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Dynamics of a charged particle in progressive plane waves propagating in vacuum or plasma: Stochastic acceleration

Published online by Cambridge University Press:  14 September 2009

A. Bourdier  and
M. Drouin
A. Bourdier*
Affiliation:
CEA, DAM, DIF, 91297 Arpajon Cedex, France
M. Drouin
Affiliation:
CEA, DAM, DIF, 91297 Arpajon Cedex, France
*
Address correspondence and reprint requests to: A. Bourdier, CEA, DAM, Arpajon Cedex, France. E-mail: [email protected]
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Abstract

The dynamics of a charged particle in a relativistic strong electromagnetic plane wave propagating in a nonmagnetized medium is studied first. The problem is shown to be integrable when the wave propagates in vacuum. When it propagates in plasma, and when the full plasma response is considered, an exhaustive numerical work allows us to conclude that the problem is not integrable. The dynamics of a charged particle in a relativistic strong electromagnetic plane wave propagating along a constant homogeneous magnetic field is studied next. The problem is integrable when the wave propagates in vacuum. When it propagates in plasma, the problem becomes nonintegrable. Finally, one particle in a high intensity wave, propagating in a nonmagnetized medium, perturbed by a low intensity traveling wave is considered. Resonances are identified and conditions for resonance overlap are studied. Stochastic acceleration is shown by considering a single particle. It is confirmed in plasma in realistic situations with particle-in-cell code simulations.

