Light Sources IITakashi TANAKARIKEN SPring-8 Center

Cheiron 2014, Light Source II1

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

2

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

N

N

S

S

N

N

S

S

N

N

S

S

N

N

S

S

NN

S

S

NN

S

N

S

N
Insertion Device (ID)S

Cheiron 2014, Light Source II

3

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 fieldquality and stability.
• Superconducting magnets are used in a
few facilities in pursuit of harder x rays.
Cheiron 2014, Light Source II4

Insertion Device• Installed (inserted) into the straightsection of the storage ring between
two adjacent BMs.
• Generate a periodic magnetic field tolet 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
Cheiron 2014, Light Source II5

Magnetic Circuit of IDsygx
uz

Halbach typepole piece
Hybrid typeIn each type, a sinusoidal
magnetic field is obtained:
Cheiron 2014, Light Source II6

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

e- Beam

NdFeB Magnet

cooling channel
Cheiron 2014, Light Source II7

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 BMg = 50 mm
Cheiron 2014, Light Source IIg = 20 mm
8Photon Flux Density(photons/sec/mrad2/0.1%b.w.)

Comparison of SR Light Sources
10191018101710

16101510

1410

131012

Undulator (BL09XU)

Wiggler (BL08W)

Bending Magnet

101

Cheiron 2014, Light Source II102341010
Photon Energy (eV)1051069

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 SR10

Directionality of BM Radiation
e-e-Directional(V-plane)
Isotropic(H-plane)

Cheiron 2014, Light Source IIBM radiation is similar
to a beacon lamp Sheet beam 2D directionality

11

Pulse Structure of BM Radiation

Cheiron 2014, Light Source II

12Intensity

Pulse Structure of BM Radiation

Cheiron 2014, Light Source IITime13

Whatʼs the Pulse Duration?

Pulse duration for eTime Squeezing
Pulse duration for observer
Cheiron 2014, Light Source II14

Spectrum of BM Radiation
FourierTransform BM radiation has a white spectrum
reaching the frequency of(“critical frequency”) givesa criterion for BM spectrum.
 In practical units,
Cheiron 2014, Light Source II15

Example of Spectrum
Larger aperture collects
photons with lower energies

13

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

10x=0.1mrad
1210

y=10mrad

1110

y=0.1mrad

1010

CriticalEnergy

910010Cheiron 2014, Light Source II

1102

3

4101010
Photon Energy (eV)

510

61016

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

1.2

/c=101.0/c=10.8



0.6-1

/c=100.4
0.2-2

/c=10-1

Power Profile

0.0
0.00

0.05

0.100.15
y(mrad)Empirical formulafor angular0.20of profile
BM radiation
 power divergenceprofile ~ fluxat c larger angular divergence for lower energy
Cheiron 2014, Light Source II17

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 SR18

Coordinate Systems,,Assuming(farfield approximation), theradiation pattern depends
only onCheiron 2014, Light Source II19

Field Integrals

Equation of motion of an electron
moving in a magnetic field B,: 1st and 2nd field integrals of the ID

Cheiron 2014, Light Source II20

Trajectory in an Ideal ID

Magnetic Field

Velocity

Position K Value Deflection Parameter

E=8GeV,K=1,u=5cm：xmax=64rad, xmax=0.5m
Cheiron 2014, Light Source II21

Effects due to the ID Magnetic Field
transverse
velocity
Oscillating Term

longitudinalvelocity
Original value

Average ValueID field induces: transverse (x) oscillation
 longitudinal (z) oscillation
 effective deceleration (Cheiron 2014, Light Source II)
22

General Form of Time Squeezing

Time squeezing takes place most significantly
when the electron is moving in the directionof observation ().
Cheiron 2014, Light Source II23

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
24

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.

Flux :Emittance :,,Brilliance :Cheiron 2014, Light Source II

25

Photon Distribution in Phase Space
phase ellipse ofyʼxʼ,diffraction-limitedxʼ,yʼ lightx,yxʼ,yʼxʼ,yʼ
x,yx,y,xʼ,yʼ
x,yx,y,Beam Waist Position• Larger N results in larger area ofphoton distribution in the phasespace, i.e., larger emittance.
• B does not linearly depend on NCheiron 2014, Light Source II

26

Comparison with BM Radiation
BM (c=29keV),

1710Wiggler (c=38keV), N=37

Flux Density, Brilliance

Flux Density

Brilliance

1610151014101310310410510

Photon Energy (eV)Cheiron 2014, Light Source II

610310410510610

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 SR28Fundamental Wavelength of URuzperiod of electron motion= period of emitted light

TimeSequeezing

period of observed light

Fundamental Wavelength 1

H. Kitamura et al.,CheironJ.2014,
SourceIIAppl.LightPhys.
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.
infiniteperiodsf1

Cheiron 2014, Light Source IIfiniteperiodsf

1


30

Effects due to Finite Periods
1/cElectric Field at Observer
tT=N1/c

Fourier Transform

Square of “sinc” function dominates UR

Cheiron 2014, Light Source II31

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  and K, and needs to be
calculated by Fourier transforming
the electric field derived from the
Lienard-Wiecherd potential.
• However, the simple derivation gives
us a clear understanding on UR
properties.

