Light Source I

Takashi TANAKA (RIKEN SPring-8 Center)

Cheiron 2011: Light Source I

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

Cheiron 2011: Light Source I

Introduction

Cheiron 2011: Light Source I

Introduction

SR Facility and Light Source• SR: Definition– Electromagnetic wave emitted by a charged
particle deflected by a magnetic force• SR Facility– Accelerators to generate a high-energy electronbeam– Magnetic devices (SR light source) togenerate intense SR– Optical elements (monochromators, mirrors,..)– Experimental stations

Cheiron 2011: Light Source I

Introduction

SR as a Probe for Research• SR has a lot of advantages over otherconventional light sources– Highly collimated (laser-like)– Wavelength tunability– Polarization– .....

• However, the total radiation power does
not differ significantly.
Comprehensive understanding of SR (and lightsource) is required for efficient experiments.
Cheiron 2011: Light Source I

Introduction

Topics in This Lecture (1)• Fundamentals of Light and SR– 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• Characteristics of SR (1)– Radiation from bending magnets
Cheiron 2011: Light Source I

Introduction

Topics in This Lecture (2)• Characteristics of SR (2)– Electron Trajectory in IDs– Radiation from wigglers– Radiation from undulators• 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 2011: Light Source I

Fundamentals of Light and SR• Why we need SR?
• Physical Quantity of Light• Uncertainty of Light• SR: Light from a Moving Electron

Cheiron 2011: Light Source I

Why SR?

Observation with Light
Light Source(Bulb)

ComputerSR

Analyzer(Brain)
High-quality lightsource foran accurate observation!

Reflection
Diffraction

Object(flower)
Protein Crystal

Detector(eye)ＣＣＤ Camera
Cheiron 2011: Light Source I

Why SR?

Which Quality is Better?
Specs of SPring-8- E = 8GeV

- I = 100mA- L = 1500m

1mW Laser (pointer)

100W Bulb

Lighting equipment in a room:
Pointer during a presentation:

Bulb
Laser

Depends on the Object!
Cheiron 2011: Light Source I

Why SR?

How to Define the Quality of Light?(1)• The performance of the light source
depends on the dimension of the object
and the method to detect light.
• For observation, the photons emitted by
the light source should be– illuminated on the object for interaction– recognized by the detector for analysis

Quality of Light Source:
How efficiently the above
conditions are satisfied?
Cheiron 2011: Light Source I

Why SR?

How to Define the Quality of Light?(2)Important Features of the Light Source
ObjectFlowerProteinRadiation Power◎○# Emitted
Photons

Source Size×△△◎◎◎

IlluminatedAreaDirectivity
Monochromaticity

Related Items

Accuracy ofAnalysis

Brilliance

Cheiron 2011: Light Source I

Why SR?

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 light for
observation of microscopic objects.
• The brilliance of a light source with ahigh total power is not necessarily high.

Cheiron 2011: Light Source I

Why SR?

Examples of BrillianceTotal Power (W)Bulb

Laser Pointer

100

10-3

Angular Div. (mrad2) 4px106

1

Source Size: (mm2)1021Bandwidth: (%)

100

0.01

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

Laser is the best light source toobserve the microscopic object!
Cheiron 2011: Light Source I

Why SR?

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!!

Synchrotron Radation(SR)Cheiron 2011: Light Source I

Fundamentals of Light and SR• Why we need SR?
• Physical Quantity of Light• Uncertainty of Light• SR: Light from a Moving Electron

Cheiron 2011: Light Source I

Physical Quantity of Light

Phase Space
Virtual Experiment toMeasure Photon Counts

slit 3slit 2slit 1w

detectorN(x,y,x’,y’,t,w)x,yx’,y’prism

Av. Photon Density

Volume in 6-D
Phase Space
Cheiron 2011: Light Source I

Physical Quantity of Light

Brilliance (Brightness)• Brilliance (photons/sec/mm2/mrad2/0.1%B.W.)
is defined as the photon density in the 6D
phase space, i.e.,• In practice, DW can never be 0 due touncertainty of light, thus brilliance is not aphysical quantity that can be actuallymeasured.
Cheiron 2011: Light Source I

Physical Quantity of Light

Photon Flux and Flux Density• Removing the 1st slit gives the angular flux
density (photons/sec/mrad2/0.1%B.W), i.e.,• Removing the 1st & 2nd slits gives the total
flux (photons/sec/0.1%B.W), i.e.,• Estimation of number of photons to bedelivered to the sample.
Cheiron 2011: Light Source I

