DOCSLIB.ORG

Principles of Synchrotron Radia2on

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Principles of Synchrotron Radia2on Principles of Synchrotron Radiaon Boaz Nash Accelerator Source Division ESRF X-Ray and Neutron Science Summer Program August 30, 2016 Proper4es of radiaon spectrum flux (photons/second) coherence polarization (single wavefront? “directionality” of radiation field ability to make an interference pattern) linear, circular partial/full polarization brightness Synchrotron light sources give some control over flux divided by source size all these properties, in may cases providing the only such source for particular parameters. Other lectures tell you why x-rays are useful. Here, I will talk about where x-rays come from! Outline (1) X-rays from electrons radiation electricity and magnetism some relativity + (2) Where do the electrons come from? synchrotron particle accelerators = electron storage ring beam dynamics synchrotron radiation PART 1 radiation Radiaon from charged par4cles- generali4es Maxwell’s equations: In vacuum, one derives the wave equation, where one gets plane waves representing electromagnetic radiation. A source for such radiation requires a time dependent current. Accelerating charged particles will thus provide a source of radiation. Dipole radiaon Example of radiation source: Consider a charge oscillating in sinusoidal motion. ! x θ r It produces a radiation pattern: sin2 (θ) S ∼ rˆ r2 ω The radiation will have a frequency f = 2π x(t) = Acos(ωt) c and wavelength λ = remember c = λ f f Polarization is linear in direction ˆ θ c = 2.99792e8 m/sec = speed of light Now, consider a moving, wiggling charge x s λu Observed from a distance in the plane of oscillation, this looks (almost) like the oscillating dipole again! The motion creates two important differences: 1) wavelength shifted by Doppler effect, and in case of relativistic speed, there is a time contraction effect. Net effect: λ λ = u γ 2 2) Pattern of radiation gets distorted from motion. For high energy gets bent into cone of angle 1 γ Undulator magnet causes electron wiggle magnetic array or alternating field direction N S N S N S N S N S Brief review of relavity electron moving with velocity v v define β = c 1 speed of light γ = 2 1− β E[MeV ] E = γ mc2 γ = = 1.96 × E[MeV ] 1 0.5109989 β = 1− 2 γ Kinetic energy: 1 E = (γ − 1)mc2 → E = mv2 , for β << 1 k k 2 Relavity (2) Note that for gamma>5, However, effects as gamma gets large: velocity increase becomes length contraction negligible time dilation General expression for Radiaon from a trajectory ⎛ R⎞ ∞ ! iω τ + ! ! ⎡ nˆ(τ ) ⎛ ic ⎞ ⎤ ⎝⎜ c ⎠⎟ E(R,ω) = β(τ ) − ⎜1+ ⎟ e dτ ∫−∞ ⎢ R ⎝ ωR⎠ ⎥ ⎣ ⎦ ! R 2π ω ! k = = R λ c ! nˆ = β(τ ) R Derived from Liénard-Wiechert potentials ! ! v β = c So, given the electron orbit, we can compute the radiated electric field at a given frequency Undulator/wiggler orbit 2πs eB B = B cos( ) 0λu y 0 K = 2 = 0.934B0[T ]λu [cm] λu 2πmc (simplest planar undulator) K N periods x' = max γ λu K ⎛ 2πs⎞ 1 K 2 K 2 4πs x' = β (s) = sin β (s) = 1− − + cos( ) x ⎜ ⎟ s 2 2 2 γ ⎝ λu ⎠ 2γ 4γ 4γ λ0 transverse velocity long. velocity modulation Single electron radiation Undulator/Wiggler spectrum N −1 for K<1, all radiation contained in same cone inωT SN (ω) = ∑ e n=0 sin(NωT / 2) i(N −1)ωT /2 = e sin(ωT / 2) Transition between undulator and Wiggler spectrum We also get radiaon out of a dipole magnet By = B0 1 γ combining with time compression, we get a characteristic time ρ ρ 1 dT ' = (1+ (αγ )2 ) orbit length dL = γ 3 γ 2cγ ρ dT ' = characteristic time cγ Dipole magnet orbit Consider electron in constant magnetic field ! β(τ ) ρ ! ⎛ βcτ ⎛ βcτ ⎞ ⎞ r(τ ) = ρ sin ,ρ 1− cos ,0 ⎝⎜ ρ ⎝⎜ ρ ⎠⎟ ⎠⎟ B=.85 T p/c=6.04 GeV Be ω = ρ = 23m 0 γ m Dipole magnet spectrum cri4cal freQuency defined as (18.8 KeV for current ESRF ) hc (E = hf = ) λ Computing spectrum, one finds h=Planck’s constant 9 3 ∞ S(ξ) = ξ K5/3(ξ )dξ 8π ∫ξ Note that spectrum is much broader than for the undulator. PART 2 synchrotron Par4cle accelerators and storage rings Two things to understand: 1) Single electrons: How to store an electron and what kind of orbit will it have? 2) What kind of distribution of electrons will we get in the synchrotron? How to store a high energy electron? First accelerate: 6 GeV for ESRF To move in a circle, we use dipole magnets