1. Photoinjectors & Beam Manipulations for LCs and FELs & Collimation [MCCPB, Chapters 5,6] manipulations in photoinjectors –space-charge compensation –flat beam generation emittance exchange some other beam manipulations for FELs collimation in linacs & storage rings

2. sources of electron beams requirements: small emittance high charge, high repetition rate, possibly high degree of polarization thermionic guns dc guns with laser photocathodes photo-cathode rf guns (SLC) rf wave laser beam e-

3. cross section of an early BNL S-band rf gun (J. Clendenin, 1996)

4. most popular in modern e- accelerators (in particular, if low emittances are desired); high-power pulsed laser illuminates photocathode placed on the end wall of an accelerating cavity, electrons are immediately accelerated in rf field normalized emittance determined by three effects: thermal emittance – initial transverse momenta rf emittancee – from time-dependent focusing force space-charge force techniques for shaping and preserving the beam emittance from such injector: space-charge compensation using solenoids generation of a flat-beam transverse-longitudinal emittance exchange rf photo-injector

5. z space-charge force longitudinal bunch profile assume transverse uniform distribution with radius a transverse view if (z) not constant, different longitudinal slices will experience different focusing force F r x x’ different slices rotate at different speed projected emittance is increased space-charge compensation radius a

6. after drift of length s: depends on shape of distribution place lens of focal length f after distance z l after total distance z d +z l : emittance is indeed 0 at chosen value of f in reality  not constant but above scheme reduced the emittance by a factor 10 in Los Alamos studies ‘space-charge compensation” (B. Carlsten, ~1993) bunch slices are realigned assume  constant  normalized longitudinal coordinate  normalized transverse coordinate

7. aa after first drift after solenoid after final drift all particles are on one line! center edge

8. beware of bifurcation! r r’ r strong space charge weak space charge bunch center bunch edge phase-space bifurcation important design criterion for photo-injectors: minimize fraction of beam crossing over! “crossover” similar techniques to correct correlated growth in projected emittance due to nonlinear force can be applied elsewhere

9. flat-beam transformation proposed by Y. Derbenev to convert round beam into flat or vice versa (1998) in particular can produce a flat beam from a photoinjector if source is placed in solenoid field and afterwards passed through a (skew) FODO channel with  /2 different phase advance in x & y

10. kick at exit of solenoid phase-space vector at exit of solenoid quadrupole channel with phase advance difference  /2 in x and y choose  =1/k this is a flat beam tilted by 45 degree! if we use skew-quad. channel, could get a flat beam in x

11. however initial beam has also some rms slope (temperature) assuming product of x and y emittances approximately conserved experimental tests at Fermilab A0 line demonstrated the feasibility of this scheme

12. simulated evolution of transverse emittances along the FNPL beamline for standard nominal settings FNAL Flat Beam Experiment schematic layout Y.-E. Sun

13. Simulated and measured beam transverse density evolution. The consecutive plots corresponds to location X3, X4, X5, X6, X7 and X8. Dimensions are in mm. Overview of the RFTB section. The letters N, S and X represents normal and skew quadrupoles, and diagnostic stations. Dimension are in mm. simulated measured FNAL Flat Beam Experiment – cont’d Y.-E. Sun

14. general emittance exchange between two planes with  2 magnitude of the coupling and is the sum of the squares of the four elements of the normalized coupling block of the transfer matrix, i.e. U : where and M. Cornacchia and P. Emma which can be rewritten as

15. equal initial uncoupled emittances will always remain equal through a symplectic map; similarly, equal uncoupled emittances cannot be generated from unequal uncoupled initial emittances - setting |A| = 1/2 produces equal emittances, but they are then highly coupled with 2 ≠0

16. transverse to longitudinal emittance exchange - EEX proposed by M. Cornacchia and P. Emma to reduced the transverse emittance (and also shrink the bunch length) for FELs (2002) realized by placing a transverse deflecting mode radio-frequency cavity (“crab cavity”) in a magnetic chicane

17. Initial (top) and final (bottom) phase space tracking plots. The horizontal and longitudinal emittances are completely exchanged, as predicted. M. Cornacchia and P. Emma

18. transverse to longitudinal emittance exchange – experimental EEX demonstration at FNAL A0 line T. Koeth, 2009 Layout of the A0 Photoinjector with straight ahead and EEX beamline sections.

