Energy Recovered Linacs and Ponderomotive Spectral Broadening

1. Energy Recovered Linacs andPonderomotive Spectral Broadening G. A. Krafft Jefferson Lab

2. Recirculating linacs defined and described Review of recirculating SRF linacs Energy recovered linacs Energy recovered linacs as light sources Ancient history: lasers and electrons Dipole emission from a free electron Thomson scattering Motion of an electron in a plane wave Equations of motion Exact solution for classical electron in a plane wave Applications to scattered spectrum General solution for small a Finite a effects Ponderomotive broadening Sum Rules Conclusions Outline

3. Schematic Representation of Accelerator Types RF Installation Beam injector and dump Beamline Ring Recirculating Linac Linac

4. Performance upgrade of a previously installed linac Stanford Superconducting Accelerator and MIT Bates doubled their energy this way Cheaper design to get a given performance Microtrons, by many passes, reuse expensive RF many times to get energy up. Penalty is that the average current has to be reduced proportional to 1/number passes, for the same installed RF. Jefferson Lab CEBAF type machines: add passes until the “decremental” gain in RF system and operating costs no longer pays for an additional recirculating loop Jefferson Lab FEL and other Energy Recovered Linacs (ERLs) save the cost of higher average power RF equipment (and much higher operating costs) at higher CW operating currents by “reusing” beam energy through beam recirculation. Why Recirculate?

5. Beam Energy Recovery Recirculation path length in standard configuration recirculated linac. For energy recovery choose it to be (n + 1/2)λRF.Then

6. Beam Energy Recovery Recirculation Path Length Linac Cavity Center Linac Cavity Center Recirculation path length in herring-bone configuration recirculated linac. For energy recovery choose it to be nλRF. Note additional complication: path length has to be an integer at each and every different accelerating cavity location in the linac.

7. Advantage Linacs Emittance dominated by source emittance and emittance growth down linac Beam polarization “easily” produced at the source, switched, and preserved Total transit time is quite short Beam is easily extracted. Utilizing source laser control, flexible bunch patterns possible Long undulaters are a natural addition Bunch durations can be SMALL (10-100 fsec) Comparison between Linacs and Storage Rings

8. Advantage Storage Rings Up to now, the stored average current is much larger Very efficient use of accelerating voltage Technology well developed and mature Disadvantage Storage Rings Technology well developed and mature (maybe!) The synchrotron radiation damping equilibrium, and the emittance and bunch length it generates, must be accepted Comparison Linacs and Storage Rings

9. Power Multiplication Factor • Energy recovered beam recirculation is nicely quantified by the notion of a power multiplication factor: • where Prf is the RF power needed to accelerate the beam • By the first law of thermodynamics (energy conservation!) k < 1 • in any linac not recirculated. Beam recirculation with beam deceleration somewhere is necessary to achieve k > 1 • If energy IS very efficiently recycled from the accelerating to the decelerating beam

10. High Multiplication Factor Linacs Recirculated Linacs Normal Conducting Recirculators k<<1 LBNL Short Pulse X-ray Facility (proposed) k=0.1 CEBAF (matched beam load) k=0.99; (typical) k=0.8 High Multiplication Factor Superconducting Linacs JLAB IR DEMO k=16 JLAB 10 kW Upgrade k=33 Cornell/JLAB ERL k=200 (proposed) BNL PERL k=500 (proposed) Will use the words “High Multiplication Factor Linac” for those designs that feature high k.

11. Comparison Accelerator Types Typical results by accelerator type

12. A renewed general interest in beam recirculation has arisen due to the success of Jefferson Lab’s high average current energy recovered Free Electron Lasers (FELs), and the broader realization that it may be possible to achieve beam parameters “Unachievable” in storage rings or linacs without recirculation. ERL synchrotron source: Beam power in a typical synchrotron source is (100 mA)(5 GeV)=500 MW. Realistically, even the federal govt. will be unable to provide a third of a nuclear plant to run a synchrotron source. Idea is to use the high multiplication factor possible in energy recovered designs to reduce the power load. Pulse lengths of order 100 fsec or smaller may in be possible in an ERL source; “impossible” at a storage ring. Better emittance may be possible too. The limits, in particular the average current carrying capacity of possible recirculated linac designs, are not yet determined and may be far in excess of what the FELs can do! More Modern Reason to Recirculate!

