Transverse evolution of a long relativistic electron beam governed by the Vlasov-Poisson-type pair of equations within the plasma wake field dynamics in the local regime

  • Renato Fedele
  • Tahmina AkhterEmail author
  • Dušan Jovanović
  • Sergio De Nicola
  • Abdul Mannan
Regular Article
Part of the following topical collections:
  1. Topical issue: Theory and Applications of the Vlasov Equation


An analysis of the transverse plasma wake field dynamics excited by a long relativistic electron beam is carried out in a purely local regime, in which the transverse beam spot-size is much bigger than the plasma wavelength. This is done by using the Vlasov equation, that governs the kinetic spatiotemporal evolution of the transverse paraxial beam transport. A self-consistent description of the beam dynamics is then provided by coupling the Vlasov equation with a Poisson-type equation. Furthermore, the latter relates the beam density with the plasma wake potential energy. Remarkably, the approach here proposed seems to be suitable for describing the beam self-modulation and the prediction of the beam collapse.


Free Electron Laser Vlasov Equation Relativistic Electron Beam Beam Density Betatron Oscillation 
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  1. 1.
    M.N. Rosenbluth, C.S. Liu, Phys. Rev. Lett. 29, 701 (1972)ADSCrossRefGoogle Scholar
  2. 2.
    T. Tajima, J.M. Dawson, Phys. Rev. Lett. 43, 267 (1979)ADSCrossRefGoogle Scholar
  3. 3.
    L.M. Gorbunov, V.I. Kirsanov, Sov. Phys. J. Exp. Theor. Phys. 66, 290 (1987)Google Scholar
  4. 4.
    P. Sprangle, E. Esarey, A. Ting, G. Joyce, Appl. Phys. Lett. 53, 2146 (1988)ADSCrossRefGoogle Scholar
  5. 5.
    P. Chen, J.M. Dawson, R.W. Huff, T. Katsouleas, Phys. Rev. Lett. 54, 693 (1985)ADSCrossRefGoogle Scholar
  6. 6.
    R.D. Ruth, A.W. Chao, P.L. Morton, P.B. Wilson, Part. Accel. 17, 171 (1985)Google Scholar
  7. 7.
    P. Chen, J.J. Su, J.M. Dawson, K.L.F. Bane, P.B. Wilson, Phys. Rev. Lett. 56, 1252 (1986)ADSCrossRefGoogle Scholar
  8. 8.
    J. Rosenzweig, IEEE Trans. Plasma Sci. PS-15, 186 (1987)ADSCrossRefGoogle Scholar
  9. 9.
    J.B. Rozenzweig, D.B. Cline, B. Cole, H. Figueroa, W. Gai, R. Konecny, J. Norem, P. Schoessow, J. Simpson, Phys. Rev. Lett. 61, 98 (1988)ADSCrossRefGoogle Scholar
  10. 10.
    T. Katsouleas, Phys. Rev. A 33, 2056 (1986)ADSCrossRefGoogle Scholar
  11. 11.
    R. Fedele, U. de Angelis, T. Katsouleas, Phys. Rev. A 33, 4412 (1986)ADSCrossRefGoogle Scholar
  12. 12.
    U. de Angelis, R. Fedele, G. Miano, C. Nappi, Plasma Phys. Control. Fusion 29, 789 (1987)ADSCrossRefGoogle Scholar
  13. 13.
    C. Joshi, T. Katsouleas, J.M. Dawson, Y.T. Yan, J.M. Slater, IEEE Trans. J. Quantum Electron. QE-23, 1571 (1987)ADSCrossRefGoogle Scholar
  14. 14.
    R. Fedele, G. Miano, V.G. Vaccaro, Phys. Scr. T30, 192 (1990)ADSCrossRefGoogle Scholar
  15. 15.
    P. Chen, Part. Accel. 20, 171 (1987)Google Scholar
  16. 16.
    J.B. Rosenzweig, P. Chen, Phys. Rev. D 39, 2039 (1989)ADSCrossRefGoogle Scholar
  17. 17.
    J.J. Su, T. Katsouleas, J.M. Dawson, R. Fedele, Phys. Rev. A 41, 3321 (1990)ADSCrossRefGoogle Scholar
  18. 18.
    A.K. Malik, H.K. Malik, U. Stroth, Appl. Phys. Lett. 99, 071107 (2011)CrossRefGoogle Scholar
  19. 19.
    M. Singh, R.K. Singh, R.P. Sharma, Europhys. Lett. 104, 35002 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    J.B. Rosenzweig, B. Breizman, T. Katsouleas, J.J. Su, Phys. Rev. A 44, R6189 (1991)ADSCrossRefGoogle Scholar
