Skip to main content Accessibility help

Coherent quantum hollow beam creation in a plasma wakefield accelerator

  • D. JOVANOVIĆ (a1), R. FEDELE (a2), F. TANJIA (a2), S. DE NICOLA (a2) (a3) and M. BELIĆ (a4)...


A theoretical investigation of the propagation of a relativistic electron (or positron) particle beam in an overdense magnetoactive plasma is carried out within a fluid plasma model, taking into account the individual quantum properties of beam particles. It is demonstrated that the collective character of the particle beam manifests mostly through the self-consistent macroscopic plasma wakefield created by the charge and the current densities of the beam. The transverse dynamics of the beam–plasma system is governed by the Schrödinger equation for a single-particle wavefunction derived under the Hartree mean field approximation, coupled with a Poisson-like equation for the wake potential. These two coupled equations are subsequently reduced to a nonlinear, non-local Schrödinger equation and solved in a strongly non-local regime. An approximate Glauber solution is found analytically in the form of a Hermite–Gauss ring soliton. Such non-stationary (‘breathing’ and ‘wiggling’) coherent structure may be parametrically unstable and the corresponding growth rates are estimated analytically.



Hide All
Belić, M. R. and Zhong, W.-P. 2009 Two-dimensional spatial solitons in highly nonlocal nonlinear media. EPJ D 53, 97106.
Bonifacio, R., Cola, M. M., Piovella, N. and Robb, G. R. M. 2005 A quantum model for collective recoil lasing. EPL (Europhys. Lett.) 69, 5560.
Briedis, D., Petersen, D. E., Edmundson, D., Krolikowski, W. and Bang, O. 2005 Ring vortex solitons in nonlocal nonlinear media. Opt. Exp. 13, 435.
Chen, P., Dawson, J. M., Huff, R. W. and Katsouleas, T. 1985 Acceleration of electrons by the interaction of a bunched electron beam with a plasma. Phys. Rev. Lett. 54, 693696.
de Martino, S., de Siena, S. and Fedele, R. 1997 Locally controlled coherence in the longitudinal dynamics of electron bunches in particle accelerators. Phys. Scr. 56, 426429.
de Nicola, S., Fedele, R., ManZ'ko, V. I. and Miele, G. 1995 Coherent states for particle beams in the thermal wave model. Phys. Scr. 52, 191198.
Fedele, R., Tanjia, F., de Nicola, S., Jovanović, D. and Shukla, P. K. 2012 Quantum ring solitons and nonlocal effects in plasma wake field excitations. Phys. Plasmas 19, 102106.
Glauber, R. J. 1963 The quantum theory of optical coherence. Phys. Rev. 130, 25292539.
He, Y. J., Malomed, B. A., Mihalache, D. and Wang, H. Z. 2008 Crescent vortex solitons in strongly nonlocal nonlinear media. Phys. Rev. A 78 (2), 023824.
Huang, Z., Chen, P. and Ruth, R. D. 1995 Radiation reaction in a continuous focusing channel. Phys. Rev. Lett. 74, 17591762.
Huang, Z. and Ruth, R. D. 1998 Effects of focusing on radiation damping and quantum excitation in electron storage rings. Phys. Rev. Lett. 80, 23182321.
Jagannathan, R., Simon, R., Sudarshan, E. C. G. and Mukunda, N. 1989 Quantum theory of magnetic electron lenses based on the Dirac equation. Phys. Lett. A 134, 457464.
Khan, S. A. and Jagannathan, R. 1995 Quantum mechanics of charged-particle beam transport through magnetic lenses. Phys. Rev. E 51, 25102515.
Królikowski, W., Bang, O., Nikolov, N. I., Neshev, D., Wyller, J., Rasmussen, J. J. and Edmundson, D. 2004 Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media. J. Opt. B 6, 288.
Preparata, G. 1988 Quantum field theory of the free-electron laser. Phys. Rev. A 38, 233237.
Rosenzweig, J. B., Cline, D. B., Cole, B., Figueroa, H. and Gai, W. 1988 Experimental observation of plasma wake-field acceleration. Phys. Rev. Lett. 61, 98101.
Schrödinger, E. 1926 Der stetige Übergang von der Mikro-zur Makromechanik. Naturwissenschaften 14, 664666.
Schulten, K. 2000 Notes on Quantum Mechanics. Urbana, IL: University of Illinois at Urbana Champaign.
Sokolov, A. A. and Ternov, I. M. 1963 O . Doklady Akad. Nauk SSSR (in Russian) 153, 1052.
Zhang, S. and Yi, L. 2009 Two-dimensional Hermite–Gaussian solitons in strongly nonlocal, nonlinear medium with rectangular boundaries. Opt. Comm. 282, 16541658.
MathJax is a JavaScript display engine for mathematics. For more information see


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed