Skip to main content
Log in

Field Distribution of a Planar Electrostatic Wiggler and Modulation Effect on the Motion of Relativistic Electrons

  • Published:
Journal of Infrared, Millimeter, and Terahertz Waves Aims and scope Submit manuscript

Abstract

A planar electrostatic wiggler is formed by two parallel metallic plates, where the upper-plate is corrugated with sinusoidal ripples and connected to a negative voltage and the lower-plate is smooth and grounded. The field distribution is mathematically derived in detail. It is demonstrated that this planar electrostatic wiggler can efficiently modulate the motion of relativistic electrons just as a magneto-static wiggler does in a free-electron laser. Results obtained here will provide basis to analyze the amplification mechanism of a fast wave by a relativistic electron beam in a planar electrostatic wiggler.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. J. M. J. Madey, “Stimulated emission of bremsstrahlung in a periodic magnetic field,” J. Appl. Phys. 42, 1906 (1971).

    Article  Google Scholar 

  2. L. R. Elias, W. M. Fairbank, J. M. J. Madey, H. A. Schwettman, and T. I. Smith, “Observation of simulated emission of radiation by relativistic electrons in a spatially periodic transverse magnetic field,” Phys. Rev. Lett. 36, 717–720 (1976).

    Article  Google Scholar 

  3. T. C. Mashall, Free-electron lasers (New York, Macmillan, 1985).

    Google Scholar 

  4. C. A. Brau, Free-electron lasers (Boston, Academic Press, 1990).

    Google Scholar 

  5. P. Luchini and H. Motz, Undulators and free-electron lasers (Oxford, Clarendon Press, 1990).

    Google Scholar 

  6. W. B. Colson, C. Pellegrini, and A. Renieri, Free-electron lasers. Laser handbook (North Holland, Amsterdam, 1990), Vol. 6.

    Google Scholar 

  7. G. Dattoli, A. Renieri, and A. Torre ‘Lectures on the Free Electron Laser Theory and Related Topics” (World Scientific, 1993).

  8. S.-C. Zhang, Introduction to free-electron lasers (SWJTU Press, Chengdu, 1993).

    Google Scholar 

  9. H. P. Freund and T. M. Antosen, Principles of free-electron lasers (Chapman & Hall, New York, 1996).

    Google Scholar 

  10. E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, The physics of free electron lasers (New York, Springer-Verlag, 1999).

    Google Scholar 

  11. B. N. Murdin, “Far-infrared free-electron lasers and their applications,” Contemp. Phys. 50, 391–406 (2009).

    Article  Google Scholar 

  12. P. Sprangle and V. L. Granatstein, “Stimulated cyclotron resonance scattering and production of powerful submillimeter radiation,” Appl. Phys. Lett. 25, 377–379 (1974).

    Article  Google Scholar 

  13. A. Gover, “A free-electron laser based on periodic longitudinal electrostatic bremsstrahlung,” in Free-electron generators of coherent radiation, edited by S. Jacobe, H. Pilloff, M. Sargent, M. Scully, and R. Spitzer (Addison-Wesley Publishing Company, Massachusetts, 1979), pp. 701–727.

    Google Scholar 

  14. G. Bekefi and R. E. Shefer, “Stimulated Raman scattering by an intense relativistic electron beam subjected to a rippled electric field,” J. Appl. Phys. 50, 5158–5164 (1979).

    Article  Google Scholar 

  15. J. A. Nation, “On the coupling of an high-current relativistic electron beam to a slow-wave structure,” Appl. Phys. Lett. 17, 491 (1970).

    Article  Google Scholar 

  16. Y. Carmel, J. Ivers, R. E. Kribel, and J. A. Nation, “Intense coherent Cherenkov radiation due to the interaction of a relativistic electron beam with a slow-wave structure,” Phys. Rev. Lett. 33, 1278 (1974).

    Article  Google Scholar 

  17. C. K. Birdsall, “Rippled wall and rippled stream amplifiers,” Proc. IRE 42, 1628 (1954).

    Article  Google Scholar 

  18. J. F. Decker and J. L. Hirshfield, “Absorption of electrostatic waves by plasma electrons,” Phys. Fluids 11, 372 (1968).

    Article  Google Scholar 

  19. G. Bekifi, “Electrically pumped relativistic free-electron wave generation,” J. Appl. Phys. 51, 3081 (1980).

    Article  Google Scholar 

  20. A. Anselmo and J. A. Nation, “Wave excitation in waveguides below cut-off,” IEEE Trans. Nucl. Sci NS-32, 3494 (1985).

    Article  Google Scholar 

  21. N. S. Ginzburg, N. Y. Peskov, A. S. Sergeev, A. D. R. Phelps, A. W. Cross, and I. V. Konoplev, “The use of a hybrid resonator consisting of one-dimensional and two-dimensional Bragg reflector for generation of spatially coherent radiation in a coaxial free-electron laser,” Phys. Plasmas 9, 2798 (2002).

    Article  Google Scholar 

  22. I. V. Konoplev, P. McGrane, A. D. R. Phelps, A. W. Cross, and K. Ronald, “Observation of photonic band-gap control in one-dimensional Bragg structures,” Appl. Phys. Lett. 87, 121104 (2005).

    Article  Google Scholar 

  23. J. J. Barroso and J. P. Leite Neto, “Design of coaxial Bragg reflectors,” IEEE Trans. Plasma Sci. 34, 666 (2006).

    Article  Google Scholar 

  24. S.-C. Zhang, X.-H. Chen, and Y.-X. Lai, “Effect of eccentricity on transmission in a coaxial Bragg structure,” Int. J. Infrared Millim. Waves 28, 1043–1050 (2007).

    Article  Google Scholar 

  25. Y.-X. Lai and S.-C. Zhang, “Seoaration of band-gap overlap in a coaxial Bragg structur operating in higher-order mode at Terahertz frequency,” Phys. Plasmas 15, 033301 (2008).

    Article  Google Scholar 

  26. I. V. Konoplev, A. W. Cross, P. Maclnnes, W. He, A. D. R. Phelps, C. G. Whyte, K. Ronald, and C. W. Robertson, Appl. Phys. Lett. 92, 211501 (2008).

    Article  Google Scholar 

  27. S.-C. Zhang, “Wave amplification by relativistic electron beam in a planar electrostatic system with sinusoidal-ripples boundary”, Phys. Plasmas 16, 093107 (2009).

    Google Scholar 

  28. Computer Simulation Technology (CST), User’s manual 5, in CST-Microwave Studio, 2003.

  29. V. Kumar and K.-J. Kim, “Analysis of Smith-Purcell free-electron laser,” Phys. Rev E 73, 026501 (2006).

    Google Scholar 

Download references

Acknowledgments

The author thanks Mr. Y. Zhang for his assistance of the CST simulation in Fig. 3. This work is partly supported by the China University-College PhD Science Foundation (No. 200806130012) and the NSFC (no. 60871023).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shi-Chang Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, SC. Field Distribution of a Planar Electrostatic Wiggler and Modulation Effect on the Motion of Relativistic Electrons. J Infrared Milli Terahz Waves 31, 249–258 (2010). https://doi.org/10.1007/s10762-009-9586-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10762-009-9586-3

Keywords

Navigation