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Coherent Harmonic Radiation

  • H. P. Freund
  • T. M. AntonsenJr.
Chapter

Abstract

In this chapter, we discuss harmonic generation in free-electron lasers. Harmonic generation in free-electron lasers occurs by both linear and nonlinear mechanisms. The principal difficulty with linear harmonic generation, however, is that the beam quality requirement associated with the growth rate of the linear instability increases with the harmonic number. Nonlinear harmonic generation is driven parasitically off of a high-power fundamental and is less sensitive to the electron beam quality than the linear instability. Harmonics are not commonly seeded in free-electron lasers. The growth of harmonic radiation starts by a combination of shot noise on the electron beam and the initiation of harmonic bunching due to the growth of power at the fundamental. This gives rise to a rapid initial growth of the harmonic power which quickly rolls over to the slower growth associated with the linear instability. The linear instability drives harmonic growth until the fundamental reaches a power level necessary for the nonlinear mechanism to take over, after which the harmonic power grows exponentially with a growth rate that scales as the product of the harmonic number and the growth rate of the fundamental. In this regime, the harmonic grows substantially faster than the fundamental until the harmonic saturates. Saturation of the harmonic typically occurs slightly prior to that of the fundamental due to over-bunching of the electrons at the harmonic wavelengths.

Keywords

Coherent harmonic radiation Linear harmonic generation LHG Nonlinear harmonic generation NHG Periodic position interaction 