Physical Quantity of Light

Radiation Power and Power Density• Removing the 1st & 3rd slits gives theangular power density (W/mrad2), i.e.,

conversion from photons/sec/0.1%B.W. to W

• Removing all the slits gives the total power(W), i.e.,• Estimation of heat load on BL components.
Cheiron 2011: Light Source I

Physical Quantity of Light

Photons in 4D Phase Space• Photon distribution in the 4-D phase spaceat different longitudinal positions.
x’ ,y’x’ ,y’x,yConvergent

x’ ,y’x,yx,yWaist

Beam Envelope along
Propagation Axis

DivergentCheiron 2011: Light Source I

Physical Quantity of Light

Beam Size, Divergence, Emittancex’,y’sx’,y’• Beam size (sx,y) is definedas the beam envelope at thebeam waist position.

• Angular divergence (sx’,y’) isconstant along the axis ofx,ypropagation, as far as nooptical elements are present.
• Emittance (ex,ey) is definedas sx,y x sx’,y’, which is equal
to the area of the phasesx,yellipse divided by p.
Cheiron 2011: Light Source I

Fundamentals of Light and SR• Why we need SR?
• Physical Quantity of Light• Uncertainty of Light• SR: Light from a Moving Electron

Cheiron 2011: Light Source I

Uncertainty of Light

Uncertainty of Light• The photon distribution in the 6D phasespace (x,y,x’,y’,t,w) gives us the full
information on the properties of SR.
• Due to wave nature of light, however,
we have two uncertainty relations totake care, which are well characterizedby the Fourier transform.
• These relations imposes two
restrictions on SR, Fourier andDiffraction limits.
Cheiron 2011: Light Source I

Uncertainty of Light

Fourier Transform: Example
Important Fourier Transform in SR Formulae

DtFourier Transformst

Dw=2p/Dt

sw=1/stCheiron 2011: Light Source I

Uncertainty of Light

Temporal Fourier Transformw
Dt

Light with a finite
time duration of Dt

Dw

spectrometer =temporal Fourier transformDt

If the light is monochromatic,then DwDt=const.

Dw

Cheiron 2011: Light Source I

Uncertainty of Light

Fourier Limit of Light• Temporal Fourier transform imposes• Uncertainty of light in the (w,t) plane.
• When equality holds, light is said to be– Fourier-limited– Temporally coherent• Important to understand the spectral
properties of SR.
Cheiron 2011: Light Source I

Uncertainty of Light

Spatial Fourier Transform
qx
Dx

D

Clipping by a slit witha finite width of Dx

diffraction pattern in the far region= spatial Fourier transformD

If the injected light is a planewave, then DxDx’=const.

Cheiron 2011: Light Source I

Uncertainty of Light

Diffraction Limit of Light• Spatial Fourier transform imposes
kx=(2p/l)x’• Uncertainty of light in (x,x’) plane• When equality holds, light is said to be– Diffraction limited– Spatially coherent• In the case of Gaussian beam,Natural emittanceof light
Cheiron 2011: Light Source I

Fundamentals of Light and SR• Why we need SR?
• Physical Quantity of Light• Uncertainty of Light• SR: Light from a Moving Electron

Cheiron 2011: Light Source I

Light from a Moving Electron

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 due to 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 2011: Light Source I

Light from a Moving Electron

Speed-of-Light Limit
Within the framework of relativity, the velocityof an electron never exceeds the speed of light.
Energyb

1MeV

0.941

10MeV

0.9988100MeV

0.999987

8GeV

0.999999998

Lorentz Factor(relative electron energy,mc2=0.511MeV)
Cheiron 2011: Light Source ILight from a Moving Electron

Squeezing of Light Pulse Duration

P1

P2g>>1,q=0
time squeezing

Cheiron 2011: Light Source I

Light from a Moving Electron

Conversion of Emission Anglesq’qb
Isotropic emission
from a rest electron

g-1

Emission from anelectron with b=0.95

Light emitted from a moving object(b~1) concentrates within g-1
Cheiron 2011: Light Source I

