Advertisement

The Wiggler Field and Electron Dynamics

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

Abstract

The electron trajectories in the external magnetostatic fields in free-electron lasers are fundamental to any understanding of the operational principles and have been the object of study for a considerable time. The concept relies upon a spatially periodic magnetic field, called either a wiggler or undulator, to induce an oscillatory motion in the electron beam, and the emission of radiation is derived from the corresponding acceleration. The specific character of the wiggler field can take on a variety of forms exhibiting both helical and planar symmetries. The most common wiggler configurations that have been employed to date include helically symmetric fields generated by bifilar current windings and linearly symmetric fields generated by alternating stacks of permanent magnets. However, wiggler fields generated by rotating quadrupole fields (helical symmetry) and pinched solenoidal fields (cylindrical symmetry) have also been considered. This chapter deals with the single-particle trajectories in both helical and planar wigglers in both one and three dimensions. Detailed expressions for the trajectories are given, and concepts such as betatron oscillations are discussed.

Keywords

Wiggler Undulator Helical wiggler Planar wiggler Flat-pole-face wiggler Parabolic-pole-face wiggler Lorentz force equations Steady-state trajectories Stability Betatron period Betatron oscillation Group I orbits Group II orbits Negative-mass trajectories Tapered wiggler 

References

  1. 1.
    J.P. Blewett, R. Chasman, Orbits and fields in the helical wiggler. J. Appl. Phys. 48, 2692 (1977)CrossRefGoogle Scholar
  2. 2.
    L. Friedland, Electron beam dynamics in combined guide and pump magnetic fields for free-electron laser applications. Phys. Fluids 23, 2376 (1980)CrossRefGoogle Scholar
  3. 3.
    P. Diament, Electron orbits and stability in realizable and unrealizable wigglers of free-electron lasers. Phys. Rev. A 23, 2537 (1981)CrossRefGoogle Scholar
  4. 4.
    R.D. Jones, Constants of the motion in a helical magnetic field. Phys. Fluids 24, 564 (1981)MathSciNetCrossRefGoogle Scholar
  5. 5.
    J.A. Pasour, F. Mako, C.W. Roberson, Electron drift in a linear magnetic wiggler with an axial guide field. J. Appl. Phys. 53, 7174 (1982)CrossRefGoogle Scholar
  6. 6.
    H.P. Freund, A.T. Drobot, Relativistic electron trajectories in free-electron lasers with an axial guide field. Phys. Fluids 25, 736 (1982)CrossRefGoogle Scholar
  7. 7.
    H.P. Freund, A.K. Ganguly, Electron orbits in free-electron lasers with helical wiggler and axial guide magnetic fields. IEEE J. Quantum Electron. QE-21, 1073 (1985)CrossRefGoogle Scholar
  8. 8.
    J. Fajans, D.A. Kirkpatrick, G. Bekefi, Off-axis electron orbits in realistic helical wigglers for free-electron laser applications. Phys. Rev. A 32, 3448 (1985)CrossRefGoogle Scholar
  9. 9.
    R.G. Littlejohn, A.N. Kaufman, Hamiltonian structure of particle motion in an ideal helical wiggler with guide field. Phys. Lett. A 120, 291 (1987)MathSciNetCrossRefGoogle Scholar
  10. 10.
    R.M. Phillips, History of the ubitron. Nucl. Instr. Meth. A272, 1 (1988)CrossRefGoogle Scholar
  11. 11.
    E.T. Scharlemann, Wiggler plane focussing in linear wigglers. J. Appl. Phys. 58, 2154 (1985)CrossRefGoogle Scholar
  12. 12.
    B. Levush, T.M. Antonsen Jr., W.M. Manheimer, P. Sprangle, A free-electron laser with a rotating quadrupole wiggler. Phys. Fluids 28, 2273 (1985)CrossRefGoogle Scholar
  13. 13.
    B. Levush, T.M. Antonsen Jr., W.M. Manheimer, Spontaneous radiation of an electron beam in a free-electron laser with a quadrupole wiggler. J. Appl. Phys. 60, 1584 (1986)CrossRefGoogle Scholar
  14. 14.
    T.M. Antonsen Jr., B. Levush, Nonlinear theory of a quadrupole free-electron laser. IEEE J. Qunatum Electron. QE-23, 1621 (1987)CrossRefGoogle Scholar
  15. 15.
    S.F. Chang, O.C. Eldridge, J.E. Sharer, Analysis and nonlinear simulation of a quadrupole wiggler free-electron laser at millimeter wavelengths. IEEE J. Quantum Electron. QE-24, 2309 (1988)Google Scholar
  16. 16.
    R.E. Shefer, G. Bekefi, Cyclotron emission from intense relativistic electron beams in uniform and rippled magnetic fields. Int. J. Electron. 51, 569 (1981)CrossRefGoogle Scholar
  17. 17.
    W.A. McMullin, G. Bekefi, Stimulated emission from relativistic electrons passing through a spatially periodic longitudinal magnetic field. Phys. Rev. A 25, 1826 (1982)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

Personalised recommendations