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Physics of Incoherent Synchrotron Radiation Kent Wootton SLAC National Accelerator Laboratory

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SLAC-PUB-17214 Physics of Incoherent Synchrotron Radiation Kent Wootton SLAC National Accelerator Laboratory US Particle Accelerator School Fundamentals of Accelerator Physics 23rd Jan 2018 Old Dominion University Norfolk, VA This work was supported by the Department of Energy contract DE-AC02-76SF00515. Circular accelerators – observation of SR in 1947 “A small, very bright, bluish- white spot appeared at the side of the chamber where the beam was approaching the observer. At lower energies, the spot changed color.” “The visible beam of “synchrotron radiation” was an immediate sensation. Charles E. Wilson, president of G.E. brought the whole Board of Directors to see it. During the next two years there were visits from six Nobel Prize winners.” J. P. Blewett, Nucl. Instrum. Methods Phys. Res., Sect. A, 266, 1 (1988). 2 Circular electron colliders – SR is a nuisance • “… the radiative energy loss accompanying the Source: Australian Synchrotron circular motion.” 4휋 푒2 훿퐸 = 훾4 3 푅 • Limits max energy • Damps beam size Source: CERN D. Iwanenko and I. Pomeranchuk, Phys. Rev., 65, 343 (1944). J. Schwinger, Phys. Rev., 70 (9-10), 798 (1946). 3 ‘Discovery machines’ and ‘Flavour factories’ • Livingston plot • Proton, electron colliders • Protons, colliding partons (quarks) • Linear colliders Linear colliders proposed Source: Australian Synchrotron 4 Future energy frontier colliders FCC-ee/ FCC/ SPPC d=32 km LEP/ Source: Fermilab 5 SR can be useful – accelerator light sources • Unique source of electromagnetic radiation • Wavelength-tunable • High intensity • Spatial coherence • Polarised • Pulsed Source: lightsources.org More in the next lecture – Storage Ring Light Sources 6 Outline – Synchrotron Radiation • Physics of synchrotron radiation • Characteristics of synchrotron radiation • Power, spectrum, flux • Universal spectrum of bending magnet SR • Critical photon energy • Accelerator physics implications • Damping rates • Equilibrium emittances 7 Electric field of an electric charge • Stationary charge • Field lines extend radially outward – • Acceleration • Finite speed of light, – causality • ‘Kinks’ in electric field distribution manifest as radiation 8 Electric field of an accelerated charge (휷 = ퟎ. ퟏ) http://www.shintakelab.com/en/enEducationalSoft.htm 9 Electric field of an accelerated charge (휷 = ퟎ. ퟗ) Detector http://www.shintakelab.com/en/enEducationalSoft.htm 10 Electric field, synchrotron radiation • Acceleration of a relativistic electron – – • Do virtual photons become real photons? • How much more power from transverse acceleration? 