19. EEX - key ingredients 1. half chicane (dipole magnets) creates correlations between x and  2. deflecting cavity changes energy of particles with transverse offset x and  and deflects particles horizontally depending on the longitudinal position  3. another half chicane thin lens deflecting cavity P. Emma and M. Cornacchia

20. The 4x4 (horizontal-longitudinal) emittance exchange matrix as a function of TM110 cavity strength. The cavity is off at k=0% and is energized to the ideal emittance exchange strength at k=100%. The circles are measured points, the green (lighter) lines are fits to the data, and the red (darker) lines are calculated values. T. Koeth, 2009

21. calculated matrix elements the 4x4 (horizontal-longitudinal) measured matrix T. Koeth, 2009 nonzero due to finite cavity length

22. Relative output 1/σ p ·σ z product map against input quadrupole currents. The white cross hairs indicate a choice for EEX operation. Calculated ratio of ε x,in /(σ p ·σ z ) out over input quad scan. The white and green cross hairs indicate the operating points for Feb 6 and Feb 11 data sets respectively. T. Koeth Transverse input parameters were tuned (by adjusting input quadrupoles) for a minimum output bunch-length energy- spread product.

23. February 11, 2009, Direct EEX Data Set, Reflecting Input and Output rms Normalized Emittances T. Koeth, 2009

24. Undulator Radiation P. Schmüser

25. Undulators & Free Electron Lasers Z. Huang, P. Schmuser undulator undulator parameter fundamental wavelength of undulator radiation in forward direction condition for sustained energy transfer from electron to light wave

26. exponential growth and saturation of the FEL power in SLAC LCLS at =0.15 nm; initiated by Self Amplified Spontaneous Emission (SASE) process P. Emma, PAC09 linac based X-ray FEL - LCLS 1-D power gain length e - density Pierce parameters saturation power typical requirements Z. Huang, P. Schmuser

27. combination flat-beam gun & EEX standard rf photocathode gun:  x,y gun ~ 1  m,  z gun ~ 0.1  m flat beam scheme:  x,,  y   z ) → (10, 0.1, 0.1)  m followed by transverse-to-longitudinal exchange:  x,,  y   z ) → (0.1, 0.1, 10)  m with much improved FEL performance (3x shorter undulator) P. Emma et al, 2006 =0.4 Å

28. FEL power as a function of z/L g0 (1D power gain length) in a seeded FEL and a SASE FEL (soft X-ray FEL FLASH) P. Schmuser et al. SASE and seeded FEL - FLASH

29. FEL seeding SASE exhibits shot-to-shot fluctuations in wavelength and limited coherence length (many uncorrelated spikes along the bunch length) various seeding methods proposed to improve coherence length of SASE radiation: High harmonic generation (HHG) in gas; VUV Self seeding: SASE signal produced by short undulator passed through monochromator and serves as seed radiation for main undulator High-gain harmonic generation (HGHG) electron is energy-modulated by interaction in an undulator by interaction with powerful laser; magnetic chicane converts energy modulation into density modulation; then second undulator for coherent emission from density modulated beam at higher harmonic frequency Echo enabled harmonic generation (EEHG): second modulator followed by second chicane; electron beam interacts twice with two laser pulses in two modulators; density modulation at a very high harmonic number

30. HGHG FEL scheme R 56 laser modulator radiator phase space distribution D. Xiang G. Stupakov e- shift by /4

31. EEHG FEL scheme R 56 (1) laser  1 modulator 1 radiator laser  2 Modulator 2 R 56 (2) phase space distribution e - shift by >10 current distribution D. Xiang G. Stupakov

32. A.A. Zholends, M.S. Zolotorev, PRL 76, 6 (1996) what happens in a modulator? laser laser radiationspontaneous undulator radiation total electric field total field energy  : relative phase of the laser light wave and electron wiggling trajectory in undulator spontaneous radiation of electrons in an undulator

33. → amplitude of e - energy modulation after the modulator applications of modulators: -laser heating (suppression of microbunching instability in bunch compressors), e.g. for FELs -FEL HGHG -FEL EEHG -femtosecond pulse generation (bunch “slicing”) in storage rings … A.A. Zholends, M.S. Zolotorev, PRL 76, 6 (1996) an alternative formula can be found in Z. Huang et al. PRST-AB 7, 074401 (2004)

34. femtosecond pulse generation at the ALS R.W. Schoenlein et al, SCIENCE, Vol. 287 March 2000 Laser interaction with electron bunch in a resonantly tuned wiggler. Transverse separation of modulated electrons in dispersive bend of the storage ring Separation of femtosecond synchrotron radiation at the beamline image plane. E=1.5 GeV,  E =1.2 MeV M u =19 periods, u =16 cm, K=13,  L =100 fs, A L =400  J, L =800 nm electron bunch distribution (as a function of horizontal displacement  x and time) at the radiating bend magnet, following inter-action with the laser pulse in the wiggler, and propagation through 1.5 arc sectors of the storage ring

