Light Source II

Takashi TANAKA (RIKEN SPring-8 Center)

Cheiron 2010: Light Source II

Characteristics of SR (2)• Electron Trajectory in the ID• Qualitative Description of Wiggler
Radiation• Qualitative Description of Undulator
Radiation

Cheiron 2010: Light Source IITrajectory in the ID

Coordinate Systems

SR emitted by an electron moving at r = (x,y,z)
Observation of SR at R = (X,Y,Z)

If the far-field approximation (|r|<<Z) isapplicable, the radiation pattern depends
only on the observation angle q = (qx,qy).
Cheiron 2010: Light Source IITrajectory in the ID

Field Integrals

Equation of motion of an electron
moving in a magnetic field B: 1st and 2nd field integrals of the ID
Cheiron 2010: Light Source IITrajectory in the ID

Trajectory in an Ideal ID

magnetic field

velocity

position

Ｋ value, Deflection parameter
vvxvz

Ee=8GeV,K=1,lu=5cm：bxmax=64mrad,xmax=0.5mm
Cheiron 2010: Light Source IITrajectory in the ID

Effects due to the ID Magnetic Field
transverse
velocity
longitudinalvelocity

total velocity:average velocity

oscillating term

ID field induces:• transverse(x) oscillation• longitudinal (z) oscillation• effective deceleration(Dbz=K2/4g2)
Cheiron 2010: Light Source IITrajectory in the ID

General Form of Time Squeezing

Time squeezing takes place most significantly
when the direction of the electron motion
coincides with that of observation (b = q ).
Cheiron 2010: Light Source II

Characteristics of SR (2)• Electron Trajectory in the ID• Qualitative Description of Wiggler
Radiation• Qualitative Description of Undulator
Radiation

Cheiron 2010: Light Source II

Radiation from Wigglers

Wiggler Radiation• Wiggler radiation (WR) is regarded asincoherent sum of SR at each position.
– Summation as photons in the framework ofgeometrical optics.

Flux:Emittance:
Brilliance:
Cheiron 2010: Light Source II

Radiation from Wigglers

Photon Distribution in Phase Spacex’,y’x’,y’x,yx’,y’x,yx’,y’x,yx’,y’x,yx,yphase ellipse ofdiffraction-limited light

Beam Waist Position• Larger N results in larger area ofphoton distribution in the phasespace, i.e., larger emittance.
• B does not linearly depend on N
Cheiron 2010: Light Source II

Radiation from Wigglers

Polarization• No circular polarized radiation (CPR) isobserved unlike the BM radiation even offaxis, due to cancellation of CPR components.
right-hand CPR

left-hand CPR• EMPW is a special wiggler to utilize CPR byintroducing a vertical motion.
Cheiron 2010: Light Source II

Radiation from Wigglers

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

1710Wiggler (c=38keV), N=37

Flux Density, Brilliance

Flux Density

Brilliance

16101510

Gauss approx. is notnecessarily valid inthe low energy region

14101310310410510

Photon Energy (eV)610310410510610

Photon Energy (eV)Cheiron 2010: Light Source II

Characteristics of SR (2)• Electron Trajectory in the ID• Qualitative Description of Wiggler
Radiation• Qualitative Description of Undulator
Radiation

Cheiron 2010: Light Source IIQualitative Descriptions of UR

Fundamental Wavelengthluz
period of electron motion time squeezing= period of emitted lightq

period of observed light

Fundamental Wavelength l1

H. Kitamura et al.,J. Appl. Phys. 21 (1982) 1728

Cheiron 2010: Light Source IIQualitative Descriptions of UR

UR with Infinite Periods• If the undulator length is infinite, the pulse
duration is infinitely long, and thus the radiationis completely monochromatic with line spectrum.

