Synchrotron Radiation - PDF Free Download

Synchrotron Radiation Lenny Rivkin Paul Scherrer Institute (PSI) and Swiss Federal Institute of Technology Lausanne (EPFL) Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Click Useful to books edit Master and references title style H. Wiedemann, Synchrotron Radiation Springer-Verlag Berlin Heidelberg 2003 H. Wiedemann, Particle Accelerator Physics I and II Springer Study Edition, 2003 A.Hofmann, The Physics of Synchrotron Radiation Cambridge University Press 2004 A. W. Chao, M. Tigner, Handbook of Accelerator Physics and Engineering, World Scientific 1999 Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Click CERN to Accelerator edit Master School title style Proceedings Synchrotron Radiation and Free Electron Lasers Grenoble, France, 22-27 April 1996 (A. Hofmann s lectures on synchrotron radiation) CERN Yellow Report 98-04 Brunnen, Switzerland, 2 9 July 2003 CERN Yellow Report 2005-012 Previous CAS Schools Proceedings Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Curved orbit of electrons in magnet field Accelerated charge Electromagnetic radiation Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Electromagnetic waves Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Crab Nebula 6000 light years away GE Synchrotron New York State First light observed 1054 AD First light observed 1947

Click Synchrotron to edit Master radiation: title some style dates 1873 Maxwell s equations 1887 Hertz: electromagnetic waves 1898 Liénard: retarded potentials 1900 Wiechert: retarded potentials 1908 Schott: Adams Prize Essay... waiting for accelerators 1940: 2.3 MeV betatron,kerst, Serber Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Maxwell equations (poetry) War es ein Gott, der diese Zeichen schrieb Die mit geheimnisvoll verborg nem Trieb Die Kräfte der Natur um mich enthüllen Und mir das Herz mit stiller Freude füllen. Ludwig Boltzman Was it a God whose inspiration Led him to write these fine equations Nature s fields to me he shows And so my heart with pleasure glows. translated by John P. Blewett

THEORETICAL UNDERSTANDING 1873 Maxwell s equations made evident that changing charge densities would result in electric fields that would radiate outward 1887 Heinrich Hertz demonstrated such waves: It's of no use whatsoever[...] this is just an experiment that proves Maestro Maxwell was right we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there.

Electromagnetic waves

1898 Liénard: ELECTRIC AND MAGNETIC FIELDS PRODUCED BY A POINT CHARGE MOVING ON AN ARBITRARY PATH (by means of retarded potentials proposed first by Ludwig Lorenz in 1867)

1912 Schott: COMPLETE THEORY OF SYNCHROTRON RADIATION IN ALL THE GORY DETAILS (327 pages long) to be forgotten for 30 years (on the usefulness of prizes)

Donald Kerst: first betatron (1940) "Ausserordentlichhochgeschwindigkeitelektronenent wickelndenschwerarbeitsbeigollitron"

Click Synchrotron to edit Master radiation: title some style dates 1946 Blewett observes energy loss due to synchrotron radiation 100 MeV betatron 1947 First visual observation of SR 70 MeV synchrotron, GE Lab NAME! 1949 Schwinger PhysRev paper 1976 Madey: first demonstration of Free Electron laser Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

GENERATION OF SYNCHROTRON RADIATION Swiss Light Source, Paul Scherrer Institute, Switzerland

60 000 SR users world-wide Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Why do they radiate? Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Synchrotron Radiation is not as simple as it seems I will try to show that it is much simpler Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Charge at rest Coulomb field, no radiation Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Uniformly moving charge does not radiate v = constant But! Cerenkov! Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Click Free isolated to edit Master electron title cannot style emit a photon Easy proof using 4-vectors and relativity momentum conservation if a photon is emitted PP ii = PP ff + PP γγ square both sides mm 2 = mm 2 + 2PP ff PP γγ + 0 PP ff PP γγ = 0 in the rest frame of the electron PP ff = (mm, 0) PP γγ = (EE γγ, pp γγ ) this means that the photon energy must be zero. Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

We need to separate the field from charge

Bremsstrahlung or braking radiation

Transition Radiation εε 11 εε 22 cc 1 = 1 εε 1 μμ 1 cc 2 = 1 εε 2 μμ 2

Liénard-Wiechert potentials ϕ t = 1 4πε 0 q r 1 n β ret A t = q 4πε 0 c 2 v r 1 n β ret and the electromagnetic fields: A + 1 c 2 ϕ t = 0 (Lorentz gauge) B = A E = ϕ A t

Fields of a moving charge E t = q 4πε 0 n β 1 n β 3 γ 2 1 r 2 ret + q 4πε 0 c n n β β 1 n β 3 γ 2 1 r ret B t = 1 c n E

Transverse acceleration a v Radiation field quickly separates itself from the Coulomb field

Longitudinal acceleration a Radiation field cannot separate itself from the Coulomb field v

