Characteristics and Properties of Synchrotron Radiation
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1 Characteristics and Properties of Synchrotron Radiation Giorgio Margaritondo Vice-président pour les affaires académiques Ecole Polytechnique Fédérale de Lausanne (EPFL)
2 Outline: How to build an excellent x-ray source using Einstein s relativity Some examples of applications Coherent x-rays: a revolution in radiology The future: from storage rings to free electron lasers
3 THE BEACH OPTION PROGRAM : STEP A (3.5 minutes) OBJECTIVES: how are x-ray produced? NEXT OPTIONS: (1) go to step B, or (2) go to the beach STEP B (9.5 minutes) OBJECTIVES: how to get collimation again, how are x-ray produced? NEXT OPTIONS: (1) go to step C, or (2) go to the beach STEP C (the rest of the time maybe more) OBJECTIVES: everything else
4 Synchrotron light in 3.5 minutes for lazy students (and teachers): Electron: Speed At time zero, the electron enters the magnet, is accelerated and emits photons Magnet: Lorentz force acceleration photon emission L At the time L /u, the electron leaves the magnet D The first photons arrive at the detector at the time (L + D)/c The last photons arrive at the time L /u + D /c Photon detector Photon pulse duration: Δt = L/u - L/c = (L/u) (1-u/c) Characteristic frequency: ν = 1/Δt = u/[l(1-u/c)] = u γ 2 (1+u/c)/L For u c, (1+u/c) 2 and ν 2cγ 2 /L γ 2 = 1/(1-u 2 /c 2 ) For L = 0.1 m and γ = 4000, ν s x-rays!
5 Synchrotron light in 9.5 minutes for (not entirely) lazy students (and teachers): Electrons circulating at a speed u c in a storage ring emit photons in a narrow angular cone, like a flashlight : why? Answer: RELATIVITY But in the laboratory frame the emission shrinks to a narrow cone Seen in the electron reference frame, the photon are emitted in a wide angular range Take a photon emitted (blue arrow) in a near-trasverse direction in the (black) electron frame, with velocity components c x 0, c y c. In the (green) laboratory frame the velocity (red arrow) components become c x u, c y (c 2 -u 2 ) 1/2 = c/γ. The angle θ is c y /c = 1/γ -- very narrow!!!
6 The emitted photons are x-rays: why (a second look)? Seen from the side of the ring, each electron looks like an oscillating charge in an antenna, emitting photons with a frequency 2πR/c -- in the radio wave range. What shifts the emission to the x-ray range? RELATIVITY AGAIN! L R (1/γ) 1 γ A torchlight-electron illuminates a small-area detector once per turn around the ring for a short time Δt Photons start to be detected at the time D/c Photon pulse duration: D Detection ends at the time L/u + (D - L)/c Δt = L/u + (D - L)/c - D/c = L/u - L/c = (L/u) (1-u/c) = (L/u)γ 2 /(1+u/c) For u c, (1+u/c) 2 and Δt L/(2cγ 2 ) R/(2cγ 3 ). Characteristic frequency ν = 1/Δt 2cγ 3 /R -- again, x-rays
7 Fireplaces and torchlights : A fireplace is not very effective in "illuminating" a specific target: its emitted power is spread in all directions A torchlight is much more effective: it is a small-size source with emission concentrated within a narrow angular spread This can be expressed using the brightness
8 The brightness (or brilliance) of a source of light : Source area, ξ 2 ξ Angular divergence, solid angle Ω Flux, F Brightness = constant F ξ 2 Ω
9 The historical growth in x-ray brightness/brilliance Between 1955 and 2000, the brightness increased by more than 15 orders of magnitude whereas the top power of computing increased only by 6-7 orders of magnitude
10 Heat flux (watt/mm 2 ) Surface of the sun 100 Swiss Light Source (SLS) Interior of rocket nozzle 10 ALS, Elettra, SRRC, PAL Nuclear reactor core 1
11 A real synchrotron facility: Diamond (UK)
12 Why x-rays and ultraviolet? Chemical bond lengths Wavelength (Å) Photon energy Core electrons Molecules (ev) 100 Proteins Valence electrons
13 synchrotron radiation molecular atom or fragments molecule fragmentation spectroscopy scattered photons, fluorescence photoelectrons, Auger electrons small-angle scattering fluorescence spectroscopy photoelectron/auger spectroscopy transmitted absorption spectroscopy photons EXAFS Synchrotron x-rays: Many different interactions scattered photons scattering solid Many different fluorescence applications fluorescence spectroscopy photoelectrons, Auger electrons photoelectron/auger spectroscopy diffracted photons X-graphy transmitted absorption spectroscopy photons EXAFS Atoms & molecules desorption spectroscopy
14 General scheme of a synchrotron facility
15 Objective: building a very bright x-ray source using an undulator and relativity electron Speed u c Undulator (periodic B-field, period L centimeters In the undulator (laboratory) frame, the electron moves at speed c The period L is Lorentz-contracted becoming L /γ In the electron frame: The periodic B-field is accompanied by a perpendicular periodic E-field. Moving at a speed c towards the electron, the undulator looks like an electromagnetic wave with wavelength L /γ. Synchrotron radiation is produced by the elastic scattering of this wave by the electron. Back to the laboratory frame, the wavelength L /γ emitted by the moving electron is Doppler-shifted by a factor 2γ, becoming L /2γ 2. The macroscopic undulator period is transformed into x-ray wavelengths!