13. Additional Linac Instability Multipass Beam Breakup (BBU) Observed first at Illinois Superconducting Racetrack Microtron Limits the average current at a given installation Made better by damping non-fundamental electromagnetic High Order Modes (HOMs) in the cavities Best we can tell at CEBAF, threshold current is around 20 mA, measured to be several mA in the FEL Changes based on beam recirculation optics Turn around optics tends to be a bit different than in storage rings or more conventional linacs. Longitudinal beam dynamics gets coupled more strongly to the transverse dynamics and nonlinear corrections different HOM cooling will perhaps limit the average current in such devices. Challenges for Beam Recirculation

14. High average current sources needed to provide beam Right now, looks like a good way to get there is with DC photocathode sources as we have in the Jefferson Lab FEL. Need higher fields in the acceleration gap in the gun. Need better vacuum performance in the beam creation region to increase the photocathode lifetimes. Goal is to get the photocathode decay times above the present storage ring Toushek lifetimes Beam dumping of the recirculated beam can be a challenge. Challenges for Beam Recirculation

15. Recirculating SRF Linacs

16. Most radical innovations (had not been done before on the scale of CEBAF): choice of Superconducting Radio Frequency (SRF) technology use of multipass beam recirculation Until LEP II came into operation, CEBAF was the world’s largest implementation of SRF technology. The CEBAF at Jefferson Lab

17. CEBAF Accelerator Layout* *C. W. Leemann, D. R. Douglas, G. A. Krafft, “The Continuous Electron Beam Accelerator Facility: CEBAF at the Jefferson Laboratory”, Annual Reviews of Nuclear and Particle Science, 51, 413-50 (2001) has a long reference list on the CEBAF accelerator. Many references on Energy Recovered Linacs may be found in a recent ICFA Beam Dynamics Newsletter, #26, Dec. 2001: http://icfa-usa/archive/newsletter/icfa_bd_nl_26.pdf

18. CEBAF Beam Parameters

19. Short Bunches in CEBAF Wang, Krafft, and Sinclair, Phys. Rev. E, 2283 (1998)

20. Short Bunch Configuration Kazimi, Sinclair, and Krafft, Proc. 2000 LINAC Conf., 125 (2000)

21. dp/p data: 2-Week Sample Record 1.2 1.2 0.8 0.8 0.4 0.4 0 0 X Position => relative energy Drift rms X width => Energy Spread Energy Spread less than 50 ppm in Hall C, 100 ppm in Hall A Secondary Hall (Hall A) Primary Hall (Hall C) Energy drift X and sigma X in mm Energy drift Energy spread 1E-4 Energy spread 23-Mar 27-Mar 31-Mar 4-Apr 23-Mar 27-Mar 31-Mar 4-Apr Date Time Courtesy: Jean-Claude Denard

22. Energy Recovered Linacs • The concept of energy recovery first appears in literature by Maury Tigner, as a suggestion for alternate HEP colliders* • There have been several energy recovery experiments to date, the first one in a superconducting linac at the Stanford SCA/FEL** • Same-cell energy recovery with cw beam current up to 10 mA and energy up to 150 MeV has been demonstrated at the Jefferson Lab 10 kW FEL. Energy recovery is used routinely for the operation of the FEL as a user facility * Maury Tigner, Nuovo Cimento 37 (1965) ** T.I. Smith, et al., “Development of the SCA/FEL for use in Biomedical and Materials Science Experiments,” NIMA 259 (1987)

