Light Source I

Takashi TANAKA (RIKEN SPring-8 Center)

Cheiron2009: 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 and Useful Knowledge

Cheiron2009: Light Source I

Introduction

Cheiron2009: 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

Cheiron2009: 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.
Cheiron2009: Light Source I

Introduction

Topics in This Lecture (1)• Fundamentals of Light and SR– General description– 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
Cheiron2009: Light Source I

Introduction

Topics in This Lecture (2)• Characteristics of SR (2)– Radiation from wigglers– Radiation from undulators
Electron motion in the undulator¾ Fundamental energy¾ Spectral function¾ Spatial profile of radiation¾ Higher harmonics¾• Practical and Useful Knowledge on SR– Finite emittance and energy spread– Heat load and photon flux
– Definition of undulators and wigglers
Cheiron2009: Light Source I

Fundamentals of Light and SR• General Description• Physical Quantity of Light• Uncertainty of Light• SR: Light from a Moving Electron

Cheiron2009: Light Source I

General Description

Light as an Electromagnetic Wave
• Electric and magnetic fields can propagate invacuum as a transverse wave, with a relation
vacuum impedance (377Ω)• Analysis of the electric field gives all theinformation on light.

HEz
Cheiron2009: Light Source IGeneral Description

Light as a Photon• In the quantum theory, light is not only anelectromagnetic wave but also a particle, or aphoton.
• The energy of a photon with a wavelength of
λ is given by• For example, a photon with the wavelength of
0.1nm (1Å=10-10m) is calculated as 12.4 keV.
Cheiron2009: Light Source I

General Description

Relation Between EM Wave and Photon
E-field in Frequency Domain
Complex Amplitude

E-field of Radiationin Time Domain

Phase Problem

Number ofPhotons at ω

Energy/Single Photon
Cheiron2009: Light Source I

Fundamentals of Light and SR• General Description• Physical Quantity of Light• Uncertainty of Light• SR: Light from a Moving Electron

Cheiron2009: Light Source I

Physical Quantity of Light

Phase Space
Virtual Experiment toMeasure Photon Counts

slit 3slit 2slit 1ωdetectorN(x,y,x’,y’,t,ω)x,yx’,y’prism

Av. Photon Density

Volume in 6-D
Phase Space
Cheiron2009: 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, ΔΩ can never be 0 due touncertainty of light, thus brilliance is not aphysical quantity that can be actually
measured.
Cheiron2009: 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.
Cheiron2009: 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.
Cheiron2009: 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
Convergent

x’,y’x’,y’x,yx,yWaist

Beam Envelope along
Propagation Axis

DivergentCheiron2009: Light Source I

Physical Quantity of Light

Beam Size, Divergence, Emittancex’,y’

σx’,y’• Beam size (σx,y) is definedas the beam envelope at thebeam waist position.
• Angular divergence (σx’,y’) isconstant along the axis ofx,ypropagation, as far as no
optical elements are present.
• Emittance (εx,εy) is defined
as σx,y x σx’,y’, which is equal
to the area of the phase
σx,yellipse divided by π.
Cheiron2009: Light Source I

Physical Quantity of Light

Estimation of On-Axis Brilliance• Gaussian Approximation of B

estimation of on-axis brilliancewith measurable values

Cheiron2009: Light Source I

Physical Quantity of Light

Example: Laser Pointer and Light Bulb
Specs of SPring-8- E = 8GeV
- I = 100mA- L = 1500m

Light Bulb

Laser PointerBand Width:
Total Power: W
Angular Divergence
Beam Size:

Bulb
Laser
500nm (2.5eV)
100 (%) 0.01 (%)
100 W
1 mW
1 mrad2
4π rad
1 mm2
1 cm2
Cheiron2009: Light Source I