11 Power – linear acceleration 2 1 푒 푐 2 푃푅 = 2 2 푎 (charge rest frame) 6휋휖0 푚푐 1 푒2푐 d푝 2 1 d퐸 2 푃퐿 = 2 2 − 2 (lab frame) 6휋휖0 푚푐 d휏 푐 d휏 2 2 2 2 2 Using 퐸 = 푚0푐 + 푝 푐 , d푡 → 훾d휏 it can be shown that 1 푒2푐 d푝 2 1 푒2푐 d푝 2 푃퐿∥ = 2 2 = 2 2 (lab) 6휋휖0 푚푐 훾d휏 6휋휖0 푚푐 d푡 d푝 d퐸 Using = , d푡 d푠 1 푒2푐 d퐸 2 푃퐿∥ = 2 2 (lab) 6휋휖0 푚푐 d푠 J. Schwinger, Phys. Rev., 75, 1912 (1949). 12 Power – transverse acceleration 0 1 푒2푐 d푝 2 1 d퐸 2 푃퐿 = 2 2 − 2 (lab) 6휋휖0 푚푐 d휏 푐 d휏 1 푒2푐 d푝 2 푃퐿⊥ = 2 2 (lab) 6휋휖0 푚푐 d휏 Using d푡 → 훾d휏, 2 2 1 푒 푐 2 d푝 푃 = 훾2푃 푃퐿⊥ = 2 2 훾 (lab) 퐿⊥ 퐿∥ 6휋휖0 푚푐 d푡 d푝 2 퐸2 Using = 훽4 , d푡 휌2 2 4 4 푒 푐 4 훾 훾 푃퐿⊥ = 훽 2 (lab) 푃 ∝ 6휋휖0 휌 휌2 J. Schwinger, Phys. Rev., 75, 1912 (1949). J. Schwinger, ‘On Radiation by Electrons in a Betatron’, (2000), LBNL-39088. 13 Power – summary 2 4 푒 푐 4 훾 푃퐿⊥ = 훽 2 6휋휖0 휌 • Transverse a factor of 훾2 larger than longitudinal • 푃 ∝ 훾4 • Factor of 1013 for 푒−/푝+ (109 for 푒−/휇−) • Proton (or muon) circular colliders for high energy 1 • 푃 ∝ , large bending radius beneficial 휌2 Source: Australian Synchrotron 14 Energy loss per turn • Energy loss per turn 푈0 = ׯ 푃퐿⊥ d푡 2휋휌 • Isomagnetic lattice (only one bending radius 휌), d푡 = 훽푐 2 4 푒 3 훾 푈0 = 훽 3휖0 휌 퐸 GeV 4 푈 GeV = 퐶 , 0 훾 휌 m −5 −3 퐶훾 = 8.85 × 10 m GeV 15 Spectrum – Universal function of synchrotron radiation • Critical photon energy 3 ℏ푐훾3 휀 = ≡ ℏ휔 푐 2 휌 푐 • For electrons 퐸 GeV 3 휀 keV = 2.218 푐 휌 m = 0.665퐸 GeV 2퐵[T] • Synchrotron radiation spectrum 휔푐 - half the power above, half below ∞ d푃훾 푃훾 9 3 휔 푃훾 휔 = න 퐾 푥 d푥 = 푆 d휔 휔 8휋 휔 5 휔 휔 푐 푐 푥0 3 푐 푐 • Universal function 푆 H. Wiedemann, (2007) Particle Accelerator Physics, Springer-Verlag, p. 823 16 Angular distribution Spatial and spectral flux distribution of photon flux 2 2 d 푁ph 2 Δ휔 휔 훾 2 = 퐶Ω퐸 퐼 2 2 5/2 퐾2/3 휉 퐹 휉, 휃 d휃d휓 휔 휔푐 1+훾 휃 3훼 22 photons 퐶Ω = 2 2 = 1.3255 × 10 2 2 4휋 푒 푚푒푐 s rad GeV A 퐾 is the modified Bessel’s function, 2 2 퐾2 휉 2 2 2 훾 휃 1/3 퐹 휉, 휃 = 1 + 훾 휃 1 + 2 2 2 1 + 훾 휃 퐾2/3 휉 H. Wiedemann, Particle Accelerator Physics, Springer-Verlag, (2007). 17 Angular distribution – relativistic acceleration • Narrow cone of radiation 1 훾 • Tangential to the direction of acceleration D. H. Tomboulian and P. L. Hartman, Phys. Rev., 102, 1423 (1956). 18 Polarisation 퐵 (휋) (휎) • Synchrotron radiation highly polarised • Linear polarisations denoted with respect to magnetic field • Rings usually have a vertical main dipole field • 휎 – ‘senkrecht’, German for perpendicular (horizontal) • 휋 – parallel (vertical) 7 1 • Power 푃 = 푃, 푃 = 푃 휎 8 휋 8 19 Polarisation – angular distribution 휎 (horizontal) 휋 (vertical) • Typical electron, 퐸 = 3 GeV, 퐵 = 1.2 T, 휀푐 = 7.2 keV • Horizontal polarisation in orbit plane • Vertical polarisation above and below the orbit plane H. Wiedemann, (2007) Particle Accelerator Physics, Springer-Verlag, p. 814 20 Accelerator physics implications Protons are like elephants… … electrons (in rings) are like goldfish Source: http://www.mrwallpaper.com Source: http://www.theresponsiblepet.com 21 