23. The SCA/FEL Energy Recovery Experiment • The former Recyclotron beam recirculation system could not be used to obtain the peak current required for FEL lasing and was replaced by a doubly achromatic single-turn recirculation line. • Same-cell energy recovery was first demonstrated in an SRF linac at the SCA/FEL in July 1986 • Beam was injected at 5 MeV into a ~50 MeV linac (up to 95 MeV in 2 passes) • Nearly all the imparted energy was recovered. No FEL inside the recirculation loop. T. I. Smith, et al., NIM A259, 1 (1987)

24. N. R. Sereno, “Experimental Studies of Multipass Beam Breakup and Energy Recovery using the CEBAF Injector Linac,” Ph.D. Thesis, University of Illinois (1994) CEBAF Injector Energy Recovery Experiment

25. Instability Mechanism Courtesy: N. Sereno, Ph.D. Thesis (1994)

26. Threshold Current Growth Rate where If the average current exceeds the threshold current have instability (exponentially growing cavity amplitude!) Krafft, Bisognano, and Laubach, unpublished (1988)

27. Jefferson Lab IR DEMO FEL Wiggler assembly Neil, G. R., et. al, Physical Review Letters, 84, 622 (2000)

28. Parameter Designed Measured FEL Accelerator Parameters Kinetic Energy 48 MeV 48.0 MeV Average current 5 mA 4.8 mA Bunch charge 60 pC Up to 135 pC Bunch length (rms) <1 ps 0.40.1 ps Peak current 22 A Up to 60 A Trans. Emittance (rms) <8.7 mm-mr 7.51.5 mm-mr Long. Emittance (rms) 33 keV-deg 267 keV-deg Pulse repetition frequency (PRF) 18.7 MHz, x2 18.7 MHz, x0.25, x0.5, x2, and x4

29. ENERGY RECOVERY WORKS Gradient modulator drive signal in a linac cavity measured without energy recovery (signal level around 2 V) and with energy recovery (signal level around 0). Courtesy: Lia Merminga

30. Longitudinal Phase Space Manipulations Simulation calculations of longitudinal dynamics of JLAB FEL Piot, Douglas, and Krafft, Phys. Rev. ST-AB, 6, 0030702 (2003)

31. Phase Transfer Function Measurements Krafft, G. A., et. al, ERL2005 Workshop Proc. in NIMA

32. Longitudinal Nonlinearities Corrected by Sextupoles Sextupoles Off Nominal Settings Basic Idea is to use sextupoles to get T566 in the bending arc to compensate any curvature in the phase space.

33. IR FEL Upgrade

34. IR FEL 10 kW Upgrade Parameters Parameter Design Value Kinetic Energy 160 MeV Average Current 10 mA Bunch Charge 135 pC <300 fsec Bunch Length 10 mm mrad Transverse Emittance Longitudinal Emittance 30 keV deg Repetition Rate 75 MHz

35. ERL X-ray Source Conceptual Layout CHESS / LEPP

36. Why ERLs for X-rays? CHESS / LEPP ESRF 6 GeV @ 200 mA ERL 5 GeV @ 10-100 mA εx = εy  0.01 nm mrad B ~ 1023 ph/s/mm2/mrad2/0.1%BW LID = 25 m εx = 4 nm mrad εy = 0.02 nm mrad B ~ 1020 ph/s/mm2/mrad2/0.1%BW LID = 5 m ERL (no compression) ESRF ERL (w/ compression) t

37. Brilliance Scaling and Optimization • For 8 keV photons, 25 m undulator, and 1 micron normalized emittance, X-ray source brilliance • For any power law dependence on charge-per-bunch, Q, the optimum is • If the “space charge/wake” generated emittance exceeds the thermal emittance εth from whatever source, you’ve already lost the game! • BEST BRILLIANCE AT LOW CHARGES, once a given design and bunch length is chosen! Therefore, higher RF frequencies preferred • Unfortunately, best flux at high charge

38. Parameter Value Unit Beam Energy 5-7 GeV Average Current 100 / 10 mA Fundamental frequency 1.3 GHz Charge per bunch 77 / 8 pC Injection Energy 10 MeV Normalized emittance 2 / 0.2* μm Energy spread 0.02-0.3 % CHESS / LEPP Bunch length in IDs 0.1-2* ps Total radiated power 400 kW ERL Phase II Sample Parameters * * rms values

