1. KoPAS 2015, IBS, Daejeon 28-31 July 2015 1 Physics of Synchrotron Radiation John Byrd Lawrence Berkeley National Laboratory

2. KoPAS 2015, IBS, Daejeon 28-31 July 2015 2 Electron accelerators were initially developed to probe elementary (subnuclear) particles for the study of the fundamental nature of matter, space, time, and energy.Electron accelerators were initially developed to probe elementary (subnuclear) particles for the study of the fundamental nature of matter, space, time, and energy. Synchrotron radiation was first observed in an accelerator in 1947 from the 70 MeV electron beam at the General Electric Synchrotron in Schenectady, New York.Synchrotron radiation was first observed in an accelerator in 1947 from the 70 MeV electron beam at the General Electric Synchrotron in Schenectady, New York. For some time it was only considered as a limited factor to reaching higher beam energies.For some time it was only considered as a limited factor to reaching higher beam energies. Researchers soon realized that synchrotron radiation was the brightest source of infrared, ultraviolet, and x-rays, and that could be very useful for studying matter on the scale of atoms and molecules.Researchers soon realized that synchrotron radiation was the brightest source of infrared, ultraviolet, and x-rays, and that could be very useful for studying matter on the scale of atoms and molecules. Introduction

3. KoPAS 2015, IBS, Daejeon 28-31 July 2015 3 The EM field of a relativistic particle approximates a plane wave. We can consider the EM field as a cloud of virtual photons.This is known as the Weiszacker-Williams approximation.The EM field of a relativistic particle approximates a plane wave. We can consider the EM field as a cloud of virtual photons.This is known as the Weiszacker-Williams approximation. The acceleration process acts as a “kick” that can separate the particle from the cloud of virtual photons that become real and independently observable. The acceleration process acts as a “kick” that can separate the particle from the cloud of virtual photons that become real and independently observable. In the field of the magnets in a synchrotron, charged particles moves on a curved trajectory. The transverse acceleration allows for the separation and synchrotron radiation is generated. Lighter particles are “easier” to accelerate and radiate photons more efficiently than heavier particles.Lighter particles are “easier” to accelerate and radiate photons more efficiently than heavier particles. Why Do Particles Radiateunder Acceleration? Why Do Particles Radiate under Acceleration?

4. KoPAS 2015, IBS, Daejeon 28-31 July 2015 4 Historically, the theory of radiation from charged particles was developed well before quantum mechanics was even conceived: Historically, the theory of radiation from charged particles was developed well before quantum mechanics was even conceived: - in 1897 Joseph Larmor derived the expression for the instantaneous total power radiated by an accelerated charged particle. - and in 1898 Alfred Lienard (before the relativity theory!) extended Larmor’s result to the case of a relativistic particle undergoing centripetal acceleration in a circular trajectory 1857-1942 1869-1958 The Classical Picture

5. KoPAS 2015, IBS, Daejeon 28-31 July 2015 5 negligible! Radiated power for transverse acceleration increases dramatically with energy. This sets a practical limit for the maximum energy obtainable with a storage ring, but makes the construction of synchrotron light sources extremely appealing! Radiated power for transverse acceleration increases dramatically with energy. This sets a practical limit for the maximum energy obtainable with a storage ring, but makes the construction of synchrotron light sources extremely appealing! Longitudinal vs. Transverse Acceleration

6. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Synchrotron Radiation= Electromagnetism +Relativity The observation of the radiation in the direction of motion creates a blueshift of the radiated wavelength The blueshift will be largest when observing along the direction of the electron. Therefore, off- axis radiation has lower frequency (less blueshift). 6

7. KoPAS 2015, IBS, Daejeon 28-31 July 2015 7 Radiation becomes more focused at higher energies. Radiation becomes more focused at higher energies. Cone aperture ~ 1/  Synchrotron Radiation Angular Distribution

8. KoPAS 2015, IBS, Daejeon 28-31 July 2015 8 (Doppler effect) Strong wavelength shortening for relativistic beams! Relativistic Doppler Shift

9. KoPAS 2015, IBS, Daejeon 28-31 July 2015 9 Coherent Synchrotron Radiation THz Synchrotron Light Sources Synchrotron Light Sources Synchrotron RadiationElectromagnetic Spectrum Synchrotron Radiation Electromagnetic Spectrum