For transverse focussing/stability, use quadrupoles To fix chromatic aberration, we need sextupoles To give energy back lost to synchrotron radiation, and to provide longitudinal stability, use RF cavities ESRF Acceleraon Complex 1− β = 3.6 × 10−9 E 0.025eV Ek = 200MeV E = 6.03GeV k = Ek = 100keV Ek = 11MeV k γ = 1 γ = 1.2 γ = 22.5 γ = 391 γ = 11,800 electron buncher linac TL1 booster TL2 gun prebuncher storage ring Electron Gun and pre-buncher impulse to gun determines bunch shape and length pre-buncher does not accelerate 100 keV triode gun γ = 1.2 gun is triggered either at 10 Hz or at 1 Hz Storage ring components dipole quadrupole sextupole RF cavity Quadrupoles for strong focusing of electrons ¼ of an ESRF quadrupole B Apply Lorentz force law 1 Opposite signs! kx = − Field in body and we get focal strengths Bρ Requires clever given by quad placement B ! k = 1 and polarity to get B B (y xˆ x yˆ) y overall focussing! = 1 + Bρ Sextupoles Sextupoles may be used to correct energy effect from quadrupoles (chromaticity). Then causes additional stability problems which need to be corrected! ! Beam lifetime and dynamic aperture for injection B B (xy xˆ (x2 y2 )yˆ) hard problem in non-linear = 2 + − dynamics! RF cavity Gives energy back that was lost from radiation and provides longitudinal focussing. Most of the ESRF energy use (around 1.5 MW of power) is in these cavities; What happens to stored electrons? Phase space x x=0 time px,y = γ mvx,y configuration space x vs. time for electron, we normalize with phase P0 = γ mvs space x vs. p and use p dx x' = x = P0 ds What kind of distribu4on of electrons will we have in a storage ring? several stored electrons with different amplitudes. x’ Another effect: radiation x 4 4π r m cC e −5 γ E Cγ = 2 3 = 8.85 *10 3 radiated power 3 (mc ) GeV Pγ = 2 in a dipole: 2π ρ radiation constant Higher energy radiates more Lower energy radiates less: Radiation Damping! Radiaon effect on Longu4dinal dynamics E = E0 + ΔE E = E0 E = E0 − ΔE bending RF cavity magnets energy • Higher energy radiates more, lower energy less. Causes damping towards reference energy. position along ring Radiaon damping All electrons damp towards the same orbit! What sets the size of the electron beam? Where does the electron beam size come from? quantum excitation Graininess of photon emission Two sources of randomness: emission time of photons are random: Poisson process Energy emitted is also a random process, with the power spectrum as the probability distribution for each photon. For ESRF, only about 800 photons per turn! Or, about 1 photon emi_ed per meter! (approx. 12 photons per dipole) This quantum mechanical diffusion process accounts for the size of the electron beam, which (usually) determines the size of the x-ray beam! Where does the electron beam size come from? quantum excitation Quantum fluctuaon effect on electron dynamics without QFluct with QFluct damping synchrotron oscillations Electron motion and without quantum fluctuations. Result of damping/diffusion The electron beam reaches a unique Gaussian distribution– independent of how one injects into the ring. This is a major difference between electron synchrotrons and proton synchrotrons (e.g. LHC) By careful choice of where the dipoles and quadrupoles are, one can reduce the size of this equilibrium beam size (emittance = beam size in phase space). So called “Low emittance ring design” In fact, due to developments in lattice design, ESRF is completely replacing the storage ring in 2018 to reduce the electron beam emittance. 4nm -> 150 pm Coherent versus incoherent SR In storage ring, average interparticle spacing is larger than radiation wavelength, thus each electron emits independently. Power scales with N, number of electrons. An FEL (Free Electron Laser) is a different kind of accelerator where the electron beam is designed to have a microbunching structure on the scale of the radiation. This gives coherent radiation with a power proportional to N^2. There are several XFEL projects, e.g. LCLS (US), European XFEL (Germany) , SACLA (Japan), and more Because these are single pass (vs. storage ring) the energy requirement and repetition rate is typically much lower than storage rings. It looks like both storage ring synchrotron sources and FEL sources will fulfill different requirements and can complement