SYNCHROTRON RADIATION

Transcription

1 SYNCHROTRON RADIATION Lenny Rivkin Ecole Polythechnique Federale de Lausanne (EPFL) and Paul Scherrer Institute (PSI), Switzerland CERN Accelerator School: Introduction to Accelerator Physics November 5, 2012, Granada, Spain

2 Useful books and references A. Hofmann, The Physics of Synchrotron Radiation Cambridge University Press 2004 H. Wiedemann, Synchrotron Radiation Springer-Verlag Berlin Heidelberg 2003 H. Wiedemann, Particle Accelerator Physics I and II Springer Study Edition, 2003 A. W. Chao, M. Tigner, Handbook of Accelerator Physics and Engineering, World Scientific 1999

3 CERN Accelerator School Proceedings Synchrotron Radiation and Free Electron Lasers Grenoble, France, April 1996 (A. Hofmann s lectures on synchrotron radiation) CERN Yellow Report Brunnen, Switzerland, 2 9 July 2003 CERN Yellow Report

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

5 Curved orbit of electrons in magnet field Accelerated charge Electromagnetic radiation

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

7 Synchrotron radiation: some dates 1873 Maxwell s equations 1887 Hertz: electromagnetic waves Liénard: retarded potentials Wiechert: retarded potentials 1908 Schott: Adams Prize Essay... waiting for accelerators 1940: 2.3 MeV betatron,kerst, Serber

8 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

9 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:.. this is of no use whatsoever!

10 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)

11 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)

12 Donald Kerst: first betatron (1940) "Ausserordentlichhochgeschwindigkeitelektronen entwickelndenschwerarbeitsbeigollitron"

13 Synchrotron radiation: some dates Blewett observes energy loss due to synchrotron radiation 100 MeV betatron First visual observation of SR 70 MeV synchrotron, GE Lab Schwinger PhysRev paper Madey: first demonstration of Free Electron laser

14 A larger view

15 Storage ring based synchrotron light source Crab Nebula 6000 light years away GE Synchrotron New York State First light observed 1054 AD First light observed 1947

16 Why do they radiate? Charge at rest: Coulomb field, no radiation Uniformly moving charge does not radiate But! Cerenkov! v = const. Accelerated charge

17 Bremsstrahlung or braking radiation

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

19 Fields of a moving charge E t = q 4 0 n 1 n r 2 ret + q 4 0 c n n 1 n r ret B t = 1 c n E

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

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

22 Moving Source of Waves

23 Time compression Electron with velocity 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 The wavelength is shortened by the same factor in ultra-relativistic case, looking along a tangent to the trajectory obs = emit since T ( 1 nβ) obs T emit ( 1 cos ) obs emit 1 =

24 Radiation is emitted into a narrow cone e v ~ c = 1 e v << c vc

25 Sound waves (non-relativistic) Angular collimation = e v v s v s + v = v s v 1 s 1 + v v e v s v s v Doppler effect (moving source of sound) heard emitted 1 v v s

26 Synchrotron radiation power Power emitted is proportional to: P E 2 B 2 P cc E C = 4 3 r e m e c 2 3 = m GeV 3

27 The power is all too real! P cc E 2 4 2

28 Synchrotron radiation power Power emitted is proportional to: P E 2 B 2 P 4 cc E 2 2 P 2 c C = 4 3 r e m e c 2 3 = m GeV 3 = Energy loss per turn: U 0 = C E 4 hc = 197 Mev fm U 0 = 4 3 hc 4

29 Typical frequency of synchrotron light Due to extreme collimation of light observer sees only a small portion of electron trajectory (a few mm) l ~ 2 1/ ~ 1 t ~ 3 0 Pulse length: difference in times it takes an electron and a photon to cover this distance t ~ l c l c = l c 1 t ~ c 1 2 2

30 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 0 1 T 0 time flashes are extremely short: harmonics reach up to very high frequencies At high frequencies the individual harmonics overlap 3 typ 0 continuous spectrum! ~ 1 MHz ~ 4000 ~ 10 Hz! 0 typ 16

31 Wavelength continuously tunable!

32 dp d = P tot c S c S x = x K5 5 3 x dx x 0 S x dx = 1 P tot = 2 3 hc2 4 c = 3 c ~ 2.1x 1 3 G 1 x = x K 5 3 x dx x c ev = 665 E 2 GeV B T 50% ~ 1.3 xe x x = c

33 A useful approximation Spectral flux from a dipole magnet with field B Flux photons s mrad 0.1%BW = E[GeV] I[A]G 1 x Approximation: G 1 A x 1/3 g(x) 1 spectral Flux G1 g( x) [(1 ( x x L ) N ] 1 S G A = 2.11, N = x L = 28.17, S = x Werner Joho, PSI

34 Flux [photons/s/mrad/0.1%bw] Synchrotron radiation flux for different electron energies LEP Dipole Flux I = 1 ma 100 GeV 50 GeV GeV Photon energy [ev]

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

36 Electron in a storage ring: TOP VIEW TILTED VIEW SIDE VIEW

37 Polarisation Synchrotron radiation observed in the plane of the particle orbit is horizontally polarized, i.e. the electric field vector is horizontal Observed out of the horizontal plane, the radiation is elliptically polarized E E

38 x Polarisation: spectral distribution dp d Ptot c S x Ptot S S c x x 7 S 8 S 3:1 1 S 8 S

39 Angular divergence of radiation at the critical frequency well below 0. 2 c well above 2 c

40 Seeing the electron beam (SLS) X rays visible light, vertically polarised x ~ 55m

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

42 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 m

43 END