16 In summary, what produces the high brightness of a real synchrotron source? Free electrons can emit more power than bound electrons high flux The control of the electron beam trajectories in the storage ring is very sophisticated: small transverse beam cross section small photon source size Relativity drastically reduces the angular divergence of the emitted synchrotron radiation
17 3 types of sources: 1. Undulators: small undulations detector continuously illuminated detector long signal pulse narrow band hν/δhν N time frequency
18 3 types of sources: 2. Bending magnets: short signal pulse broad band time frequency
19 3 types of sources: 3. Wigglers: large undulations Series of short pulses broad band time frequency
20 3 types of sources - summary: Undulators: time frequency Bending magnets: time frequency Wigglers: More intensity than bending magnets time frequency
21 Undulator emission spectrum: Central wavelength: L/2γ 2 L = period θ First correction: out of axis, the Doppler factor is not 2γ 2 but changes with θ Central wavelength: (L/2γ 2 )/(1+ 2γ 2 θ 2 ) Second correction: stronerer B-field means stronger undulations and less on-axis electron speed. This changes γ so that: Central wavelength: (L/2γ 2 )/(1+ ab 2 )
22 Bending magnet emission spectrum: The (relativistic) rotation frequency of the electron determines the (Dopplershifted) central wavelength: λ o = (1/2γ 2 )(2πcm o /e)(1/b) The sweep time δt of the emitted light cone determines the frequency spread δν and the wavelength bandwidth: Δλ / λ o = 1 λ 0 Δλ λ A peak centered at λ c with width Δλ: is this really the well-known synchrotron spectrum? YES -- see the log-log plot: log(emission) λ o log(λ)
23 Synchrotron light polarization: Electron in a storage ring: TOP VIEW TILTED VIEW SIDE VIEW Polarization: Linear in the plane of the ring, elliptical out of the plane Special (elliptical) wigglers and undulators can provide ellipticaly polarized light with high intensity
24 Synchrotron Facilities in the World (2007): 69 in 25 Countries (operating or under construction) Historical Growth: Worldwide ISI data , Keyword: synchrotron
25 Photoelectron spectroscopy: basic ideas Formation of chemical bonds: atom solid electron energy The photon absorption increases the electron energy by hν before ejection of the electron from the solid Photoelectric effect: Photon (hν) electron energy hν Photoelectron
26 Photoelectron spectroscopy of high-temperature superconductivity: electrons superconducting state normal state energy High-resolution spectra taken with ultrabright synchrotron radiation The limited energy resolution of conventional photoemission makes it impossible to observe the phenomenon Energy (ev)
27 From spectroscopy to spectromicroscopy: Spectroscopy (energy and momentum resolution) Microscopy (spatial resolution) Chemical information Spectromicroscopy
28 The ESCA Microscopy Beamline at ELETTRA (Maya Kiskinova)
29 Coherence: the property that enables a wave to produce visible diffraction and interference effects Example: screen with pinhole ξ θ source (Δλ) fluorescent screen The diffraction pattern may or may not be visible on the fluorescent screen depending on the source size ξ, on its angular divergence θ and on its wavelength bandwidth Δλ
30 Longitudinal (time) coherence: source (Δλ) Condition to see the pattern: Δλ/λ < 1 Parameter characterizing the longitudinal coherence: coherence length : L c = λ 2 /Δλ Condition of longitudinal coherence: L c > λ
31 Lateral (space) coherence analyzed with a source formed by two point sources: Two point sources produce overlapping patterns: diffraction effects are no longer visible. However, if the two source are close to each other an overall diffraction pattern may still be visible: the condition is to have a large coherent power (2λ/ξθ) 2
32 Coherence summary: Large coherence length L c = λ 2 /Δλ Large coherent power (2λ/ξθ) 2 Both difficult to achieve for small wavelengths (x-rays) The conditions for large coherent power are equivalent to the geometric conditions for high brightness
33 Light-matter Interactions in Radiology: Absorption -- described by the absorption coefficient α Refraction (and diffraction/interference) -- described by the refractive index n For over one century, radiology was based on absorption: why not on refraction /diffraction?
34 Conventional radiology Refractive-index radiology (Giuliana Tromba)
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