1. Accelerator Physics: Synchrotron radiation Lecture 2 Henrik Kjeldsen – ISA

2. Synchrotron Radiation (SR) Acceleration of charged particles –Emission of EM radiation –In accelerators: Synchrotron radiation Our goals –Effect on particle/accelerator –Characterization and use Litterature –Chap. 2 + 8 + notes

3. General Electric synchrotron accelerator built in 1946, the origin of the discovery of synchrotron radiation. The arrow indicates the evidence of arcing. synchrotron acceleratorarcing

5. Emission of Synchrotron Radiation Goal –Details (e.g.): Jackson – Classical Electrodynamics –Here: Key physical elements Acceleration of charged particles: EM radiation Lamor: Non-relativistic, total power Angular distribution (Hertz dipole)

6. Relativistic particles Lorenz-invariant form Result

8. Linear acceleration Using dp/dt = dE/dx: Energy gain: dE/dx ≈ 15 MeV/m –Ratio between energy lost and gain: –  = 5 * 10 -14 (for v ≈ c) Negligible

9. Circular accelerators Perpendicular acceleration: –Energy constant... –dp = pd  → dp/dt = p  = pv/R –E ≈ pc,  = E/m 0 c 2 In praxis: Only SR from electrons

10. Energy loss per turn Max E in praxis: 100 GeV (for electrons)

11. Angular distribution I Similar to Hertz dipole in frame of electron –Relativistic transformation

13. Spectrum of SR Spectrum: Harmonics of f rev Characteristic/critical frequency Divide power in ½

15. ASTRID2 Horizontal emittance [nm] –ASTRID2:12.1 –ASTRID: 140 Diffraction limit:

16. Storage rings for SR SR – unique broad spectrum! 0th generation: Paracitic use 1st generation: Dedicated rings for SR 2nd generation: Smaller beams –ASTRID? 3rd generation: Insertion devices (straight sections), small beam –ASTRID2 4th generation: FEL

17. Insertion devices

18. Wigglers and undulators (Insertion devices) The magnetic field configuration Technical construction Equation of motion Wigglers vs. Undulators Undulator radiation The ASTRID undulator

19. Coordinate system

20. Magnetic field Potential: Solution: Peak field on axis:

21. Magnetic field on axis Construction a) Electromagnet; b) permanet magnets; c) hybrid magnets

22. Insertion devices Single period, strong field (2T / 6T) –Wavelength shifters Several periods –Multipole wigglers –Undulators Requirement –no steering of beam

23. Example (ASTRID2): Proposed multi-pole wiggler (MPW) B 0 = 2.0 T = 11.6 cm Number of periods = 6 K = 21.7 Critical energy = 447 eV

24. Summary – multi-pole wiggler (MPW) Insertion device in straight section of storage ring Shift SR spectrum towards higher energies by larger magnetic fields Gain multiplied by number of periods

25. Equation of motion Set B x = 0, v z = 0 → coupl. eq.

26. Undulator/wiggler parameter: K K – undulator/wiggler parameter –K < 1: Undulator  w < 1/  –K > 1: Wiggler  w > 1/  Equation of motion: s(t)

27. Undulator radiation I Coherent superposition of radiation produced from each periode Electron motion in lab frame: Radiation in co-moving frame (c  *): Radiation in lab:

28. Undulator radiation II If not K << 1: Harmonics of  w

29. Undulator radiation III

30. Insertion devices: Summary Wiggler (K > 1,  > 1/  ) –Broad broom of radiation –Broad spectrum –Stronger mag. field: Wavelength shifter (higher energies!) –Several periods: Intensity increase Undulator (K < 1,  < 1/  ) –Narrow cone of radiation: Very high brightness Brightness ~ N 2 –Peaked spectrum (adjustable) Harmonics if not K<<1 –Ideal source!

31. Use of SR Advantage: broad, intense spectrum! Examples of use: –Photoionization/absorption e.g. h + C + → C ++ + e - –X-ray diffraction –X-ray microscopy –...

32. Optical systems for SR I Purpose –Select wavelength: E/DE ~ 1000 – 10000 –Focus: Spot size of 0.1∙0.1 mm 2

33. Optical systems for SR II Photon energy: few eV’s to 10’s of keV –Conventional optics cannot be used Always absorption –UV, VUV, XUV (ASTRID/ASTRID2) Optical systems based on mirrors –X-rays Crystal monochromators based on diffraction

34. Mirrors & Gratings Curved mirrors for focusing Gratings for selection of wavelength r and r’ – distances to object and image Normally  ~ 80 – 90º –Reflectivity!

35. Mirrors: Geometry of surface: Plane, spherical, toriodal, ellipsoidal, hypobolic,... Plane: No focusing (r’ = -r) Spherical: simplest, but not perfect... –Tangential/meridian –Saggital Toriodal: Rt ≠ Rs Parabola: Perfect focusing of parallel beam Ellipse: Perfect focusing of point source

36. Focusing by mirrors: Example

37. Gratings kN = sin(  )+sin(  ) –NB:  < 0 –N < 2500 lines/mm Optimization –Max eff. for k = (-)1 –Min eff. for k = 2, 3 Typical max. eff. ≈ 0.2

38. Design of ‘beamlines’ Analytically –1st order: Matrix formalism –Higher orders: Taylor expansion Optical Path Function Theory (OPFT) –Optical path is stationary Only one element Numerically –Raytracing (Shadow)

42. Useful equations Bending radius Critical energy Total power radiated by ring Total power radiated by wiggler Undulator/wiggler parameter Undulator radiation Grating equation Focusing by curved mirror (targentical=meridian / saggital)