• In practice, the undulator length is finite, so theline spectrum is broadened.
infinite
periods

finiteperiods

FF

w1w

w1w
Cheiron 2010: Light Source IIQualitative Descriptions of UR

Effects due to Finite Periods
l1/cElectric Field at Observert

T=Nl1/c

Fourier Transform

Square of “sinc” function dominates the UR
Cheiron 2010: Light Source IIQualitative Descriptions of UR

Brief Note on UR Formulae• In the previous derivations of UR spectral
function, no knowledge on electrodynamics is required.
• In practice, E0 is a complicated functionof q 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 aclear understanding on UR properties.
Cheiron 2010: Light Source IIQualitative Descriptions of UR

Energy and Angular Profile of UR

Energy Profile at q = 0

Angular Profile at w=aw1(0)Cheiron 2010: Light Source IIQualitative Descriptions of UR

Flux Density (arb.unit)

Energy Profile: Example

1.0

N=5
N=10
N=500.50.0-0.4-0.2
0.00.2
Relative Energy 0.4
Cheiron 2010: Light Source IIQualitative Descriptions of UR

Angular Profile: Example-1.0-0.5

x0.0

0.5
1.0 -1.0

-0.5

0.0

0.5

1.0

y

w=0.9w1(0)w=w1(0)

w=1.05w1(0)lower energy

fundamentalenergy

higher energy
Cheiron 2010: Light Source IIQualitative Descriptions of UR

Angular Divergence and Beam Size
Angular Profile at w=w1(0)approximation

Gaussian Profile with sr’Angular Divergenceof UR (L=Nlu)
Diffraction Limit (UR isSpatially Coherent)

Beam Size of UR
Cheiron 2010: Light Source IIQualitative Descriptions of UR

Higher Harmonics• In addition to w1, photons with the energy at
nw1 is also observed, where n is an integer.
18x10

Flux Density

10

K=0.1

K=0.5

K=1

K=35
5th
3rd

1st0050

100 050

100 050

Photon Energy (eV)

100 050100

Cheiron 2010: Light Source IIQualitative Descriptions of UR

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

Electron Orbit

Deflection Angleg-1

Kg-1

Radiation E-fieldCheiron 2010: Light Source IIQualitative Descriptions of UR

Optical Properties of Higher Harmonics
For the n-th harmonic radiation,band width
angular divergence

beam size
Cheiron 2010: Light Source IIPractical Knowledge onUndulator Radiation

Cheiron 2010: Light Source IIPractical Knowledge on UR“Practical Knowledge” on UR• The undulator is a “double-edged sword”!
–Much higher brilliance is available than the BM andwiggler, if appropriately used.
–High heat load on optical elements–Quasi-monochromatic and small angular spread
imposes an accurate adjustment of BL components.

• Practical knowledge for the utilization of UR–Effects due to the electron beam quality–Simple evaluation of optical properties–Heat load reduction–…….
Cheiron 2010: Light Source IIPractical Knowledge on UR

Electron Beam Quality (1)• The property of UR from a single electron issimilar to a laser– Small Size & Angular Divergence, Narrow Bandwidth• In practice, UR in the beamline is emitted by thebeam comprising a huge number of electrons.
• These electrons have different positions, angle,and energies.
E-beam＝Group of electrons

The performanceof UR depends
largely on the ebeam quality
Cheiron 2010: Light Source IIPractical Knowledge on UR

Electron Beam Quality (2)• Electron-beam parameters related to theperformance of UR–Beam Size sx,sy → Source Size
–Angular Divergence sx’,sy’ → Directivity
 The minimum value of the product sxsx
and sysy are called the electron beamemittances in the x and y directions.
–Energy Spread sE/E → Monochromaticity

Cheiron 2010: Light Source IIPractical Knowledge on UR

Effects due to Finite Emittance (1)• Effects due to Finite Emittance of theElectron Beam– Injection to the undulator with angular andpositional offset
SR with Position and Slope Offset

qeff
Off-Axis Observation at qeff

Cheiron 2010: Light Source IIPractical Knowledge on UR

Effects due to Finite Emittance (2)Off-axis observation at qeff
Peak shift tolower energy

