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Accelerator Physics Topic IX Wigglers, Undulators, and FELs

Accelerator Physics Topic IX Wigglers, Undulators, and FELs. Joseph Bisognano Engineering Physics & Synchrotron Radiation Center University of Wisconsin. Bending Magnet Radiation. CERN School 1998. Wiggler or Undulator (Insertion Devices). CERN School 1998. More flux or higher brightness

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Accelerator Physics Topic IX Wigglers, Undulators, and FELs

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  1. Accelerator PhysicsTopic IXWigglers, Undulators, and FELs Joseph Bisognano Engineering Physics & Synchrotron Radiation Center University of Wisconsin J. J. Bisognano

  2. Bending Magnet Radiation CERN School 1998 J. J. Bisognano

  3. Wiggler or Undulator (Insertion Devices) CERN School 1998 More flux or higher brightness Wigglers: high field, broad spectrum Undulators: low field, interference peaked spectrum J. J. Bisognano

  4. Insertion Devices CERN School 1998 J. J. Bisognano

  5. Light Source CERN School 1998 J. J. Bisognano

  6. Ideal ID Field Pattern(infinite pole tips in x) Gap and period go hand in hand J. J. Bisognano

  7. Gap Dependence of Magnetic Field CERN School 1998 J. J. Bisognano

  8. Equation of Motion of Electrons in IDs Neglecting vertical motion, we have J. J. Bisognano

  9. First Order Solution Since there is a Bs, one can get a vertical force; i.e., focusing J. J. Bisognano

  10. Basic Parameters J. J. Bisognano

  11. Second Order Energy Conservation says that if x is moving it’s at the expense of longitudinal energy J. J. Bisognano

  12. In Beam Frame Beam frame coordinates t and frequency J. J. Bisognano

  13. Lorentz Transforms and Radiating J. J. Bisognano

  14. J. J. Bisognano

  15. Photon Frequency in Lab Expect a “blue” shift since waves get pushed together as beam is moving toward observer Use fact that energy of photon is hf, momentum is hf/c J. J. Bisognano

  16. Undulator Spectrum Since train is of finite length (N cycles), there is a width to spectrum, but it is very narrow, order 1/N If one includes that motion is really not perfectly sinusoidal (remember the figure 8 and energy modulation) but that it does repeat in time, there is harmonic generation J. J. Bisognano

  17. Higher harmonics add to reach of an undulator Require care in phase errors of undulator periodic fields Cern School J. J. Bisognano

  18. Cern School R Walker Fundamental power/total power=1/(1+K2/2)1/2 J. J. Bisognano

  19. J. J. Bisognano

  20. Spontaneous Emission Note that for higher frequency, you need higher energy or shorter undulator period Shorter undulator period implies smaller gap J. J. Bisognano

  21. R Walker, CERN School J. J. Bisognano

  22. Brightness/Brilliance J. J. Bisognano

  23. Physics of FELs • An electron beam moving on a linear trajectory will have no net energy coupling to a co-moving E&M wave, just “jiggled” • In a wiggler (really undulator), an electron beam develops a transverse oscillation, as we’ve just seen • If the oscillation stays in phase with the fields, there can be a net exchange of beam energy to the wave; i.e., the electron beam acts to amplify the electromagnetic wave J. J. Bisognano

  24. Oscillators and SASEs • If one puts beam/wiggler into optical resonantor, there is a feedback loop that generates an oscillator and a laser • If the wiggler is long enough, the energy modulation of the electron beam can generate “microbunches” which can radiate coherently, generation self-amplified spontaneous emission (SASE) from the Schottky noise on the beam, lasing without mirrors from a beam instability • Or one can “seed” the beam with an energy modulation induced by an external laser • Sources are tunable (beam energy or wiggler field) and coherent J. J. Bisognano

  25. Basic FEL Configuration J. J. Bisognano

  26. Jlab FEL J. J. Bisognano

  27. Spontaneous Emission J. J. Bisognano

  28. FEL Dynamics I J. J. Bisognano

  29. FEL Dynamics II J. J. Bisognano

  30. FEL Dynamics III J. J. Bisognano

  31. Another Pendulum Equation J. J. Bisognano

  32. η φ Gain only when energy of beam doesn’t quite match “ideal” energy If wiggler is two long, process reverses, unless wiggler is “tapered” CERN School J. J. Bisognano

  33. FEL parameters Need high beam density J. J. Bisognano

  34. SYLee Text J. J. Bisognano

  35. SYLee Text J. J. Bisognano

  36. Looks like derivative of undulator power spectrum: fluctuation-dissipation or Madey’s theorem SYLee Text J. J. Bisognano

  37. High Gain Regime So far, we haven’t included how the increasing electromagnetic wave affects the continued electron motion Also, there is a density variation developing Also, at high enough frequencies there are no good mirrors to make an optical resonator “High Gain” regime, really an instability saves the day, and points to X-ray lasers J. J. Bisognano

  38. Basic Principle: Coherent Synchrotron Radiation If we can get “microbunching” of electron beam, strong enhancement over incoherent synchrotron radiation J. J. Bisognano

  39. High Gain FEL to the Rescue: Basic Feedback Loop • Electron beam responds to co-traveling electromagnetic wave in a wiggler/undulator • Electrons radiate by stimulated emission in wiggler • Electrons move relative to each other: density variations at wavelength of radiation • Density variations radiate coherently in wiggler/undulator • Electromagnetic field is enhanced, with changes to both its amplitude and phase • Electron move relative to each other in response to to co-traveling electromagnetic other: density variations grow at wavelength of radiation • Genuine instability with exponential growth of both the density variation and the electromagnetic radiation J. J. Bisognano

  40. Further Details • Can send beam through a dispersive compressor where the microbunching through energy variation is enhanced, “optical klystron” • Generates higher harmonics • Since Schottky (shot) noise is “noisy,” can instead seed with laser J. J. Bisognano

  41. Zhirong Huang, SLAC J. J. Bisognano

  42. J. J. Bisognano

  43. J. J. Bisognano

  44. J. J. Bisognano

  45. J. J. Bisognano

  46. The SASE radiation is powerful, but noisy! Dw/w (%) t (fs) Spectrum From a SASE FEL A SASE FEL amplifies random electron density modulations Graves Solution: Impose a strong coherent modulation with an external laser source J. J. Bisognano

  47. Bill Graves J. J. Bisognano

  48. e- output Laser 266 nm 800 nm Modulator Buncher Radiator High Gain Harmonic Generation (HGHG) HGHG • Suppressed SASE noise • Amplified coherent signal • Narrowed bandwidth • Shifted wavelength SASE x105 Brookhaven Laser Seeding Demonstration J. J. Bisognano L.H. Yu et al., Phys. Rev. Lett. 91, 74801 (2003).

  49. Stage 1 output at 5w0 seeds 2nd stage Stage 2 output at 25w0 seeds 3rd stage …Nth stage output at 5Nw0 Input seed w0 …Nth stage 1st stage 2nd stage To Produce Transform-Limited Hard X-ray Pulses Use “cascaded” High Gain Harmonic Generation methods W. Graves, MIT J. J. Bisognano

  50. Key facility elements Bunch compressor Bunch compressor Undulators Ebeam switch Photoinjector SRF linac SRF linac Seed laser Photocathode laser W. Graves, MIT J. J. Bisognano

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