Liouville’s theorem • Liouville’s theorem • Emittance conserved under acceleration • SR introduces damping 푥′ 푥 22 Accelerator physics implications • Implications mostly for electron rings • So far, described synchrotron radiation using statistical distributions • Average energy loss per turn from SR results in damping • SR photons are both waves and quanta • Random quantised SR emission results in random excitation of electrons • Balance leads to equilibrium L. Rivkin, ‘Electron Dynamics with Synchrotron Radiation’, CERN Accelerator School: Introduction to Accelerator Physics, 5th Sep 2014, Prague, Czech Republic (2014). 23 Damping rates B • Synchrotron radiation damping means that the amplitude of single particle oscillations (betatron, synchrotron oscillations) are damped • Equilibrium determined by damping rates and lattice • At the instantaneous rate, the time for an electron to lose all its energy through synchrotron radiation • Damping time typically ~ms 24 SR damping – vertical • Electron performing vertical betatron oscillations • SR photons emitted in a very narrow cone, essentially parallel to electron trajectory with momentum 푝0 • Photon with momentum 푝훾 carries away transverse momentum of electrons • RF system replenishes only longitudinal momentum • Transverse momentum asymptotically damps 25 Damping rate – vertical • Consider betatron oscillation 퐴 푦 = 퐴 cos 휙 , 푦′ = sin 휙 훽(푠) • Oscillation amplitude 퐴2 = 푦2 + 훽 푠 푦′ 2 • Electron loses momentum to SR, gains only 훿퐸 energy at cavity 훿푦′ = −푦′ 퐸 • Change of amplitude 푑퐴 2퐴 = 훽2 푠 2푦′ 푑푦′ 훿퐸 퐴훿퐴 = −훽2 푠 푦′2 퐸 • Averaging over all betatron phases, 퐴2 2휋 퐴2 = 훽2 푠 푦′2 = ׬ sin2 휙d휙 2휋 0 2 M. Sands, ‘The Physics of Electron Storage Rings: An Introduction’, Stanford Linear Accelerator Center, Menlo Park, CA, SLAC-R-121 (1970). 26 Damping rate – vertical 퐴2 훿퐸 • Change in action 퐴훿퐴 = − 2 퐸 훿퐴 훿퐸 • Therefore = − 퐴 2퐸 • Summing all the energy losses around the ring must equal the total energy loss 푈0, therefore for one turn 푇0 Δ퐴 푈 Δ퐴 1 푑퐴 푈 = − 0 → = = − 0 퐴 2퐸 퐴푇0 퐴 푑푡 2퐸푇0 • Exponential damping 푒−휁푦푡 with damping coefficient 1 푈0 휁푦 = = 휏y 2퐸푇0 M. Sands, ‘The Physics of Electron Storage Rings: An Introduction’, Stanford Linear Accelerator Center, Menlo Park, CA, SLAC-R-121 (1970). 27 SR damping – longitudinal • SR photon emission carries away longitudinal momentum • Electron rings need significant RF voltage to maintain beam • SR emission is • Quantised – some electrons emit more, some less • Deterministic – high energy electrons emit more, low energy emit less • Design for phase stability B 28 Damping rate – longitudinal • An off-energy particle traverses a dispersive orbit Δ푥 퐷 Δ퐸 d푠′ = 1 + 푑푠 = 1 + 푥 푑푠 휌 휌 휌 퐸 d푠 Δ푥 • This particle radiates energy 푈′ over one turn d푠′ 1 1 퐷 Δ퐸 푈′ = ׯ 푃d푡 = ׯ 푃 d푠′ = ׯ 푃 1 + 푥 d푠 푐 푐 휌 퐸 • Differentiating with respect to energy d푈 1 d푃 퐷 d푃 Δ퐸 푃 ׯ + 푥 + d푠 = d퐸 푐 d퐸 휌 d퐸 퐸 퐸 • The average energy offset Δ퐸 should be zero, therefore 퐸 d푈 1 d푃 퐷 푃 ׯ + 푥 d푠 = d퐸 푐 d퐸 휌 퐸 K. Wille, The Physics of Particle Accelerators: An Introduction, Oxford University Press, Oxford, UK (2000). M. Sands, ‘The Physics of Electron Storage Rings: An Introduction’, Stanford Linear Accelerator Center, Menlo Park, CA, SLAC-R-121 (1970). Y. Papaphilippou, ‘Fundamentals of Storage Ring Design’, USPAS, Santa Cruz, CA, USA (2008). 29 Damping rate – longitudinal d퐵 d퐵 d푥 d퐵 퐷 퐷 • Using 푃 = 퐶 퐸2퐵2, = = 푥 = 퐵푘휌 푥 훾 d퐸 d푥 d퐸 d푥 퐸 퐸 d푃 푃 = 2 1 + 푘휌퐷 d퐸 퐸 푥 • Substituting this in to the equation on the previous slide d푈 2푈 1 퐷 1 ׯ 푃 푥 2푘 + d푠 + 0 = d퐸 퐸 푐퐸 휌 휌2 퐶 퐸4 1 퐶 퐸4 1 Using P = 훾 , therefore U = ׯ 푃d푠 = 훾 ׯ d푠 • 푒2푐2 휌2 0 푐 푒2푐3 휌2 1 1 ׯ 퐷푥 2푘+ d푠 d푈 푈0 휌 휌2 = 2 + 1 d퐸 퐸 ׯ d푠 휌2 • Energy oscillations exponentially damped 푒−휁푠푡 with the form 1 1 ׯ 퐷푥 2푘+ d푠 1 d푈 푈0 휌 휌2 휁푠 = = 2 + 풟 , 풟 = 1 2푇0 d퐸 2푇0퐸 ׯ d푠 휌2 K.
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    Introduction to Synchrotron Radiation Frederico Alves Lima International School on Laser-Beam Interactions Centro Nacional de Pesquisa em Energia e Materiais - CNPEM UFRN - Natal, Brazil Laboratório Nacional de Luz Síncrotron - LNLS September 2016 Outline ✓ Tools for structural analysis ✓ History of X-rays ✓ Synchrotron Radiation ✓ LNLS & SIRIUS: Synchrotron Radiation in Brazil Why do we need to study “structure” Structure Dynamics - X-ray crystallography - Laser spectroscopy - electron microscopy - NMR - atomic force microscopy - Time-resolved diffraction & XAS - electron diffraction - Time-resolved PES - X-ray absorption spectroscopy - NMR Manganite: atomic motion coupled by charge and orbital order Graphene Fullerene Layer-selective spin dynamics in Nanotube magnetic multilayers Photosystem II Rotating hydrated Mb molecule What are the length scales involved ? http://www.newgrounds.com/portal/view/525347 The Electromagnetic Spectrum Electromagnetic wave ➟ Light! Orthogonal and alternating electric and magnetic fields that propagate into space. Set of equations describing how electric and magnetic fields are generated and altered by each other and by charges and currents. Maxwell’s equation of electromagnetism James Clerk Maxwell The Electromagnetic Spectrum 700 nm 400 nm X-ray ➟ proper tool to investigate atoms. History of X-rays In the evening of Nov. 8th 1895 Wilhem Röntgen first detected x-rays He found that when running a high-voltage discharge tube enclosed in thick black cardboard which excluded all visible light, in his darkened room, a paper plate covered on one side with barium platinocyanide would fluoresce, even when it was as far as 2 m from the discharge tube. ➟ X-rays! He soon discovered that these ‘x-rays’ also stained photographic plates and latter demonstrated that objects of different thicknesses showed different degrees of transparency.