each other. Further References Synchrotron Radiation Elleaume, Onuki, “Undulators, Wigglers and their Applicaons”, Taylor and Francis (2003) Electron Storage rings Ma Sands, “The Physics of Electron Storage Rings” Slac report 121 (1970) General accelerator physics references Helmut Wiedemann, ‘Particle Accelerator Physics’, 1&2, Springer-Verlag, 1993, (1999) S.Y. Lee, ‘Accelerator Physics’, World Scientific, (1999) Klaus Wille, ‘The Physics of Particle Accelerators’, Oxford University Press, (1996) Thank you for your attention!! Extra Slides Single electron radiation Time compression factor B C A α Electron moves at speed β, emitting wavefront at A, B, C Δt time between (c − v) v wavefronts Δt = Δt ' = βe cosα c c t (1 cos ) t ' t ' time for Δ = − βe α Δ Δ electron to emit 1+ (αγ )2 Δt ≈ Δt ' 2γ 2 dt = (1− β cosα) continuous generalization dt '.
Load more

Recommended publications
  • FROM KEK-PS to J-PARC Yoshishige Yamazaki, J-PARC, KEK & JAEA, Japan
    FROM KEK-PS TO J-PARC Yoshishige Yamazaki, J-PARC, KEK & JAEA, Japan Abstract target are located in series. Every 3 s or so, depending The user experiments at J-PARC have just started. upon the usage of the main ring (MR), the beam is JPARC, which stands for Japan Proton Accelerator extracted from the RCS to be injected to the MR. Here, it Research Complex, comprises a 400-MeV linac (at is ramped up to 30 GeV at present and slowly extracted to present: 180 MeV, being upgraded), a 3-GeV rapid- Hadron Experimental Hall, where the kaon-production cycling synchrotron (RCS), and a 50-GeV main ring target is located. The experiments using the kaons are (MR) synchrotron, which is now in operation at 30 GeV. conducted there. Sometimes, it is fast extracted to The RCS will provide the muon-production target and the produce the neutrinos, which are sent to the Super spallation-neutron-production target with a beam power Kamiokande detector, which is located 295-km west of of 1 MW (at present: 120 kW) at a repetition rate of 25 the J-PARC site. In the future, we are conceiving the Hz. The muons and neutrons thus generated will be used possibility of constructing a test facility for an in materials science, life science, and others, including accelerator-driven nuclear waste transmutation system, industrial applications. The beams that are fast extracted which was shifted to Phase II. We are trying every effort from the MR generate neutrinos to be sent to the Super to get funding for this facility.
    [Show full text]
  • Synchrotron Light Source
    Synchrotron Light Source The evolution of light sources echoes the progress of civilization in technology, and carries with it mankind's hopes to make life's dreams come true. The synchrotron light source is one of the most influential light sources in scientific research in our times. Bright light generated by ultra-rapidly orbiting electrons leads human beings to explore the microscopic world. Located in Hsinchu Science Park, the NSRRC operates a high-performance synchrotron, providing X-rays of great brightness that is unattainable in conventional laboratories and that draws NSRRC users from academic and technological communities worldwide. Each year, scientists and students have been paying over ten thousand visits to the NSRRC to perform experiments day and night in various scientific fields, using cutting-edge technologies and apparatus. These endeavors aim to explore the vast universe, scrutinize the complicated structures of life, discover novel nanomaterials, create a sustainable environment of green energy, unveil living things in the distant past, and deliver better and richer material and spiritual lives to mankind. Synchrotron Light Source Light, also known as electromagnetic waves, has always been an important means for humans to observe and study the natural world. The electromagnetic spectrum includes not only visible light, which can be seen with a naked human eye, but also radiowaves, microwaves, infrared light, ultraviolet light, X-rays, and gamma rays, classified according to their wave lengths. Light of Trajectory of the electron beam varied kind, based on its varied energetic characteristics, plays varied roles in the daily lives of human beings. The synchrotron light source, accidentally discovered at the synchrotron accelerator of General Electric Company in the U.S.