10. KoPAS 2015, IBS, Daejeon 28-31 July 2015 10 Continuous spectrum characterized by  c = critical energy  c (keV) = 0.665 B(T)E 2 (GeV) For example: for B = 1.35 T E = 2 GeV  c = 3.6keV + harmonics at higher energy Quasi-monochromatic spectrum with peaks at lower energy than a wiggler is the angle in each pole K =  where  is the angle in each pole 1 = u   (fundamental) (1 + ) ~ (fundamental) KK 22 U  1 (keV) = 0.95 E 2 (GeV) KK u (cm) (1 + ) 2 bending magnet wiggler - incoherent superposition undulator - coherent interference How Synchrotron Radiation is Generated in Storage Rings

11. KoPAS 2015, IBS, Daejeon 28-31 July 2015 11 “C” shaped for allowing to the radiation to leave the magnet Normal-Conductive ~ 1.5 T Max Bend Magnet

12. KoPAS 2015, IBS, Daejeon 28-31 July 2015 12 Example for an electron ring with 1.9 GeV and with a bending radius of 5 m: Example for an electron ring with 1.9 GeV and with a bending radius of 5 m: Very broad band! Band-Widthof Synchrotron Radiation Band-Width of Synchrotron Radiation

13. KoPAS 2015, IBS, Daejeon 28-31 July 2015 13 Universal function Spectrum: Critical frequency Fundamental Accelerator Theory, Simulations and Measurement Lab – Michigan State University, Lansing June 4-15, 2007 Bend Magnet Synchrotron Radiation Spectrum

14. KoPAS 2015, IBS, Daejeon 28-31 July 2015 14 This characteristic of synchrotron radiation is heavily exploited in those experiments where the polarization of the light is important. Short Long Polarization

15. KoPAS 2015, IBS, Daejeon 28-31 July 2015 15 At the Advanced Light Source three of the existing thirty six 1.3 T dipoles were replaced by three 5 T superconducting dipoles (“superbends”) for extending the spectrum to higher frequencies (>10 keK photons). Superbend without cryostat Superbend with cryostat 300.0 B (T) -180.0-60.060.0180.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 distance along beam (mm) -300.0 0.0Superbend magnetic field Dipoles for Hard X-rays

16. KoPAS 2015, IBS, Daejeon 28-31 July 2015 16 Bending Magnet Remark: The distribution for longer wavelengths does not depend on energy. Spectrum Energy Dependency

17. KoPAS 2015, IBS, Daejeon 28-31 July 2015 If magnet is shorter than arc length in magnet (bending angle<1/  pulse length is further reduced. 17 Bend Radiation from a short magnet The spectrum is pushed to higher frequency. An undulator is a series of short magnets. This is used in hadron machines to push up the low critical frequency.

18. KoPAS 2015, IBS, Daejeon 28-31 July 2015 18 Particletrajectory Permanent Magnets Invented by Klaus Halbach 1924-2000 Planar Undulators

19. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Weak Undulator Radiation Weak Undulator Radiation Consider a weak undulator with deflecting angle <<1/  Each period radiates like a short magnet with the radiation observed at an angle. 19 Each period gives constructive interference for a single frequency and bandwidth given by Doppler shift reduces when observed off axis.

20. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Undulator Spectrum The undulator spectrum is a seriers of harmonics of the fundamental wavelength. 20 Each harmonic can be monochromatized with an aperture with a corresponding reduction in flux

21. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Undulator radiation: General considerations The angular deflection of the electron beam along the undulator is given by 21 The peak deflection is given by Define the deflection parameter as the ratio of the deflection angle relative to the 1/  opening angle.

22. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Undulator Radiation: Constructive Interference For constructive interference between wavefronts emitted by the same electron the electron must slip back by a whole number of wavelengths over one period 22 The time for the electron to travel one period is In this time the first wavefront will travel the distance

23. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Diffraction gratings and Phased radar arrays Very similar results for angular width and bandwidth apply to diffraction gratings and phased radar arrays because both act as a large number of equally spaced sources. 23

24. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Undulator is a tuneable source The wavelength primarily depends on the period and the energy but also on K and the observation angle . If we change B we can change. For this reason, undulators are built with smoothly adjustable B field. The amount of the adjustability sets the tuning range of the undulator. As B increases (and so K), the output wavelength increases (photon energy decreases). This is opposite to bend magnet radiation. 24 Gap

25. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Example Undulator Undulator with 50mm period, 100 periods, 3GeV, 300mA electron beam 25 Increasing K

26. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Undulator Radiation: Bandwidth and Opening Angle Opening Angle Significantly reduces opening angle from 1/  from a bend magnet. Brightness is increased. Line Bandwidth Very similar to effect of diffraction grating. 26 The interference also gives two other very useful properties of undulator radiation

27. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Undulator radiation: Electron rest frame Weak Undulator Strong undulator 27 In the electron rest frame, the undulator field looks like an (almost real) photon with a Doppler-shifted wavelength.

28. KoPAS 2015, IBS, Daejeon 28-31 July 2015 On-axis power density 28 Undulators Multipole Wigglers

29. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Multipole Wiggler With the larger wiggling, the overlap between the radiated field ( 1/  cone) decreases and the interference is reduced.A wiggler is an undulator with K>>1. With the larger wiggling, the overlap between the radiated field ( 1/  cone) decreases and the interference is reduced. For K >> 1 no interference is present and the undulator presents the continuum spectrum typical of the wiggler.For K >> 1 no interference is present and the undulator presents the continuum spectrum typical of the wiggler. 29 This example shows an undulator calculation for K = 15.

30. KoPAS 2015, IBS, Daejeon 28-31 July 2015 From Undulator Radiation to Wiggler Radiation 30 The spectrum of the undulator radiation: depends strongly on the strength parameter K : Remembering that: One can see that K is proportional to the field B: In a permanent magnet undulator, B and consequently K can be modified by changing the gap height. The larger the gap the lower the field. Gap

31. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Hybrid Insertion Devices Hybrid insertion device is a combination of steel and permanent magnet material. 31 Fe PM

32. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Helical (or Elliptical) Undulators Can we have arbitrary polarization from an undulator? Yes!!! We want two orthogonal fields of equal period but of different amplitude and phase 32

33. KoPAS 2015, IBS, Daejeon 28-31 July 2015 The APPLE-2 Design Consists of four standard PPM (pure permanent magnet) arrays Diagonally opposite arrays move longitudinally together All the arrays also move vertically like a conventional undulator 33

34. KoPAS 2015, IBS, Daejeon 28-31 July 2015 APPLE-2 Examples 34

35. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Engineering Issues for PM IDs 35

36. KoPAS 2015, IBS, Daejeon 28-31 July 2015 In-vacuum insertion devices The minimum magnet gap limits the performance of an undulator The magnet gap is determined by the aperture needed for the electron beam (i.e. vacuum chamber.) For example: –10 mm aperture –2 mm thick vacuum chamber –1 mm tolerance = 15 mm minimum gap Put the undulator in the vacuum chamber! 36

37. KoPAS 2015, IBS, Daejeon 28-31 July 2015 In-vacuum insertion devices IVIDs require significant engineering because of the direct exposure to beam fields –Cooled beam shields –Vacuum Mechanical coupling –Beam impedance –Vacuum 37

38. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Cryogenic Undulators (not SC) A relatively new idea that takes advantage of the variation of remanent field with temperature The intrinsic coercivity increases also which helps with radiation resistance and allows selection of strong grades 38 Other materials are more attractive, especially PrFeB, as it can operate at 77K – an easy temperature to maintain One issue is also wanting to bake the magnets to ~450K to improve the vacuum performance – limits the grades available

39. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Superconducting Undulators SC IDs have the promise of providing higher fields with shorter periods Engineering Challenges: –Cold beam aperture –The iron poles need to be accurately machined –The B-field dependent upon accurate positioning of the wires –Correction of the field errors is quite tricky 39 Recent successful demo of NbTi SCU at the APS

40. KoPAS 2015, IBS, Daejeon 28-31 July 2015 Summary Advances in ways to manipulate and control synchrotron radiation are continuing. New ways of extending the tuning range, polarization, brightness of IDs are appearing every year. Synchrotron radiation is a beautiful example of physics and engineering combining to make an impact in many fields of science. 40