  • X-Ray Optics for Synchrotron Radiation Beamlines

    X-Ray Optics for Synchrotron Radiation Beamlines

    ESI2013: 3rd EIROforum School on Instrumentation An Introduction to Synchrotron Radiation Ray BARRETT X-ray Optics Group European Synchrotron Radiation Facility e-mail : [email protected] Outline Part I Part II Introduction SR Research to synchrotron radiation (SR) Mostly Illustrated by examples from the ESRF 27 May 2013 ESI 2013: Synchrotron Radiation 2 Outline PART I Introduction to synchrotron radiation 1. Origin and physics 2. Historical evolution 3. Synchrotron radiation facilities 4. Three forms of synchrotron radiation 5. Sources and their operation 27 May 2013 ESI 2013: Synchrotron Radiation 3 What’s a synchrotron radiation source? • An extremely intense source of X-rays (also IR & EUV) • Typically produced by highly energetic electrons (or positrons) moving in a large circle in the synchrotron (or more usually Storage Ring). •Highly collimated X-rays are emitted tangentially to the storage ring and simultaneously serve multiple beamlines for scientific applications spanning physical, chemical and life sciences 27 May 2013 ESI 2013: Synchrotron Radiation 4 Origin of synchrotron radiation L. Shklovsky (1953) • Synchrotron radiation is electromagnetic energy emitted by charged particles (e.g., electrons and ions) that are moving at speeds close to that of light when their paths are altered, e.g. by a magnetic field. • It is thus termed because particles moving at such speeds in particle accelerators known as a synchrotrons produce electromagnetic radiation of this type. The Crab Nebula – a natural SR source CHANDRA (2001) 27 May 2013 ESI 2013: Synchrotron Radiation 5 Basic Principles Classical case Relativistic case v << c v ~ c orbit orbit Centripetal acceleration =1/ Isotropic emission Emission concentrated within a narrow forward cone E e mc2 Ee = 6 GeV (ESRF) mc2 = 511keV = 10-4 rad = a few 10-3 deg 27 May 2013 ESI 2013: Synchrotron Radiation 6 Man-made synchrotron radiation 1947 EVOLUTION 1930 First observation First particle of synchrotron accelerators radiation at General Electric First observation (USA).
  • Translational Research in FLASH Radiotherapy—From Radiobiological Mechanisms to in Vivo Results

    Translational Research in FLASH Radiotherapy—From Radiobiological Mechanisms to in Vivo Results

    biomedicines Review Translational Research in FLASH Radiotherapy—From Radiobiological Mechanisms to In Vivo Results Loredana G. Marcu 1,2,* , Eva Bezak 2,3 , Dylan D. Peukert 4,5 and Puthenparampil Wilson 5,6 1 Faculty of Informatics & Science, Department of Physics, University of Oradea, 410087 Oradea, Romania 2 Cancer Research Institute and School of Health Sciences, University of South Australia, Adelaide, SA 5001, Australia; [email protected] 3 School of Physical Sciences, Department of Physics, University of Adelaide, North Terrace, Adelaide, SA 5005, Australia 4 School of Civil, Environmental & Mining Engineering, University of Adelaide, North Terrace, Adelaide, SA 5005, Australia; [email protected] 5 STEM, University of South Australia, Adelaide, SA 5001, Australia; [email protected] 6 Department of Radiation Oncology, Royal Adelaide Hospital, Adelaide, SA 5000, Australia * Correspondence: [email protected] Abstract: FLASH radiotherapy, or the administration of ultra-high dose rate radiotherapy, is a new radiation delivery method that aims to widen the therapeutic window in radiotherapy. Thus far, most in vitro and in vivo results show a real potential of FLASH to offer superior normal tissue sparing compared to conventionally delivered radiation. While there are several postulations behind the differential behaviour among normal and cancer cells under FLASH, the full spectra of radiobiological mechanisms are yet to be clarified. Currently the number of devices delivering FLASH dose rate is few and is mainly limited to experimental and modified linear accelerators. Nevertheless, FLASH research Citation: Marcu, L.G.; Bezak, E.; is increasing with new developments in all the main areas: radiobiology, technology and clinical Peukert, D.D.; Wilson, P.