Synchrotron Radiation Basic Properties Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Moving Source of Waves Cape Hatteras, 1999

Click Time to compression edit Master title style Electron with velocity β emits a wave with period T emit while the observer sees a different period T obs because the electron was moving towards the observer n θ β T = ( 1 n β) obs T emit The wavelength is shortened by the same factor λ = ( 1 β cosθ ) obs λ emit in ultra-relativistic case, looking along a tangent to the trajectory λ obs = 2γ 1 2λ emit since 1 β = 1 β2 1 + β 1 2γ 2 Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Radiation is emitted into a narrow cone θ e v ~ c θ = 1 γ θ e θ v << c v c

Sound waves (non-relativistic) Angular collimation θ e v θ = v s v s + v = v s v 1 s 1 + v v θ e 1 1 + v s v s Doppler effect (moving source of sound) v θ λ heard 1 v = λemitted v s Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Synchrotron radiation power Power emitted is proportional to: P E 2 B 2 P γ = cc γ E 2π ρ 4 2 C γ = 4π 3 r e 5 m e c 2 3 = 8.858 10 m GeV 3 Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

The power is all too real! P γ = cc γ E 2π ρ 4 2

Synchrotron radiation power Power emitted is proportional to: P E 2 B 2 P γ = 4 ccγ E 2 2π ρ P γ 2 = α c 3 2 4 γ 2 ρ C γ = 4π 3 r e 5 m e c 2 3 = 8.858 10 m GeV 3 α = 1 137 Energy loss per turn: U 0 = C γ E 4 ρ U 0 = 4π 3 αhcγ 4 ρ Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg hc = 197 Mev fm

Typical frequency of synchrotron light Due to extreme collimation of light observer sees only a small portion of electron trajectory (a few mm) l ~ 2ρ γ 1/γ Pulse length: difference in times it takes an electron and a photon to cover this distance t ~ l βc l c = l βc 1 β ω ~ 1 t ~ γ 3 ω 0 t ~ 2ρ γ c 1 2γ 2 Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Spectrum of synchrotron radiation Synchrotron light comes in a series of flashes every T 0 (revolution period) T 0 the spectrum consists of harmonics of ω 0 = 1 T 0 time flashes are extremely short: harmonics reach up to very high frequencies At high frequencies the individual harmonics overlap ω 3 typ γ ω0 continuous spectrum! Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg ω ~ 1 γ ~ 4000 ω 0 typ ~ 10 MHz 16 Hz!

Wavelength continuously tunable! Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

dp dω = P tot ω c S ω ω c S x = 9 3 8π x K5 5 3 x dx x 0 S x dx = 1 P tot = 2 3 hc2 α γ4 ω c = 3 2 cγ 3 ρ ρ 2 1 0.1 0.01 ~ 2.1x 1 3 G 1 x = x K 5 3 x dx x ε c ev = 665 E 2 GeV B T 50% ~ 1.3 xe x 0.001 0.001 0.01 0.1 1 10 x = ω/ω c

Synchrotron radiation flux for different electron energies Flux [photons/s/mrad/0.1%bw] 10 13 10 12 10 11 10 10 LEP Dipole Flux I = 1 ma 20 GeV 50 GeV 100 GeV 10 9 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Photon energy [ev] Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Angular divergence of radiation The rms opening angle R at the critical frequency: ω = ω c R 0.54 γ well below ω «ω c R 1 γ ω c ω 1 3 1 3 0.4 λ ρ independent of γ! 1 3 well above ω» ω c R 0.6 γ ω c ω 1 2

Angular divergence of radiation at the critical frequency γθ well below γθ ω = 0. 2ω c well above ω = 2ω c γθ

The brightness of a light source: Source area, S Angular divergence, Ω Flux, F Brightness = constant x F S x Ω Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

X-rays Brightness Average Brightness XFELs Peak Brightness (3 rd Gen) (XFELs) Bertha Roentgen s hand (exposure: 20 min)

Sources of Synchrotron Radiation Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

3 types of storage ring sources: 1. Bending magnets: B ~ N e detector short signal pulse broad hν-band time frequency

3 types of storage ring sources: 2. Wigglers: large undulations B ~ N e N w x10 Series of short pulses broad hν-band time frequency

3 types of storage ring sources: 3. Undulators: small undulations detector continuously illuminated long signal pulse narrow hν-band detector B ~ N e N 2 u x10 3 hν/ hν N time frequency