39. ERL X-ray Source Average Brilliance and Flux CHESS / LEPP Courtesy: Qun Shen, CHESS Technical Memo 01-002, Cornell University

40. ERL Peak Brilliance and Ultra-Short Pulses CHESS / LEPP Courtesy: Q. Shen, I. Bazarov

41. Cornell ERL Phase I: Injector CHESS / LEPP Injector Parameters: Beam Energy Range 5 – 15a MeV Max Average Beam Current 100 mA Max Bunch Rep. Rate @ 77 pC 1.3 GHz Transverse Emittance, rms (norm.) < 1bmm Bunch Length, rms 2.1 ps Energy Spread, rms 0.2 % a at reduced average current b corresponds to 77 pC/bunch

42. Beyond the space charge limit CHESS / LEPP Cornell ERL Prototype Injector Layout 2-cell SRF cavities Solenoids 500-750 kV DC Photoemission Gun Merger dipoles into ERL linac Buncher Injector optimization 0.1 mm-mrad, 80 pC, 3ps Courtesy of I. Bazarov

43. Many of the the newer Thomson Sources are based on a PULSED laser (e.g. all of the high-energy lasers are pulsed by their very nature) Have developed a general theory to cover radiation calculations in the general case of a pulsed, high field strength laser interacting with electrons in a Thomson scattering arrangement. The new theory shows that in many situations the estimates people do to calculate flux and brilliance, based on a constant amplitude models, need to be modified. The new theory is general enough to cover all “1-D” undulator calculations and all pulsed laser Thomson scattering calculations. The main “new physics” that the new calculations include properly is the fact that the electron motion changes based on the local value of the field strength squared. Such ponderomotive forces (i.e., forces proportional to the field strength squared), lead to a red-shift detuning of the emission, angle dependent Doppler shifts of the emitted scattered radiation, and additional transverse dipole emission that this theory can calculate. Nonlinear Thomson Scattering

44. Early 1960s: Laser Invented Brown and Kibble (1964): Earliest definition of the field strength parameters K and/orain the literature that I’m aware of Interpreted frequency shifts that occur at high fields as a “relativistic mass shift”. Sarachik and Schappert (1970): Power into harmonics at high Kand/ora. Full calculation for CW (monochromatic) laser. Later referenced, corrected, and extended by workers in fusion plasma diagnostics. Alferov, Bashmakov, and Bessonov (1974): Undulator/Insertion Device theories developed under the assumption of constant field strength. Numerical codes developed to calculate “real” fields in undulators. Coisson (1979): Simplified undulator theory, which works at low Kand/ora, developed to understand the frequency distribution of “edge” emission, or emission from “short” magnets, i.e., including pulse effects Ancient History

45. Coisson’s Spectrum from a Short Magnet Coisson low-field strength undulator spectrum* *R. Coisson, Phys. Rev. A 20, 524 (1979)

46. Dipole Radiation Assume a single charge moves in the x direction Introduce scalar and vector potential for fields. Retarded solution to wave equation (Lorenz gauge),

47. Dipole Radiation Polarized in the plane containing and

48. Dipole Radiation Define the Fourier Transform With these conventions Parseval’s Theorem is Blue Sky! This equation does not follow the typical (see Jackson) convention that combines both positive and negative frequencies together in a single positive frequency integral. The reason is that we would like to apply Parseval’s Theorem easily. By symmetry, the difference is a factor of two.

49. Dipole Radiation For a motion in three dimensions Vector inside absolute value along the magnetic field Vector inside absolute value along the electric field. To get energy into specific polarization, take scaler product with the polarization vector

50. Assume radiating charge is moving with a velocity close to light in a direction taken to be the zaxis, and the charge is on average at rest in this coordinate system For the remainder of the presentation, quantities referred to the moving coordinates will have primes; unprimed quantities refer to the lab system In the co-moving system the dipole radiation pattern applies Co-moving Coordinates