty of light: Fourier anddiffraction limits– SR: Light from a moving electron50

SR: Light from a Moving Electron• Unlike the ordinary light source (sun,light bulb,... ), the light emitter of SR(electron) is ultra-relativistic.
• The characteristics of SR is thus quite
different because of relativistic effects.
• What we have to take care is:
1.Speed-of-light limit
2.Squeezing of light pulse
3.Conversion of the emission angles
Cheiron 2014, Light Source I51

Speed-of-Light LimitWithin the framework of relativity, the velocityof any object never exceeds the speed of light.
Energy
1MeV
10MeV
100MeV
8GeV


0.941
0.99880.999987
0.999999998

Lorentz Factor(relative electron energy, mc2=0.511MeV)
Cheiron 2014, Light Source I

52

Squeezing of Light Pulse Duratione-e-

Pulse Duration Ratio
Cheiron 2014, Light Source I

53

More Generally…

P2

P1

Time Squeezing

Cheiron 2014, Light Source I

>>1~054

Photons Emitted by a Moving Electrone-e-Rest ElectronMoving Electron (Cheiron 2014, Light Source I)
55

Conversion of Emission Angles
rest frameʼ

how to convert?

lab. frame
Isotropic emission
from a rest electron

-1

Emission from anelectron with =0.95

Light emitted from a moving object(~1) concentrates within -1
Cheiron 2014, Light Source I56

SR from a High-Energy ElectronHigh Energy Electron

Large Time
Squeezing

Radiation in theForward Direction

Short Wavelength

High Directivity

Cheiron 2014, Light Source I57