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    Bazouband, F. and Maraghechi, B. 2013. Efficiency enhancement of nonlinear odd harmonics in thermal free electron laser. Journal of Applied Physics, Vol. 113, Issue. 17, p. 173101.

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    Mishra, P. K. 2006. A comparative study of the full dispersion relation, Compton dispersion relation, and Raman dispersion relation of a free-electron laser in helical wiggler and guiding magnetic fields. Laser Physics, Vol. 16, Issue. 7, p. 1050.

    Mishra, P. K. and Misra, K. D. 2003. Infrared-Raman-regime free-electron laser in the presence of helical wiggler and guide magnetic fields: analysis. Journal of the Optical Society of America B, Vol. 20, Issue. 1, p. 27.

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    Davies, John A. Davidson, Ronald C. and Johnston, George L. 1988. Pulse shapes for absolute and convective free-electron-laser instabilities. Journal of Plasma Physics, Vol. 40, Issue. 01, p. 1.


Compton and Raman free electron laser stability properties for a warm electron beam propagating through a helical magnetic wiggler

  • John A. Davies (a1), Ronald C. Davidson (a2) and George L. Johnston (a2)
  • DOI:
  • Published online: 01 March 2009

This paper gives an extensive analytical and numerical characterization of the growth-rate curves (imaginary frequency versus wavenumber) derived from the free electron laser dispersion relation for a warm relativistic electron beam propagating through a constant-amplitude helical magnetic wiggler field. The electron beam is treated as infinite in transverse extent. A detailed mathematical analysis is given of the exact dispersion relation and its Compton approximation for the case of a water-bag equilibrium distribution function (uniform distribution in axial momentum pz). Applicability of the water-bag results to the case of a Gaussian equilibrium distribution in pz is tested numerically. One result of the water-bag analysis is a set of validity conditions for the Compton approximation. Numerical and analytical results indicate that these conditions are applicable to the Gaussian case far outside the parameter range where the individual water-bag and corresponding Gaussian growth rate curves agree.

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R. C. Davidson & H. S. Uhm 1980 Phys. Fluids, 23, 2076.

A. M. Dimos & R. C. Davidson 1985 Phys. Fluids, 28, 677.

G. R. Elias , W. M. Fairbank , J. M. Madey , H. A. Schwettman & T. I. Smith 1976 Phys. Rev. Lett. 36, 717.

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T. J. Orzechowski , B. Anderson , W. M. Fawley , D. Prosnitz , E. T. Scharlemann , S. Yarema , D. Hopkins , A. C. Paul , A. M. Sessler & J. Wurtele 1985 Phys. Rev. Lett. 54, 889.

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Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
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