References

  1. 1.
    W.B. Colson, The nonlinear wave equation for higher harmonics in free-electron lasers. IEEE J. Quantum Electron. QE-17, 1417 (1981)CrossRefGoogle Scholar
  2. 2.
    R. Coïsson, Generalized description of harmonic generation in a transverse optical klystron. IEEE J. Quantum Electron. QE-19, 306 (1983)CrossRefGoogle Scholar
  3. 3.
    B. Girard, Y. Lapierre, J.M. Ortega, C. Bazin, M. Billardon, P. Ellaume, M. Bergher, M. Velghe, Y. Petroff, Optical frequency multiplication by an optical klystron. Phys. Rev. Lett. 53, 2405 (1984)CrossRefGoogle Scholar
  4. 4.
    H.P. Freund, S. Johnston, P. Sprangle, Three-dimensional theory of free-electron lasers with an axial guide field. IEEE J. Quantum Electron. QE-19, 322 (1983)CrossRefGoogle Scholar
  5. 5.
    A.K. Ganguly, H.P. Freund, Nonlinear analysis of free-electron laser amplifiers in three dimensions. Phys. Rev. A 32, 2275 (1985)CrossRefGoogle Scholar
  6. 6.
    R.C. Davidson, Kinetic description of harmonic instabilities in a planar wiggler free-electron laser. Phys. Fluids 29, 267 (1986)CrossRefGoogle Scholar
  7. 7.
    M.J. Schmitt, C.J. Elliot, Even harmonic generation in free-electron lasers. Phys. Rev. A 34, 4843 (1986)CrossRefGoogle Scholar
  8. 8.
    J.M. Ortega, Harmonic generation in the VUV on a storage ring and prospects for Super-ACO at Orsay. Nucl. Instr. Meth. A250, 203 (1986)CrossRefGoogle Scholar
  9. 9.
    B.M. Kinkaid, Laser harmonic generation using the optical klystron and the effects of wiggler errors. Nucl. Instr. Meth. A250, 212 (1986)CrossRefGoogle Scholar
  10. 10.
    P. Ellaume, Theory of the optical klystron. Nucl. Instr. Meth. A250, 220 (1986)CrossRefGoogle Scholar
  11. 11.
    M.J. Schmitt, C.J. Elliot, The effects of harmonic wiggler field components on free-electron laser operation. IEEE J. Quantum Electron. QE-23, 1552 (1987)CrossRefGoogle Scholar
  12. 12.
    A. Gover, A. Friedman, A. Luccio, Three dimensional modelling and numerical analysis of super-radiant harmonic emission in a free-electron laser (optical klystron). Nucl. Instr. Meth A259, 163 (1987)CrossRefGoogle Scholar
  13. 13.
    C.J. Elliot, M.J. Schmitt, XUV harmonic enhancement by magnetic fields. Nucl. Instr. Meth. A259, 177 (1987)CrossRefGoogle Scholar
  14. 14.
    R. Prazeres, Y. Lapierre, J.M. Ortega, Monte Carlo simulation of the harmonic generation in an optical klystron or undulator. Nucl. Instr. Meth. A259, 184 (1987)CrossRefGoogle Scholar
  15. 15.
    H.P. Freund, C.L. Chang, H. Bluem, Harmonic generation in free-electron lasers. Phys. Rev. A 36, 3218 (1987)CrossRefGoogle Scholar
  16. 16.
    H. Bluem, H.P. Freund, C.L. Chang, Harmonic content in a planar wiggler based free-electron laser amplifier. Nucl. Instr. Meth. A272, 579 (1988)CrossRefGoogle Scholar
  17. 17.
    R. Prazeres, J.M. Ortega, C. Bazin, M. Bergher, M. Billardon, M.E. Couprie, M. Velghe, Y. Petroff, Coherent harmonic generation in the vacuum ultraviolet spectral range on the storage ring ACO. Nucl. Instr. Meth. A272, 68 (1988)CrossRefGoogle Scholar
  18. 18.
    K. Carlson, W. Fann, J.M.J. Madey, Spatial distribution of the visible coherent harmonics generated by the Mark III free-electron laser. Nucl. Instr. Meth. A272, 92 (1988)CrossRefGoogle Scholar
  19. 19.
    B.A. Hooper, S.V. Benson, A. Cutolo, J.M.J. Madey, Experimental results of two stage harmonic generation with picosecond pulses on the Stanford Mark III free-electron laser. Nucl. Instr. Meth. A272, 96 (1988)CrossRefGoogle Scholar
  20. 20.
    S.K. Dutt, A. Friedman, A. Gover, C. Pellegrini, Three dimensional simulation of a high harmonic transverse optical klystron. Nucl. Instr. Meth. A272, 564 (1988)CrossRefGoogle Scholar
  21. 21.
    M.J. Schmitt, C.J. Elliot, B.E. Newnam, Harmonic power implications on free-electron laser mirror design. Nucl. Instr. Meth. A272, 586 (1988)CrossRefGoogle Scholar
  22. 22.
    H.P. Freund, H. Bluem, R.H. Jackson, Nonlinear theory and design of a harmonic ubitron/free-electron laser. Nucl. Instr. Meth. A285, 169 (1989)CrossRefGoogle Scholar
  23. 23.
    S.V. Benson, J.M.J. Madey, in Demonstration of Harmonic Lasing in a Free-Electron Laser, ed. by R.C. Sze, F.J. Duarte. Proc. Int. Conf. Lasers ‘88 (STS Press, McLean, 1989), p. 189Google Scholar
  24. 24.
    D.J. Bamford, D.A.G. Deacon, Measurement of the coherent harmonic emission from a free-electron laser oscillator. Phys. Rev. Lett. 62, 1106 (1989)CrossRefGoogle Scholar
  25. 25.
    S.V. Benson, J.M.J. Madey, Demonstration of harmonic lasing in a free-electron laser. Phys. Rev. A 39, 1579 (1989)CrossRefGoogle Scholar
  26. 26.
    R.W. Warren, L.C. Haynes, D.W. Feldman, W.E. Stein, S.J. Gitomer, Lasing on the third harmonic. Nucl. Instr. Meth. A296, 84 (1990)CrossRefGoogle Scholar
  27. 27.
    D.J. Bamford, D.A.G. Deacon, Harmonic generation experiments on the Mark III free-electron laser. Nucl. Instr. Meth. A296, 89 (1990)CrossRefGoogle Scholar
  28. 28.
    W.M. Sharp, E.T. Scharlemann, W.M. Fawley, Three-dimensional simulation of free-electron laser harmonics with FRED. Nucl. Instr. Meth. A296, 335 (1990)CrossRefGoogle Scholar
  29. 29.
    H. Bluem, R.H. Jackson, D.E. Pershing, J.H. Booske, V.L. Granatstein, Final design and cold tests of a harmonic ubitron amplifier. Nucl. Instr. Meth. A296, 37 (1990)CrossRefGoogle Scholar
  30. 30.
    P.E. Latham, B. Levush, T.M. Antonsen, N. Metzler, Harmonic operation of a free-electron laser. Phys. Rev. Lett. 66, 1442 (1991)CrossRefGoogle Scholar
  31. 31.
    H.P. Freund, S.G. Biedron, S.V. Milton, Nonlinear harmonic generation in free-electron lasers. IEEE J. Quantum Electron. 36, 275 (2000)CrossRefGoogle Scholar
  32. 32.
    Z. Huang, K.-J. Kim, Three-dimensional analysis of harmonic generation in high-gain free-electron lasers. Phys. Rev. E 62, 7295 (2000)CrossRefGoogle Scholar
  33. 33.
    H.P. Freund, R.C. Davidson, D.A. Kirkpatrick, Thermal effects on the linear gain in free-electron lasers. IEEE J. Quantum Electron. QE-27, 2550 (1991)CrossRefGoogle Scholar
  34. 34.
    H. Bluem, R.H. Jackson, H.P. Freund, D.E. Pershing, V.L. Granatstein, Demonstration of a new free-electron laser harmonic interaction. Phys. Rev. Lett. 67, 824 (1991)CrossRefGoogle Scholar
  35. 35.
    M.J. Schmitt, C.J. Elliot, Generalized derivation of free-electron laser harmonic radiation from plane-polarized wigglers. Phys. Rev. A 41, 3853 (1990)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • H. P. Freund
    • 1
  • T. M. AntonsenJr.
    • 2
  1. 1.University of Maryland, University of New MexicoViennaUSA
  2. 2.University of MarylandPotomacUSA

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