Physical Quantity of Light

Example: Photon Flux
2.5eV

Bulb
100W

Laser
1mW

FF

2.5eV

Total PowerBand Width
Flux@500nm

ω

2.5x10-4
ω

2.5eV

Bulb
100 W
100 (%)
2.5 eV
1017Laser
1 mW
0.01 (%)
2.5x10-4 eV1016
Cheiron2009: Light Source I

Physical Quantity of Light

Example: Brilliance
Bulb
100 W
1017

Total Power
Flux@500nm
Angular Divergence 4π rad
Beam Size
1 cm2Brilliance
107

Laser
1 mW
1016
1 mrad2
1 mm21014• Laser is an ideal light source interms of brilliance, but ...
• No lasers exist in x-ray region¾Synchrotron Radiation
Cheiron2009: Light Source I

Fundamentals of Light and SR• General Description• Physical Quantity of Light• Uncertainty of Light• SR: Light from a Moving Electron

Cheiron2009: Light Source IUncertainty of Light

Uncertainty of Light• The photon distribution in the 6D phasespace (x,y,x’,y’,t,ω) 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 characterized
by the Fourier transform.
• These relations imposes tworestrictions on SR, Fourier andDiffraction limits.
Cheiron2009: Light Source I

Uncertainty of Light

Fourier Transform: Example
Important Fourier Transform in SR FormulaeΔtFourier TransformσtΔω=2π/Δtσω=1/σtCheiron2009: Light Source I

Uncertainty of Light

Temporal Fourier TransformωΔTlight pulse withduration of ΔTΔωspectrometer =temporal Fourier transform

ΔTlong Δtshort ΔtΔωnarrow Δω
wide Δω

Cheiron2009: Light Source I

Uncertainty of Light

Fourier Limit of Light• Temporal Fourier transform imposes• Uncertainty of light in the (ω,t) plane.
• When equality holds, light is said to be
Fourier-limited, or temporally coherent.
• Important to understand the spectral
properties of SR.
Cheiron2009: Light Source I

Uncertainty of Light

Monochromatic Light• Ideally, “monochromatic” means• In practice, perfectly monochromatic
light does not exist, but all kinds of lightare partially monochromatic.
• Temporal Fourier transform is todecompose the practical light into
components of perfectly
monochromatic light.
Cheiron2009: Light Source I

Uncertainty of Light

Spatial Fourier Transform
θx
Δx

Δθx

slit with Δx= beam size

diffraction pattern in the far region= spatial Fourier transformΔθxwide Δxnarrow Δxnarrow Δθxwide Δθx

Cheiron2009: Light Source I

Uncertainty of Light

Diffraction Limit of Light (1)Photon Beam with 1D Gaussian Profile
Photon Spatial ProfileE-field Spatial Profile
Fourier transform
E-field k-vector Profile
Photon k-vector Profile
Photon Angular Profile

Natural emittance oflight with wavelength λCheiron2009: Light Source I

Uncertainty of Light

Diffraction Limit of Light (2)• Spatial Fourier transform imposes• Uncertainty of light in the (x,x’,y,y’) plane.
• When equality holds, light is said to bediffraction-limited, or spatially coherent.
• Important to derive beam size andangular divergence SR.
Cheiron2009: Light Source I

Uncertainty of Light

Plane Wave
• Ideally, “plane wave” means• In practice, perfectly plane wave does
not exist, but all kinds of light are
partially plane-wave-like.
• Spatial Fourier transform is todecompose the practical light into
components of perfectly plane wave.

