Takashi TANAKA (RIKEN SPring-8 Center) Cheiron2008: Light Source I CONTENTS ● Introduction Light Source I • Fundamentals of Light and SR • Overview of SR Light Source • Characteristics of SR (1) (• Characteristics of SR (2) • Practical and Useful Knowledge

Cheiron2008: Light Source I

Cheiron2008: Light Source I

• SR: Definition
– Electromagnetic wave emitted by a charged particle deflected by a magnetic force • SR Facility – Accelerators to generate a high-energy electron beam – Magnetic devices (SR light source) to generate intense SR – Optical elements (monochromators, mirrors,..) – Experimental stations
Cheiron2008: Light Source I

o SR has a lot of advantages over other conventional light sources – Highly collimated (laser-like) – Wavelength tunability – Polarization •  However, the total radiation power does not differ significantly. Comprehensive understanding of SR (and light source) is required for efficient experiments.
Cheiron2008: Light Source I

•  Fundamentals of Light and SR – General description – Physical quantity of light – Uncertainty of light: Fourier and diffraction 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 – Radiation from wigglers
Cheiron2008: Light Source I

•  Characteristics of SR (2) – Radiation from undulators >  Electron motion in the undulator > Fundamental energy > Spectral function > Spatial profile of radiation >  Higher harmonics •  Practical and Useful Knowledge on SR – Finite emittance and energy spread – Heat load and photon flux – Definition of undulators and wigglers
Cheiron2008: Light Source I

•  General Description •  Physical Quantity of Light •  Uncertainty of Light •  SR: Light from a Moving Electron
Cheiron2008: Light Source I

•  Electric and magnetic fields can propagate in vacuum as a transverse wave, with a relation 1 Z × H ) C ⇒ vacuum impedance (377Ω) •  Analysis of the electric field gives all the information on light.
Cheiron2008: Light Source I

•  In a quantum theory, light is not only an electromagnetic wave but also a particle, or a photon. • The energy of a photon with a wavelength of λ is given by hc •  For example, a photon with the wavelength of 0.1nm (1Å=10-10m) is calculated as 12.4 keV.
Cheiron2008: Light Source I

E-field in Frequency Domain ⇒ Complex Amplitude E-field of Radiation in Time Domain hu Number of Photons at ω Energy/Single Photon
Cheiron2008: Light Source I
Fundamentals of Light and SR •  General Description •  Physical Quantity of Light •  Uncertainty of Light •  SR: Light from a Moving Electron
Cheiron2008: Light Source I

Virtual Experiment to Measure Photon Counts slit 2 slit 3 n N(x,y,x',y',w,t △x△y△x′△y′△t△ω/ω Av. Photon Density N Volume in 6-D Phase Space
Cheiron2008: Light Source I

•  Brilliance (photons/sec/mm²/mrad²/0.1%B.W.) is defined as the photon density in the 6D phase space, i.e., d 6 N (x,y,x',y',t,w dxdydx'dy'dtdw /w •  In practice, ΔΩ can never be 0 due to uncertainty of light, thus brilliance is not a physical quantity that can be actually measured.
• Removing the 1st slit gives the angular flux density (photons/sec/mrad²/0.1%B.W), i.e., d'- F Bdxdy • Removing the 1st & 2nd slits gives the total flux (photons/sec/0.1%B.W), i.e., Bdxdydx'dy' •  Estimation of number of photons to be delivered to the sample.
Cheiron2008: Light Source I

• Removing the 1st & 3rd slits gives the angular power density (W/mrad²), i.e., d- F dx'du' dx'du conversion from photons/sec/0.1%B.W. to W • Removing all the slits gives the total power (W), i.e., d – F
dwdx' du • Estimation of heat load on BL components.
Cheiron2008: Light Source I

•  Photon distribution in the 4-D phase space at different longitudinal positions. x',y' Beam Envelope along Propagation Axis
Cheiron2008: Light Source I

•  Beam size (σχ ν) is defined as the beam envelope at the beam waist position. • Angular divergence (σχ,ν,) is constant along the axis of propagation, as far as no optical elements are present. • Emittance (εχ,εν) is defined as σχ,y X σχ,y, which is equal to the area of the phase ellipse divided by π.
Cheiron2008: Light Source l

•  Gaussian Approximation of  B B(x,y,x',y') = Bo exp d2 F dx'dy' Bdxdy = 2πσxσyB0 Bdxdydx'dy' = 4π²σxσyσ χισ ν Bd estimation of on-axis brilliance with measurable values
Cheiron2008: Light Source I

Cheiron2008: Light Source I

• Laser is an ideal light source in terms of brilliance, but ... • No lasers exist in x-ray region > Synchrotron Radiation Fundamentals of Light and SR •  General Description • Physical Quantity of Light •  Uncertainty of Light •  SR: Light from a Moving Electron
Cheiron2008: Light Source I

• The photon distribution in the 6D phase space (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 to take care, which are well characterized by the Fourier transform. • These relations imposes two restrictions on SR, Fourier and Diffraction limits.
Cheiron2008: Light Source I

Important Fourier Transform in SR Formulae
D
Cheiron2008: Light Source I

light pulse with duration of ΔΤ long At short narrow Δω wide Δω spectrometer = temporal Fourier transform
Cheiron2008: Light Source I