    [Show full text]
  • Scaling Behavior of Circular Colliders Dominated by Synchrotron Radiation
    SCALING BEHAVIOR OF CIRCULAR COLLIDERS DOMINATED BY SYNCHROTRON RADIATION Richard Talman Laboratory for Elementary-Particle Physics Cornell University White Paper at the 2015 IAS Program on the Future of High Energy Physics Abstract time scales measured in minutes, for example causing the The scaling formulas in this paper—many of which in- beams to be flattened, wider than they are high [1] [2] [3]. volve approximation—apply primarily to electron colliders In this regime scaling relations previously valid only for like CEPC or FCC-ee. The more abstract “radiation dom- electrons will be applicable also to protons. inated” phrase in the title is intended to encourage use of This paper concentrates primarily on establishing scaling the formulas—though admittedly less precisely—to proton laws that are fully accurate for a Higgs factory such as CepC. colliders like SPPC, for which synchrotron radiation begins Dominating everything is the synchrotron radiation formula to dominate the design in spite of the large proton mass. E4 Optimizing a facility having an electron-positron Higgs ∆E / ; (1) R factory, followed decades later by a p,p collider in the same tunnel, is a formidable task. The CepC design study con- stitutes an initial “constrained parameter” collider design. relating energy loss per turn ∆E, particle energy E and bend 1 Here the constrained parameters include tunnel circumfer- radius R. This is the main formula governing tunnel ence, cell lengths, phase advance per cell, etc. This approach circumference for CepC because increasing R decreases is valuable, if the constrained parameters are self-consistent ∆E. and close to optimal.
    [Show full text]
  • Electrostatic Particle Accelerators the Cyclotron Linear Particle Accelerators the Synchrotron +
    Uses: Mass Spectrometry Uses Overview Uses: Hadron Therapy This is a technique in analytical chemistry. Ionising particles such as protons are fired into the It allows the identification of chemicals by ionising them body. They are aimed at cancerous tissue. and measuring the mass to charge ratio of each ion type Most methods like this irradiate the surrounding tissue too, against relative abundance. but protons release most of their energy at the end of their It also allows the relative atomic mass of different elements travel. (see graphs) be measured by comparing the relative abundance of the This allows the cancer cells to be targeted more precisely, with ions of different isotopes of the element. less damage to surrounding tissue. An example mass spectrum is shown below: Linear Particle Accelerators Electrostatic Particle Accelerators These are still in a straight line, but now the voltage is no longer static - it is oscillating. An electrostatic voltageis provided at one end of a vacuum tube. This means the voltage is changing - so if it were a magnet, it would be first positive, then This is like the charge on a magnet. negative. At the other end of the tube, there are particles Like the electrostatic accelerator, a charged particle is attracted to it as the charges are opposite, but just with the opposite charge. as the particle goes past the voltage changes, and the charge of the plate swaps (so it is now the same charge Like north and south poles on a magnet, the opposite charges as the particle). attract and the particle is pulled towards the voltage.