Cheiron2009: Light Source I

Fundamentals of Light and SR• General Description• Physical Quantity of Light• Uncertainty of Light• SR: Light from a Moving Electron

Cheiron2009: 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 quitedifferent 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
Cheiron2009: 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.
Energy

β

1MeV

0.941

10MeV

0.9988100MeV

0.999987

8GeV

0.999999998:Lorentz Factor(relative electron energy,mc2=0.511MeV)
Cheiron2009: Light Source I

Light from a Moving Electron

Squeezing of Light Pulse Duration

P1P2γ>>1,θ=0time squeezing

Cheiron2009: Light Source I

Light from a Moving Electron

Conversion of Emission Angles
θ’θ

βIsotropic emission
from a rest electron

γ-1

Emission from anelectron with β=0.95

Light emitted from a moving object(β~1) concentrates within γ-1
Cheiron2009: 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

Cheiron2009: Light Source I

Overview of SR Light Source

Cheiron2009: Light Source I

Overview of SR Light Source

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

SNNS

SNN

S

S

NNS

S

NN

S

S

NInsertion Device (ID)

NSS

N

N

S

Cheiron2009: 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 dueto stringent requirement on field qualityand stability.
• Superconducting magnets are used in a
few facilities in pursuit of harder x rays.
Cheiron2009: Light Source I

Overview of SR Light Source

Insertion Device• Installed (inserted) into the straightsection of the storage ring between twoadjacent BMs.
• Generate a periodic magnetic field to let
the injected electron beam move along a
periodic trajectory.
• Most IDs are composed of PMs, while
EMs are used for special use such as
helicity switching.
• Classified into wigglers and undulators.
Cheiron2009: Light Source I

Overview of SR Light Source

Magnetic Circuit of IDsyg xzHalbach typepole piece
Hybrid typeIn each type, a sinusoidal
magnetic field is obtained:
Cheiron2009: 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

Cheiron2009: Light Source I

Overview of SR Light Source

Example of SR Image
BL41XU@SP-8, First Image of SR
at Fluorescent Screen (<0.1mA)
SR from Upstream BM
SR from Undulator

SR from Downstream BMUndulator Gap = 50 mm

Undulator Gap = 20 mm
Cheiron2009: Light Source I

Overview of SR Light Source

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

Comparison of Light Sources
10191018101710161015101410131012

Undulator (BL09XU)

Wiggler (BL08W)

Bending Magnet

101102341010
Photon Energy (eV)105106Cheiron2009: Light Source I

Characteristics of SR (1)• Radiation from BMs

Cheiron2009: Light Source I

Radiation from BMs

Directivity of BM Radiation
Side View

γ-1High directivity in thevertical plane(σy’~γ-1~64μrad@SP-8)

Top View

Isotropic in the orbital plane2-dimensional directivity
Cheiron2009: Light Source I

Radiation from BMs

Spectrum of BM Radiation (1)γ-1ρBeamOrbit
γ-1
γ-1

2ργ-1

Major contribution ofradiation is from theportion painted red

Pulse duration for esqueezing

Pulse duration for observer
Cheiron2009: Light Source I

Radiation from BMs

Spectrum of BM Radiation (2)Fourier transformΔτ

t’Light pulse withduration of Δτ

Δωω’White spectrum
up to ω~Δω~1/Δτ

• By definition, ωc=(3/2)Δτ=3γ3c/2ρ iscalled “critical frequency” of SR, which
gives a criterion of the maximum energyof SR from a BM.
• In practical units,hωc(keV)=0.665Ee2(GeV)B(T)Cheiron2009: 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
1015

10

141013Flux Density
Flux (Δθx=1mrad,Δθy=5mrad)

10

1210

1110

10

CriticalEnergy
10-1

10

010

1

10

2

10

310

Photon Energy (eV)4105106

Cheiron2009: Light Source I

Radiation from BMs

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

1.2

ω/ωc=101.0

ω/ωc=10.8

γ0.6-1ω/ωc=100.4
0.2-2

ω/ωc=10-1

PowerProfile
power

0.0
0.00

0.05

0.10
θy(mrad)

0.15

0.20

• power profile ~ flux profile@ω/ωc=1• larger angular divergence for lower energy
Cheiron2009: 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
-0.5

s3/s0

-1.0
-0.10

left-hand circularhorizontal
right-hand circular

-0.05

0.00
θy(mrad)

0.05

0.10

Polarization statereflects the apparent
motion of electron.
Cheiron2009: Light Source I