35. collimation removal of beam halo, which otherwise causes background in the detector (el.-magnetic showers or muon production when lost near detector; or synchrotron radiation when passing at large amplitudes) or, for s.c. proton rings, could quench the magnets controlled removal (activation of only one area) multistage systems frequently employed collimators also serve to protect the rest of the accelerator against catastrophic beam losses due to failure (machine protection) collimator survival collimator impedance challenge for many future projects

36. example: collimator at the SNS high-energy beam-transfer line

37. beam usually not of ideal shape beam-gas Coulomb scattering beam-gas bremsstrahlung Compton scattering off thermal photons linac wake fields halo from the source or from damping rings halo from ring-to-linac transport and bunch compression,… collimation in linear colliders

38. Yes, measured beam distribution at the end of the SLAC linac (projection on the x-y plane)! Is there halo in linear colliders?

39. let us look at the SLC prediction…

42. Dispersion Space charge (?) Elastic scattering off residual gas Residual-gas bremsstrahlung Touschek scattering Intrabeam scattering Dark currents Nonlinear magnetic fields Scattering off thermal photons Scattering off laser field Incoherent & nonl. wake fields Synchrotron radiation (coherent & incoherent) Ion or electron-cloud effects More Complete List of Candidate Processes close to the source, in bends everywhere scattering photo gun cavities, linac ring, linac e.g. collimators in bends e- or e+ beams linac

43. at the SLC muons, SR, showers were all problems more and more collimators were added over the years upstream of the final focus magnetized toroids were placed between collimators and collision points to reduce the number of muons reaching the detector it was difficult to model the halo

44. schematic of a collimation system for future linear colliders consisting of spoiler and absorber pairs scattering off thin spoiler increases beam size on subsequent absorber to prevent damage collimation is done for different betatron phases and in energy

45. collimation in storage rings beam-gas Coulomb scattering beam-gas bremsstrahlung Compton scattering off thermal photons nonlinear fields (resonances, tune drifts,…) space charge intrabeam scattering, Touschek effect beam-beam interaction halo generating processes

46. measurement of beam tails in LEP-2 (80-100 GeV) using movable collimators result of Monte-Carlo simulation beam-gas scattering and thermal-photon scattering (Courtesy H.. Burkhardt, 1998)

47. halo generation rate density of residual gas or of thermal photons halo generation by scattering processes cross section total cross section  depends on limits for , 

48. Bremsstrahlung electrons lose energy in inelastic scattering events with the residual gas (e.g., SLAC-PUB-8012 and references therein) total cross section for energy loss > 1% is 6.5 barn for CO remains important at high energies k : energy of photon radiated in bremsstrahlung event

49. Elastic Coulomb scattering total cross section for scattering above minimum angle scattered electrons: scattering angle decreases at higher energies

50. at large amplitudes tail from elastic gas scattering like ~1/y 3 Tor Rauben- heimer, 1992 damping ring

51. Scattering off thermal photons total cross section is close to the Thomson cross section   =8  /(3r 0 2 )=0.665 barn density of photons is   =2x10 7 T 3 /m 3 ; at room temperature   =5.3x10 14 /m 3 number of scattered particles:  N b =     L N b maximum energy loss y max =x/(1+x), where x=15.3 [E/TeV] [E  /eV] cos 2 (  /2) average photon energy E  =2.7 k B T (10 meV at 300 K) this process becomes relevant for beam energies above 50 GeV, when the mean relative energy loss in a scattering event exceeds 1%

52. number of photons per radian: Synchrotron radiation critical energy: energy spread: emittance growth: tails:

53. at both SLC and LEP the synchrotron radiation was minimized by weakening the last bending magnet closest to the interaction point by factor ~10, which reduced the critical energy as well as the number of photons emitted per unit length in addition radiation masks were installed to absorb photons emitted in the weak bend and in upstream bends layout of the straight section around IP4 or IP8 in LEP; COLH, COLV, COLZ are masks (Courtesy H.. Burkhardt, 1998)

54. residual background in LEP arose mainly from multiply scattered photons; reflectivity of soft X-rays is close to 100% for impact below critical angle ~30 mrad keV/E  reduced by coating or surface roughening LEP masks provided complete shielding against direct photons and against singly scattered photons: (Courtesy H.. Burkhardt, 1998)

55. H. Burkhardt synchrotron-radiation shields for FCC-ee?

56. Summary photo-injectors, space-charge compensation generation of a flat beam general emittance exchange transverse-longitudinal emittance exchange FEL laser seeding and bunch slicing halo generation collimation in linear colliders & storage rings