Click to edit Master title style Bright beams of particles: phase space density Incoherent, spontaneous emission of light: Coherent, stimulated emission of light Large phase space Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Click to edit Master title style Selection of wavelength in an undulator In an undulator an electron (on a slalom) races an emitted photon N S N(orth) S(outh) A B C period λ u δl= nλ electron v β c photon c at A an electron emits a photon with wavelength λ and flies one period λ u ahead to B with velocity v = βc. There it emits another photon with the same wavelength λ. At this moment the first photon is already at C. If the path difference δl corresponds to n wavelengths, then we have a positive interference between the two photons. This enhances the intensity at this wavelength. Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Selection of wavelength in an undulator II N S N(orth) S(outh) A B C electron photon period λ u v β c c δl= nλ The path difference λ K λ = u 1 2 + 2nγ 2 θθ = KK γγ 2 δl nλ (1 β ) λ u, 1 β detour through slalom [ mm] B[ T ] K = 0.0934 λu 1 2γ 2

Click Radiation to edit cone Master of an title undulator style Undulator radiates from the whole length L into a narrow cone. Propagation of the wave front BC is suppressed under an angle θ 0, if the path length AC is just shorter by a half wavelength compared to AB (negative interference). This defines the central cone. L = AB AC = 1 2 L 2 ( 1 cosθ ) Lθ Negative interference for λ θ = 2 L 0 R0 = λ ε 0 = θ0r0 = λ L 2 Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg 0 1 4 0 L = λ 2

Undulator radiation λ = 2 500 mm K-edges λ = λu 2nγ 2 1+ K 2 2 + γ 2 θ 2 λ = 1.5 mm 1 2 ( 1 K ) λ 2 = 2n * + λ u Medium energy rings ESRF, APS

Microwave, laser undulators T. Shintake, OIST

Click When to an edit electron Master collides title style with a photon Also known as Compton or Thomson scattering e - ε f ε i θ εε ff = 4γγ2 εε ii 1 + γγ 2 θθ 2 backscattered photon has the maximum energy at an angle of 1/γ the energy drops by a factor of 2 undulator s periodic magnetic field could be viewed as a «photon», with useful parallels between the two cases Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Undulator line width Undulator of infinite length N u = λ λ =0 Finite length undulator radiation pulse has as many periods as the undulator the line width is λ λ 1 N u Due to the electron energy spread λ λ = 2σ E E

Free Electron Lasers Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

COHERENT EMISSION BY THE ELECTRONS Intensity N Intensity N 2 INCOHERENT EMISSION COHERENT EMISSION

BRIGHTNESS OF SYNCHROTRON RADIATION Bending magnet electrons ~ N e periods Wiggler ~ N e ~ N 10 Undulator ~ N e ~ N 2 10 4 FEL ~ N 2 µ-b ~ N 2 10 10 Superradiance ~ N e 2 ~ N 2 10 12

FIRST DEMONSTRATIONS OF COHERENT EMISSION (1989-1990) 180 MeV electrons 30 MeV electrons T. Nakazato et al., Tohoku University, Japan J. Ohkuma et al., Osaka University, Japan

MUCH HIGHER BRIGHTNESS CAN BE REACHED WHEN THE ELECTRONS COOPERATE WAVELENGTH INCOHERENT EMISSION COHERENT EMISSION

Particle beam emittance: Source area, S Angular divergence, Ω Emittance = S x Ω Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Undulator radiation from 6 GeV beam with zero emittance, energy spread (example ESRF) 8 th 9 th 10 th 7 th harmonic Emittance 4 nm rad, 1% coupling, finite energy spread

The storage ring generational change Riccardo Bartolini (Oxford University) 4 th low emittance rings workshop, Frascati, Sep. 17-19, 2014 Storage rings in operation ( ) and planned ( ). The old ( ) and the new ( ) generation.

Click to edit Master title style A revolution in storage ring technology Pioneer work: MAX IV (Lund, Sweden) Aperture reduction Multi-Bend Achromat (MBA) β x β y D Technological achievement: NEG* coating of small vacuum chambers short & strong multipoles short lattice cells many lattice cells low angle per bend Small magnet bore High magnet gradient *Non Evaporable Getter emittance ε (energy) 2 (bend angle) 3 Emittance reduction from nm to 10...100 pm range Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Click The MAX to edit IV Laboratory Master title in style Lund, Sweden Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Synchrotron light polarization Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

An electron in a storage ring TOP VIEW SIDE VIEW Polarization: Linear in the plane of the ring the electric field vector E TILTED VIEW elliptical out of the plane E

x Polarisation: spectral distribution dp = dω Ptot ω c S x = Ptot ω S ( ) [ ( ) ( )] c σ x + S π x 7 S σ = 8 S 3:1 1 S π = 8 S

Angular distribution of SR E γθ E

Synchrotron light based electron beam diagnostics Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Seeing the electron beam (SLS) X rays visible light, vertically polarised σ x ~ 55µm Synchrotron Radiation, L. Rivkin, CAS on FELs and ERLs, 1.06.16, Hamburg

Seeing the electron beam (SLS) Making an image of the electron beam using the vertically polarised synchrotron light

High resolution measurement Wavelength used: 364 nm For point-like source the intensity on axis is zero Peak-to-valley intensity ratio is determined by the beam height Present resolution: 3.5 µm