Photon Flux

qeff=0larger qeff

EnergyCheiron 2010: Light Source IIPractical Knowledge on UR

Effects due to the Energy Spread
Electron with an offset of Dg
Energy shift of w1

Photon Flux

Dg=0Dg < 0Dg > 0Energy

Cheiron 2010: Light Source IIPractical Knowledge on UR

Photon Flux Density (arb.unit)

ExamplesEmittance (m.rad)-1010-910-810-7
10

0.94

0.96

0.98

1.00

E-spread (%)
10.1
0.01
0.001

1.02

1.04 0.94

0.96

0.98

1.00

1.02

1.04

Relative Photon Energy(w1)Cheiron 2010: Light Source IIPractical Knowledge on UR

Effects on the Higher Harmonics
Effects due to the ebeam are larger for
higher harmonics

Optical Emittance of UR: l/4p
Bandwidth of UR: ~1/nN
191018Flux Density

101710161015

100204060

Photon Energy (keV)

80100
Cheiron 2010: Light Source IIPractical Knowledge on UR

Evaluation of Optical Properties• Optical properties of UR from the e-beam:– Calculate the UR from a single electron basedon the theory of electrodynamics.
– Integrate over the electrons in the beam
(convolution)
Requires complicated numerical computation with alarge number of parameters Dedicated computer software (SPECTRA, SRW,…)
is available• Easy evaluation with Gauss approxmation– Source size, angular divergence– Flux density, brilliance
Cheiron 2010: Light Source IIPractical Knowledge on UR

Effective Size & Divergence
Angular profile of URfrom a single electronsr'

By Gauss approx. andconvolution theorem,Sy'

Convolutionsy'Effective Angular Div.
Sx'sx'

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

Effective Source Size

Cheiron 2010: Light Source IIPractical Knowledge on UR

Effective Flux Density and Brilliance
Effective width of a Gauss function iss

Total Flux
on-axis flux density with zero-emittance beam

Effective
Flux Density

Effective
Brilliance
Cheiron 2010: Light Source IIPractical Knowledge on UR

Heat Load on Optical Elements• SR emitted from the light source isprocessed by several optical elements
before irradiation to the sample, such as thefocusing mirror, monochromator.
• These elements can be easily damaged by
the heat load brought by the SR.
• It is thus important to reduce the heat load
as much as possible without sacrificing theflux by means of the XY slit at the front-endsection.
Cheiron 2010: Light Source IIPractical Knowledge on UR

Spatial Profile of Power and Flux
22Fluxy(mm)Power1

100-1-1-2-2-2-10x(mm)12-2-1012x(mm)The power profile is much broader than the flux. Extraction ofSR with an appropriate slit significantly reduces the heat load.
Cheiron 2010: Light Source IIPractical Knowledge on UR

Optimum Slit Size?
700

1.0Flux

1.0

600

400

0.4300

Power

200

0.2

15

Power (W)500
0.6Photon Flux (10 )

0.8

15

Photon Flux (10 )

0.8

0.6

0.4

0.2
100

0.0

00246

Slit Size (Sx,Sy)

8

100.0
10000

11000

12000

13000

14000

Photon Energy (eV)Too wide aperture results in broader
bandwidth and unwanted heat load.
Cheiron 2010: Light Source IIPractical Knowledge on UR

Wiggler? Undulator? (1)• Wigglers are identical to undulator fromthe 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 the regionof photon energy to be utilized forapplication.

Cheiron 2010: Light Source IIPractical Knowledge on UR

Wiggler? Undulator? (2)15Photon Flux
(photons/sec/0.1%B.W.)

10wigglerundulator

14

10

1310

12

10

1110

10

10110

210

310

410

510Photon Energy (eV)Cheiron 2010: Light Source IIPractical Knowledge on UR

Undulator Radiation Gallery• For quantitative evaluation of SR, a computercode “SPECTRA”, which has been developed
and maintained in SPring-8 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 2010: Light Source IIOther Topics Not Addressed• Quantitative descriptions of SR• Light sources for circular polarization andschemes for fast 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 2010: Light Source II