Cheiron 2014, Light Source II32

Normalized Flux Density

Energy Spectrum of UR

1.0

N=5
N=10
N=100

0.80.60.4
0.20.0-0.4

Cheiron 2014, Light Source II-0.2
0.00.20.4
Normalized Photon Energy (-1)/133

Angular Profile of UR

Cheiron 2014, Light Source II34

Angular Divergence of UR
UR is not a Gaussian Beam
Angular Profile at =1(0)Gaussian Profile with r’

Cheiron 2014, Light Source II“Natural” Angular
Divergence of UR)(35Source Size of UR“Natural” Angular
Divergence of UR()

 Unlike WR, UR is spatiallycoherent, i.e., diffraction limited.
 This means that
“Natural” Source
size of UR

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

Cheiron 2014, Light Source II36

Higher Harmonics
Photons with at n1 are observed aswell as at 1, where n is an integer.
K=0.1

Normalized Flux Density

1.0

K=0.5

K=1

K=30.55th
3rd

1st0.0050

Cheiron 2014, Light Source II

100 050

100 050

Photon Energy (keV)

100 05010037

Electric Field

K << 1 CaseTime
Cheiron 2014, Light Source II38

Electric Field

K ~ 1 CaseTime
Cheiron 2014, Light Source II39

Electric Field

K >> 1 CaseTime
Cheiron 2014, Light Source II40

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

Electron Orbit

Radiation E-field

Spectrum

Cheiron 2014, Light Source II41

Outline• Introduction• Fundamentals of Light and SR• Overview of SR Light Source• Characteristics of SR (1)• Characteristics of SR (2)• Practical Knowledge on SR42

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.
SourceSize
Pulse
LengthCheiron 2014, Light Source II

AngularDiveergence43

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

Electron Beam

0.05psec

Undulator Radiation

Energy1%

100%

0.7fsec

BM Radiation
Cheiron 2014, Light Source IITime

44Example in SPring-8: (x,y) Space
700m
15m

Electron Beam
5.6m

y

Undulator Radiation

5.6m
1.7m

Cheiron 2014, Light Source IIxBM Radiation

45

Example in SPring-8: (xʼ,yʼ) Space
29rad2.6radElectron Beam
7.8rady'Undulator Radiation

60rad1500radBM Radiation
Cheiron 2014, Light Source IIx'

46

Convolution Between e- and Photonxʼ,yʼ,

Electrondistributionxʼ,yʼ,

x,y,txʼ,yʼ,

Convolution

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

Cheiron 2014, Light Source II

x,y,t

Photon distribution
from e- beam

Broadening of temporal (t),spectral (), spatial (x,y)
and angular profiles (xʼ,yʼ).

47

Spectral Profile (UR)
Emittance (m.rad)

E-spread (%)
0.001
0.01
0.1
1-10

Photon Flux Density (arb.unit)

10-9

10-810-710

0.94

0.96

0.98

Cheiron 2014, Light Source II

1.00

1.02

1.04

0.94

0.96

0.98

Relative Photon Energy(1)

1.00

1.02

1.04

48

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

Gauss approximation
Convolution theoremr'y'Effective Angular Div.

Convolution

y'

x'
x'

Angular profile of UR
from the e-beam

Effective Source Size

Angular profile of the e-beam
Cheiron 2014, Light Source II49

Heat Load on Optical Elements• SR is usually processed by several
optical elements before irradiation tothe sample, such as the focusingmirror, 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.
Cheiron 2014, Light Source II50

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.
Cheiron 2014, Light Source II

51

Whatʼs the Optimum Aperture Size?
700

1.0

600

0.8
500
0.6

400

0.4300PowerPower (W)15

Photon Flux (10 )Flux2000.2
100
0.000

Cheiron 2014, Light Source II

2

46Slit Size (x,y)81052

Wiggler? Undulator? (1)• Wigglers are identical to undulator
from the point of view of magneticcircuit.
• 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.

Cheiron 2014, Light Source II53

Wiggler? Undulator? (2)15undulator

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

10wiggler

141013101210

u=12cm
K=10x=y=3mm@30m

1110

10

10

1

102

10

310410510

Photon Energy (eV)Cheiron 2014, Light Source II54

Undulator Radiation Gallery• For quantitative evaluation of SR, acomputer 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
Cheiron 2014, Light Source II55

Brilliance Curve & Spectrum
Spectrum –, Peak Brilliance 1st – 3 rd – 5 th –Cheiron 2014, Light Source II56

Opening the Slit Aperture

Cheiron 2014, Light Source II57

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

Cheiron 2014, Light Source II58

Flux Angular Profile
On-Axis Spectrum

Cheiron 2014, Light Source II

Angular Profile(Finite Emittance)

Angular Profile(Zero Emittance)

59Undulator-to-Wiggler TransitionCheiron 2014, Light Source II60

Other Important Topics• Quantitative descriptions of SR• Light sources for CPR & helicity switching– helical undulator & elliptic wiggler– chicanes & choppers, kicker magnets• Effects on the electron beam
– natural focusing– beam-axis fluctuation due to COD variation• R&Ds toward shorter magnetic period– superconducting undulators– cryogenic permanent magnet undulators• Coherent SR for intense THz light• Undulators for SASE-based X-ray FEL

Cheiron 2014, Light Source II61

Announcement• Those who are going to join thelecture on “SPECTRA” scheduled on
Monday evening are recommended tobring your own PC.
• If you do not have any PC, please
consult the office.
• Before joining the lecture, download
the software from the URL below andfinish installation.
http://radiant.harima.riken.go.jp/spectra
Cheiron 2014, Light Source II62

Angular Divergence & Source SizeΔ
2 2Δ ~2~2ΔΔ
24~

Cheiron 2014, Light Source II63