    [Show full text]
  • Conceptual Design of Advanced Steady-State Tokamak Reactor -Compact and Safety Commercial Power Plant (A-SSTR2)
    Conceptual Design of Advanced Steady-State Tokamak Reactor -Compact and Safety Commercial Power Plant (A-SSTR2)- S. NISHIO 1), K. USHIGUSA 1), S. UEDA 1), A. POLEVOI 2), K. TOBITA 1), R. KURIHARA 1), I. AOKI 1), H. OKADA 1), G. HU 3), S. KONISHI 1), I. SENDA 1), Y. MURAKAMI 1), T. ANDO 1), Y. OHARA 1), M. NISHI 1), S. JITSUKAWA 1), R. YAMADA 1), H. KAWAMURA 1), S. ISHIYAMA 1), K. OKANO 4), T. SASAKI 5), G. KURITA 1), M. KURIYAMA 1), Y. SEKI 1), M. KIKUCHI 1) 1) Naka Fusion Research Establishment, Japan Atomic Energy Research Institute, Naka-machi, Naka-gun, Ibaraki-ken, 311-0193 Japan 2) STA fellow, Kurchatov Institute, RF, 3)STA scientist exchange program, SWIP, P.R.China, 4)Central Research Institute of Electric Power Industry, Japan, 5)Mitsubishi Fusion Center, Japan e-mail contact of main author : [email protected] Abstract. Based on the last decade JAERI reactor design studies, the advanced commercial reactor concept (A- SSTR2) which meets both economical and environmental requirements has been proposed. The A-SSTR2 is a compact power reactor (Rp=6.2m, ap=1.5m, Ip=12MA) with a high fusion power (Pf =4GW) and a net thermal efficiency of 51%. The machine configuration is simplified by eliminating a center solenoid (CS) coil system. SiC/SiC composite for blanket structure material, helium gas cooling with pressure of 10MPa and outlet temperature of 900˚C, and TiH2 for bulk shield material are introduced. For the toroidal field (TF) coil, a high temperature (T C) superconducting wire made of bismuth with the maximum field of 23Tand the critical current density of 1000A/mm2 at a temperature of 20K is applied.
    [Show full text]
  • Synchrotron Radiation R.P
    SYNCHROTRON RADIATION R.P. Walker Sincrotrone Trieste, Italy Abstract The basic properties of synchrotron radiation are described, and their relevance to the design of electron and proton rings is discussed. The development of specialized sources of synchrotron radiation is also considered. 1 . INTRODUCTION The electromagnetic radiation emitted by a charged particle beam in a circular accelerator is termed "synchrotron radiation" (SR) after its first visual observation nearly 50 years ago in the General Electric (G.E.) 70 MeV Synchrotron. The theoretical basis for understanding synchrotron radiation however goes back much further. Maxwell's equations (1873) made it clear that changing charge densities would radiate electromagnetic waves, and Hertz demonstrated these waves in 1887. The first more directly relevant development was the publication of Liénard's paper entitled "The electric and magnetic field produced by an electric charge concentrated at a point and in arbitrary motion" [1]. This work includes the energy loss formula for particles travelling on a circular path with relativistic velocities. Later, Schott published a detailed essay that included also the angular and frequency distribution of the radiation, as well as the polarization properties [2]. No further interest appears to have been taken in the topic until the early 1940's, when theoretical work in the Soviet Union showed that the energy loss may pose a limit on the maximum energy obtainable in the betatron [3]. Then in 1946 Blewett measured the energy loss due to SR in the G.E. 100 MeV betatron and found agreement with theory, but failed to detect the radiation after searching in the microwave region of the spectrum [4].
    [Show full text]
  • Particle Accelerators
    Particle Accelerators By Stephen Lucas The subatomic Shakespeare of St.Neots Purposes of this presentation… To be able to explain how different particle accelerators work. To be able to explain the role of magnetic fields in particle accelerators. How the magnetic force provides the centripetal force in particle accelerators. Why have particle accelerators? They enable similarly charged particles to get close to each other - e.g. Rutherford blasted alpha particles at a thin piece of gold foil, in order to get the positively charged alpha particle near to the nucleus of a gold atom, high energies were needed to overcome the electrostatic force of repulsion. The more energy given to particles, the shorter their de Broglie wavelength (λ = h/mv), therefore the greater the detail that can be investigated using them as a probe e.g. – at the Stanford Linear Accelerator, electrons were accelerated to high energies and smashed into protons and neutrons revealing charge concentrated at three points – quarks. Colliding particles together, the energy is re-distributed producing new particles. The higher the collision energy the larger the mass of the particles that can be produced. E = mc2 The types of particle accelerator Linear Accelerators or a LINAC Cyclotron Synchrotron Basic Principles All accelerators are based on the same principle. A charged particle accelerates between a gap between two electrodes when there is a potential difference between them. Energy transferred, Ek = Charge, C x p.d, V Joules (J) Coulombs (C) Volts (V) Ek = QV Converting to electron volts 1 eV is the energy transferred to an electron when it moves through a potential difference of 1V.