Light from a Moving Electron

SR from a High-Energy ElectronHigh energy electron

Large Time
Squeezing

Radiation in theForward Direction

Short Wavelength

High Directivity
Cheiron 2011: Light Source I

Overview of SR Light Source

Cheiron 2011: Light Source I

Overview of SR Light Source

What is SR Light Source?
Magnets to deflect the electron
beam and generate SR.
Bending Magnet (BM)
SNN

S

SN

N

S

SN

N

S

S

N

N

S

SNNS

SN

Insertion Device (ID)

NS

S

N

N

S

Cheiron 2011: Light Source I

Overview of SR Light Source

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 due
to stringent requirement on field qualityand stability.
• Superconducting magnets are used in afew facilities in pursuit of harder x rays.
Cheiron 2011: Light Source I

Overview of SR Light Source

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 move along aperiodic trajectory.
• Most IDs are composed of PMs, while
EMs are used for special use such as
helicity switching.
• Classified into wigglers and undulators.
Cheiron 2011: Light Source I

Overview of SR Light Source

Magnetic Circuit of IDs
yg xz

Halbach typepole piece
Hybrid typeIn each type, a sinusoidal
magnetic field is obtained:
Cheiron 2011: Light Source I

Overview of SR Light Source

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

e- Beam

NdFeB Magnet

cooling channel

Cheiron 2011: Light Source I

Overview of SR Light Source

Example of SR Image
BL47XU@SP-8, first image of SR
with a fluorescent screen (<0.1mA)
SR from Downstream BM
SR from Undulator

SR from Upstream BMUndulator Gap = 50 mm

Undulator Gap = 20 mm
Cheiron 2011: Light Source I

Overview of SR Light Source

Photon Flux Density(photons/sec/mrad2/0.1%b.w.)

Comparison of Light Sources
101910181017101610151014101310

12

Undulator (BL09XU)

Wiggler (BL08W)

Bending Magnet

1011023410
10Photon Energy (eV)105106Cheiron 2011: Light Source I

Characteristics of SR (1)• Radiation from BMs

Cheiron 2011: Light Source I

Radiation from BMs

Directivity of BM Radiation
Side View

g-1
High directivity in thevertical plane(sy’~g-1~64mrad@SP-8)

Top ViewIsotropic in the orbital plane2-dimensional directivity
Cheiron 2011: Light Source I

Radiation from BMs

Spectrum of BM Radiation (1)g-1

dd >> g-1

d ~ g-1
d << g-1
Photons emitted when d<g-1
are detected by the observer

Cheiron 2011: Light Source I

Radiation from BMs

Spectrum of BM Radiation (2)O2g-1

BeamOrbit

rg-1
A2rg-1g-1

Major contribution ofradiation is from theportion painted red

Pulse duration for esqueezing

Pulse duration for observer
Cheiron 2011: Light Source I

Radiation from BMs

Spectrum of BM Radiation (3)Fourier transform

Dtt’

Light pulse withduration of Dt

Dww’White spectrum
up to w~Dw~1/Dt• By definition, wc=(3/2)/Dt=3g3c/2r iscalled “critical frequency” of SR, which
gives a criterion of the maximum energyof SR from a BM.
• In practical units,hwc(keV)=0.665Ee2(GeV)B(T)Cheiron 2011: Light Source I

Radiation from BMs

Photon Flux (photons/sec/0.1%b.w.)
2
Photon Flux Density (photons/sec/mrad /0.1%b.w.)

Example of Spectrum
101510141013

Flux Density
Flux (Dqx=1mrad,Dqy=5mrad)

101210111010

CriticalEnergy
10-110010

110210310

Photon Energy (eV)4105106

Cheiron 2011: Light Source I

Radiation from BMs

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

1.2-2

w/wc=101.0

w/wc=10.8g

0.6-1-1

w/wc=100.4
0.2w/wc=10

Power Profile

power

0.0
0.00

0.05

0.10
qy(mrad)

0.15

0.20

• power profile ~ flux profile@w/wc=1• larger angular divergence for lower energy
Cheiron 2011: Light Source IRadiation from BMs

Polarization of BM Radiation
1.0
Stokes Parameter

Stokes parametersof BM radiation
along vertical axis

s1/s0

0.5
0.0-0.5s3/s0-1.0-0.10

left-hand circularhorizontal
right-hand circular

-0.05

0.00
qy(mrad)

0.05

0.10

Polarization state
reflects the apparent
motion of electron.
Cheiron 2011: Light Source I