  21. 21.
    J.S.T. Ng, P. Chen, H. Baldis, P. Bolton, D. Cline, W. Craddock, C. Crawford, F.J. Decker, C. Field, Y. Fukui, V. Kumar, R. Iverson, F. King, R.E. Kirby, K. Nakajima, R. Noble, A. Ogata, P. Raimondi, D. Walz, A.W. Weidemann, Phys. Rev. Lett. 67, 244801 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    S. Lee, T. Katsouleas, R.G. Hemker, E.S. Dodd, W.B. Mori, Phys. Rev. A 64, 045501(R) (2001)ADSGoogle Scholar
  23. 23.
    R. Bingham, J.T. Mendonca, P.K. Shukla, Plasma Phys. Control. Fusion 46, R1 (2004)ADSCrossRefGoogle Scholar
  24. 24.
    I. Blumenfeld, C.E. Clayton, F.-J. Decker, M.J. Hogan, C. Huang, R. Ischebeck, R. Iverson, C. Joshi, T. Katsouleas, N. Kirby, W. Lu, K.A. Marsh, W.B. Mori, P. Muggli, E. Oz, R.H. Siemann, D. Walz, M. Zhou, Nature 445, 741 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    W. Lu, W. An, M. Zhou, C. Joshi, C. Huang, W.B. Mori, New J. Phys. 12, 085002 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    D. Jovanović, R. Fedele, F. Tanjia, S. De Nicola, L.A. Gizzi, Eur. Phys. J. D 66, 328 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    T.-C. Liu, X. Shao, C.-S. Liu, M. He, B. Eliasson, V. Tripathi, J.J. Su, J. Wang, S.-H. Chen, New J. Phys. 15, 025026 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    X. Wang, R. Zgadzaj, N. Fazel, Z. Li, S.A. Yi, X. Zhang, W. Henderson, Y.-Y. Chang, R. Korzekwa, H.-E. Tsai, C.-H. Pai, H. Quevedo, G. Dyer, E. Gaul, M. Martinez, A.C. Bernstein, T. Borger, M. Spinks, M. Donovan, V. Khudik, G. Shvets, T. Ditmire, M.C. Downer, Nat. Commun. 4, 1988 (2013)ADSGoogle Scholar
  29. 29.
    D. Jovanović, R. Fedele, M. Belić, submitted to Europhys. Lett.Google Scholar
  30. 30.
    M. Sharifian, H.R. Sharifinejad, H. Golbakhsi, J. Plasma Phys. 80, 453 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    R. Fedele, F. Tanjia, S. De Nicola, D. Jovanović, P.K. Shukla, Phys. Plasmas 19, 102106 (2012)ADSCrossRefGoogle Scholar
  32. 32.
    J.D. Lawson, The Physics of Charged-particle Beams, 2nd edn. (Clarendon, Oxford, 1988)Google Scholar
  33. 33.
    P. Michel, C.B. Schroeder, B.A. Shadwick, E. Esarey, W.P. Leemans, Phys. Rev. E 74, 026501 (2006)ADSCrossRefGoogle Scholar
  34. 34.
    Y. Shi, O. Chang, P. Muggli, C. Huang, W. An, W. Mori, in Proc. 2011 Particle Accelerator Conference, New York, USA, 2011 Google Scholar
  35. 35.
    K.A. Marsh, W. An, C.E. Clayton, C. Joshi, W.B. Mori, N. Vafaei-Najafabadi, P. Muggli, C.I. Clarke, S. Corde, J.-P. Delahaye, R.J. England, A.S. Fisher, J. Frederico, S.J. Gessner, M.J. Hogan, S.Z. Li, M.D. Litos, D. Walz, Z. Wu, E. Adli, Wei Lu, in Proc. North American Particle Accelerator Conference (NA-PAC), Pasadena, CA, USA, 2013 Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Renato Fedele
    • 1
    • 2
  • Tahmina Akhter
    • 1
    • 2
    Email author
  • Dušan Jovanović
    • 2
    • 3
  • Sergio De Nicola
    • 2
    • 4
  • Abdul Mannan
    • 2
    • 5
  1. 1.Dipartimento di FisicaUniversità di Napoli “Federico II”NapoliItaly
  2. 2.INFN Sezione di NapoliNapoliItaly
  3. 3.Institute of PhysicsUniversity of BelgradeBelgradeSerbia
  4. 4.SPIN-CNR NapoliNapoliItaly
  5. 5.Dipartimento di Matematica e FisicaSeconda Università degli Studi di NapoliNapoliItaly

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