•  Temporal Fourier transform imposes AwAt 2 1 • 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.
Cheiron2008: Light Source I

•  Ideally, “monochromatic” means △ω = 0 & △t = ∞ •  In practice, perfectly monochromatic light does not exist, but all kinds of light are partially monochromatic. • Temporal Fourier transform is to decompose the practical light into components of perfectly monochromatic light.
Cheiron2008: Light Source I

slit with Δχ = beam size diffraction pattern in the far region = spatial Fourier transform wide Δχ narrow narrow Δθ , wide Δθχ
Cheiron2008: Light Source I

Photon Beam with 1D Gaussian Profile   B( x X exp( —X E-field Spatial Profile Fourier transform X  X   exp( E-field k-vector Profile Photon k-vector Profile exp( −θ≥ / 2σ) 51 Photon Angular Profile kr = (2π/X)θx Natural emittance of light with wavelength λ
Cheiron2008: Light Source I

•  Spatial Fourier transform imposes T x,yT x',y' 2 • Uncertainty of light in the (x,x',y,y') plane. • When equality holds, light is said to be diffraction-limited, or spatially coherent. • Important to derive beam size and angular divergence SR.
Cheiron2008: Light Source I

•  Ideally, “plane wave” means σ x',y' = 0 & σ x,y = ∞ • In practice, perfectly plane wave does not exist, but all kinds of light are partially plane-wave-like. •  Spatial Fourier transform is to decompose the practical light into components of perfectly plane wave.
Cheiron2008: Light Source I

•  General Description • Physical Quantity of Light •  Uncertainty of Light •  SR: Light from a Moving Electron
Cheiron2008: Light Source I

• 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
Cheiron2008: Light Source I

Within the framework of relativity, the velocity of an electron never exceeds the speed of light.
E :Lorentz Factor (relative electron energy,mc²=0.511MeV)
Cheiron2008: Light Source I

RっV (R1)² + (vAt)² − 2R1vAt cos θ R1 - (v · n ) ▲ t A T t2 − t1 = △t + R2/c − R1/c △t (1 − β・n At 2y2 γ>>1,θ=0 time squeezing Cheiron2008: Light Source I
Isotropic emission from a rest electron Emission from an electron with β=0.95 Light emitted from a moving object 5~1) concentrates within γ-1
Cheiron2008: Light Source I

High energy electron Short Wavelength 0 < < 4/ 1 Radiation in the Forward Direction High Directivity
Cheiron2008: Light Source I

Cheiron2008: Light Source I
Magnets to deflect the electron beam and generate SR. Bending Magnet (BM) Insertion Device (I Cheiron2008: Light Source I
• One of the accelerator components in the storage ring. • Generate uniform field to guide the electron beam into a circular orbit. • EMs combined with highly-stable power supplies are adopted in most BMs due to stringent requirement on field quality and stability. • Superconducting magnets are used in a few facilities in pursuit of harder x rays.
Cheiron2008: Light Source I

• Installed (inserted) into the straight section of the storage ring between two adjacent 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.
Cheiron2008: Light Source I

In each type, a sinusoidal magnetic field is obtained: 2π2
Cheiron2008: Light Source I

Halbach-type Magnet Array for SPring-8 Standard Undulators
BL41XU＠SP-8, First Image of SR at Fluorescent Screen (<0.1mA) Undulator Gap = 50 mm Undulator Gap = 20 mm
Cheiron2008: Light Source I

Characteristics of SR (1) • Radiation from BMs • Radiation from Wigglers
Side View Top View High directivity in the vertical plane ov,~y-1~64µrad@SP-8) Isotropic in the orbital plane 2-dimensional directivity
Cheiron2008: Light Source I

Major contribution of radiation is from the portion painted red Pulse duration for e- △t = 2py squeezing Pulse duration for observer
Cheiron2008: Light Source I

Light pulse with duration of Δτ White spectrum up to ω~Δω~1/Δτ o By definition, ω c=(3/2)Δτ=3γ³c/2ρ is called “critical frequency” of SR, which gives a criterion of the maximum energy of SR from a BM. • In practical units, ñω (keV)=0.665E 2 (GeV)B(T)
Cheiron2008: Light Source I

power profile ~ flux profile＠ω/ω-=1 o o larger angular divergence for lower energy
Cheiron2008: Light Source l

Stokes parameters of BM radiation along vertical axis left-hand circular horizontal Polarization state reflects the apparent motion of electron. hand circular
Cheiron2008: Light Source I
Characteristics of SR (1) • Radiation from BMs • Radiation from Wigglers
• Wiggler radiation (WR) is regarded as incoherent sum of SR at each position. – Summation as photons within the framework of geometrical optics. Flux: FW ～ 2N F B M Emittance: σ x ′ ,y ′ × σ x ,y }入⁄ 4 π Brilliance: BW ≪ 2N B B M
Cheiron2008: Light Source I

Beam Waist Position • Larger N results in larger area of photon distribution in the phase space, i.e., larger emittance. o B does not linearly depend on N
Cheiron2008: Light Source I

•  No circular polarized radiation (CPR) is observed unlike the BM radiation even off axis, due to cancellation of CPR components. right-hand CPR •  EMPW is a special wiggler to utilize CPR by introducing a vertical motion.
Cheiron2008: Light Source I