    [Show full text]
  • An Introduction to an Introduction to Particle Accelerators
    An Introduction to Particle Accelerators Erik Adli,, University of Oslo/CERN November, 2007 [email protected] v1.32 References • Bibliograp hy: – CAS 1992, Fifth General Accelerator Physics Course, Proceedings, 7-18 September 1992 – LHC Design Report [online] – K. Wille, The Physics of Particle Accelerators, 2000 • Other references – USPAS resource site, A. Chao, USPAS January 2007 – CAS 2005, Proceedings (in-print), J. Le Duff, B, Holzer et al. – O. Brüning: CERN student summer lectures – N. Pichoff: Transverse Beam Dynamics in Accelerators, JUAS January 2004 – U. Am aldi, presentation on Hadron therapy at CERN 2006 – Various CLIC and ILC presentations – Several figures in this presentation have been borrowed from the above references, thanks to all! Part 1 Introduction Particle accelerators for HEP •LHC:theworld: the world biggest accelerator, both in energy and size ((gas big as LEP) •Under construction at CERN today •End of magnet installation in 2007 •First collisions expected summer 2008 Particle accelerators for HEP The next big thing. After LHC, a Linear Collider of over 30 km lengg,th, will probably be needed (why?) Others accelerators • Histor ica lly: t he ma in dr iv ing force o f acce lerator deve lopment was collision of particles for high-energy physics experiments • However, today there are estimated to be around 17 000 particle accelerators in the world, and only a fraction is used in HEP • Over half of them used in medicine • Accelerator physics: a disipline in itself, growing field • Some examples: Medical applications • Therapy – The last decades: electron accelerators (converted to X-ray via a target) are used very successfully for cancer therapy) – Todayyp's research: proton accelerators instead (hadron therapy): energy deposition can be controlled better, but huge technical challenges • Imaging – Isotope production for PET scanners Advantages of proton / ion-therapy (() Slide borrowed from U.
    [Show full text]
  • 3Rd Generation Synchrotron Light Sources
    3rd Generation Synchrotron Light Sources Francis Perez Advanced School - oPAC 3rd Generation Synchrotron Light Sources July 9th, 2014 Outline 2 Synchrotron Radiation Synchrotron Light Sources 1st, 2nd, 3rd and Next Generation Enabling technologies Insertion devices Vacuum (NEG coating) Electronics (BPMs, LLRF, FOFB) Top UP Simulation tools … Advanced School - oPAC 3rd Generation Synchrotron Light Sources July 9th, 2014 Synchrotron Radiation 3 The theoretical basis for synchrotron radiation traces back to the time of Thomson's discovery of the electron. In 1897, Larmor derived an expression from classical electrodynamics for the instantaneous total power radiated by an accelerated charged particle. The following year, Liénard extended this result to the case of a relativistic particle undergoing centripetal acceleration in a circular trajectory. Liénard's formula showed the radiated power to be proportional to (E/mc2)4/R2, where E is particle energy, m is the rest mass, and R is the radius of the trajectory Arthur L. Robinson Advanced School - oPAC 3rd Generation Synchrotron Light Sources July 9th, 2014 Synchrotron Radiation 4 Early 20th century Advanced School - oPAC 3rd Generation Synchrotron Light Sources July 9th, 2014 Synchrotron Radiation CRAB Nebulae Radiation from the Crab Nebulae is actually the synchrotron radiation of ultra relativistic electrons in interstellar magnetic fields Recorded by Chinese astronomers in 1054 Advanced School - oPAC 3rd Generation Synchrotron Light Sources July 9th, 2014 SynchrotronWhy an accelerator?
    [Show full text]
  • Synchrotron Radiation
    Synchrotron Radiation The synchrotron radiation, the emission of very relativistic and ultrarelativistic electrons gyrating in a magnetic field, is the process which dominates much of high energy astrophysics. It was originally observed in early betatron experiments in which electrons were first accelerated to ultrarelativistic energies. This process is responsible for the radio emission from the Galaxy, from supernova remnants and extragalactic radio sources. It is also responsible for the non-thermal optical and X-ray emission observed in the Crab Nebula and possibly for the optical and X-ray continuum emission of quasars. The word non-thermal is used frequently in high energy astrophysics to describe the emission of high energy particles. This an unfortunate terminology since all emission mechanisms are ‘thermal’ in some sense. The word is conventionally taken to mean ‘continuum radiation from particles, the energy spectrum of which is not Maxwellian’. In practice, continuum emission is often referred to as ‘non-thermal’ if it cannot be described by the spectrum of thermal bremsstrahlung or black-body radiation. 1 Motion of an Electron in a Uniform, Static Magnetic field We begin by writing down the equation of motion for a particle of rest mass m0, charge ze and Lorentz factor γ = (1 − v2/c2)−1/2 in a uniform static magnetic field B. d (γm0v) = ze(v × B) (1) dt We recall that the left-hand side of this equation can be expanded as follows: d dv 3 (v · a) m0 (γv) = m0γ + m0γ v (2) dt dt c2 because the Lorentz factor γ should be written γ = (1 − v · v/c2)−1/2.
    [Show full text]
  • Induction Synchrotron Experiment in the KEK PS
    Induction Synchrotron Experiment in the KEK PS Ken Takayama High Energy Accelerator Research Organization (KEK) on behalf of Super-bunch Group which consists of staffs of KEK, TIT, NAT, and Nagaoka Tech. Univ. 25-29 June, 2007 Albuquerque, USA 2007 Particle Accelerator Conference Contents ■Brief history of the Induction Synchrotron R&D at KEK ■Outline of the Induction Synchrotron (IS) ■Experimental results using the KEK 12GeV PS ■Perspective: beyond the POP experiment ■Summary History of Induction Synchrotron Research at KEK Year Major topics & outputs Events 1999 Proposal of the Induction Synchrotron concept by K.Takayama and νFACT’99 J.Kishiro 2000 R&D works on the 1MHz switching power supply started. EPAC2000 2001 R&D works on the 2.5kV, 1MHz induction acceleration cell started. PAC2001 Proposal of a Super-bunch Hadron Collider Snowmass2001 2002 ICFA-HB2002 EPAC2002,RPIA2002 2003 5 years term Project using the KEK-PS officially started with a budget PAC2003 of 5M$. ICFA-HB2003 2004 zThe first engineering model of the switching P.S. was established. APAC2004 3 induction acceleration cells (2 kVx3=6 kV) were installed. (May) EPAC2004 zFirst experimental demonstration of induction acceleration in the KEK- ICFA-HB2004 PS (Oct. - Nov.) CARE HHH2004 zBarrier trapping at the injection energy of 500MeV and a 500 nsec-long bunch was achieved. (Dec.) 2005 Proposal of All-ion Accelerators PAC2005 Another 3 induction acceleration cells (2 kVx3=6kV) were installed (Sept). zQuasi-adiabatic non-focusing transition crossing was demonstrated in the hybrid synchrotron (RF capture + induction acceleration), (Dec.) 2006 Another 4 induction acceleration cells (2 kVx4=8 kV) were installed.(Jan.) RPIA2006, HB2006 zFull demonstration of the IS concept (March) EPAC2006, HIF06 zAll-ion Accelerator was awarded a patent.
    [Show full text]
  • Synchrotron Radiation from Protons FERMILAB Operation Successes
    collider opening up a new range of J. Bosser, L. Burnod, R. Coisson, numbers of protons to be delivered energy and with the intermediate E. d'Amico, A. Hof mann and J. Mann to experiments. At the beginning of bosons of weak interactions looming to be published in Nuclear Instru­ the year, operation changed from a on the horizon, the filmmakers could ments and Methods. three-week cycle to a weekly cycle. also find themselves in on one of the In this mode, the accelerator has biggest scientific discoveries of the operated with a 7.5 s cycle and Century. 1 s flat-top to give the average of FERMILAB 1018 protons per week from the Operation successes beginning of February through the Synchrotron radiation first week in March when a two from protons A major reliability campaign is under month shutdown began. way at Fermilab and since 1 Fe­ At the beginning of the shutdown In the September issue of 1978 bruary the accelerator has averaged an eighty hour period was devoted to (page 294) we reported the first ever 1018 protons per week. A new single studying accelerator operation at observation of synchrotron radiation pulse intensity record of 2.7 x 1013 450 GeV. The machine was off for from an orbiting proton beam in the protons was set on 21 February. only ten hours due to equipment SPS. Though the proton mass and These impressive records result problems almost entirely unrelated energy (even in the SPS and Fermi­ from a combination of a seven to the increased energy.
    [Show full text]