Keywords

ChaosIntegrabilityParticle-in-cellStochastic acceleration
Type
Research Article
Information
Laser and Particle Beams , Volume 27 , Issue 4 , December 2009 , pp. 545 - 567
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Akhiezer, A.I. & Polovin, R.V. (1956). Theory of wave motion of an electron plasma. Sov. Phys. JETP 3, 696–705.Google Scholar
Arnold, V.I. (1988). Dynamical Systems III. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Bouquet, S. & Bourdier, A. (1998). Notion of integrability for time-dependent hamiltonian systems: illustrations from the relativistic motion of a charged particle. phys. Rev. E 57, 1273–1283.Google Scholar
Bourdier, A., Valentini, M. & Valat, J. (1996). Dynamics of a relativistic charged particle in a constant homogeneous magnetic field and a transverse homogeneous rotating electric field. Phys. Rev. E 54, 5681–5691.CrossRefGoogle Scholar
Bourdier, A. & Gond, S. (2000). Dynamics of a charged particle in a circularly polarized traveling electromagnetic wave. Phys. Rev. E 62, 4189–4206.CrossRefGoogle Scholar
Bourdier, A. & Gond, S. (2001). Dynamics of a charged particle in a linearly polarized traveling electromagnetic wave. Phys. Rev. E 63, 036609/1–9.CrossRefGoogle Scholar
Bourdier, A. (2009). Dynamics of a charged particle in a progressive wave. Phys. D 238, 226–232.CrossRefGoogle Scholar
Bourdier, A. & Michel-Lours, L. (1994). Identifying chaotic electron trajectories in a helical-wiggler free-electron laser. Phys. Rev. E 49, 3353–3359.CrossRefGoogle Scholar
Bourdier, A., Patin, D. & Lefebvre, E. (2005 a). Stochastic heating in ultra high intensity laser-plasma interaction. Phys. D 206, 1–31.CrossRefGoogle Scholar
Bourdier, A. & Patin, D. (2005 b). Dynamics of a charged particle in a linearly polarized traveling wave. Hamiltonian approach to laser-matter interaction at very high intensities. Eur. Phys. J.D. 32, 361–376.CrossRefGoogle Scholar
Bourdier, A., Patin, D. & Lefebvre, E. (2007). Stochastic heating in ultra high intensity laser-plasma interaction. Laser Part. Beams 25, 169–180.CrossRefGoogle Scholar
Chirikov, B. (1979). A universal instability of many-dimensional oscillator systems. Phys. Rpt 52, 263–379.Google Scholar
Davoine, X., Lefebvre, E., Faure, J., Rechatin, C., Lifschitz, A. & Malka, V. (2008). Simulation of quasimonoenergetic electron beams produced by colliding pulse wakefield acceleration. Phys. Plasmas 15, 113102–1/113102–11.CrossRefGoogle Scholar
Davydovski, V.Ya. (1963). Possibility of resonance acceleration of charged particles by electromagnetic waves in a constant magnetic field. JETP 16, 629–630.Google Scholar
Faenov, A.Ya., Magunov, A.I., Pikuz, T.A. Skobelev, I.Yu., Giulietti, D., Betti, S., Galimberti, M., Gamucci, A., Giulietti, A., Gizzi, L.A., Labate, L., Levato, T., Tomassini, P., Marques, J.R., Bourgeois, N., Dobosz Dufrenoy, S., Ceccotti, T., Monot, P., Reau, F., Popescu, H., D'oliveira, P., Martin, Ph., Fukuda, Y., Boldarev, A.S., Gasilov, S.V. & Gasilov, V.A. (2008). Non-adiabatic cluster expansion after ultrashort laser interaction. Laser Part. Beams 26, 69–81.CrossRefGoogle Scholar
Goldstein, H. (1980). Classical Mechanics. Second Edition. New York: Addison-Wesley.Google Scholar
Grammaticos, B., Ramani, A. & Yoshida, H. (1987). The demise of a good integrability candidate. Phys. Lett. A 124, 65–67.CrossRefGoogle Scholar
Jackson, J.D. (1975). Classical Electrodynamics. Second Edition. New-York: Wiley.Google Scholar
Juillard Tosel, E. (1999). Non-intégrabilité algébrique et méromorphe de problems de N corps. Thèse. Paris: Université Paris VI.Google Scholar
Juillard Tosel, E. (2000). Meromorphic parametric non-integrability: The inverse square potential. Arch. Rat. Mech. Analy. 152, 187–205.CrossRefGoogle Scholar
Kanapathipillai, M. (2006). Nonlinear absorption of ultra short laser pulses by clusters. Laser Part. Beams 24, 9–14.CrossRefGoogle Scholar
Kapitza, P.L. & Dirac, P.A.M. (1933). The reflection of electrons from standing light waves. Proc. Cambridge Philos. Soc. 29, 297–300.CrossRefGoogle Scholar
Kaw, P.K., Sen, A. & Valeo, E.J. (1983). Coupled nonlinear stationary, waves in a plasma. Phys. 9D, 96–102.Google Scholar
Kotaki, H., Masuda, S., Kando, M. & Koga, J.K. (2004). Head-on injection of a high quality electron beam by the interaction of two laser pulses. Phys. Plasmas 11, 3296–3302.CrossRefGoogle Scholar
Kwon, D.H. & Lee, H.W. (1999). Chaos and reconnection in relativistic cyclotron motion in an elliptically polarized electric field. Phys. Rev E 60, 3896–3904.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. (1975). The Classical Theory of Fields. Fourth Edition. Oxford: Pergamon.Google Scholar
Lefebvre, E., Cochet, N., Fritzler, S., Malka, V., Aleonard, M.-M., Chemin, J.-F., Darbon, S., Disdier, L., Faure, J., Fedotoff, A., Landoas, O., Malka, G., Meot, V., Morel, P., Rabec Le Gloahec, M., Rouyer, A., Rubbelynck, Ch., Tikhonchuk, V., Wrobel, R., Audebert, P. & Rousseaux, C. (2003). Electron and photon production from relativistic laser-plasma interactions. Nucl. Fusion 43, 629–633.CrossRefGoogle Scholar
Lichtenberg, A.J. & Liebermann, M.A. (1983). Regular and Stochastic Motion. New York: Springer-Verlag.CrossRefGoogle Scholar
Michel-Lours, L., Bourdier, A. & Buzzi, J.M. (1992). Chaotic electron trajectories in a free-electron laser with a linearly polarized wiggler. Phys. Fluids B 5, 965–971.CrossRefGoogle Scholar
Mikhailov, Y.A., Nikitina, L.A., Sklizkov, G.V., Starodub, A.N. & Zhurovich, M.A. (2008). Relativistic electron heating in focused multimode laser fields with stochastic phase perturbations. Laser Part. Beams 26, 525–536.CrossRefGoogle Scholar
Mulser, P., Kanapathipillai, M. & Hoffmann, D.H.H. (2005). Two very efficient nonlinear laser absorption mechanisms in clusters. Phys. Rev. Lett. 95, 103401.CrossRefGoogle ScholarPubMed
Ott, E. (1993). Chaos in Dynamical Systems. Cambridge: University Press.Google Scholar
Patin, D. (2006). Le chauffage stochastique dans l'interaction laser-plasma à très haut flux. Thèse. Paris: Université Paris Xi.Google Scholar
Patin, D., Bourdier, A. & Lefebvre, E. (2005 a). Stochastic heating in ultra high intensity laser-plasma interaction. Laser Part. Beams 23, 599–599.CrossRefGoogle Scholar
Patin, D., Bourdier, A. & Lefebvre, E. (2005 b). Stochastic heating in ultra high intensity laser-plasma interaction. Laser Part. Beams 23, 297–302.Google Scholar
Patin, D., Lefebvre, E., Bourdier, A. & D'humieres, E. (2006). Stochastic heating in ultra high intensity laser-plasma interaction: Theory and PIC code Simulations. Laser Part. Beams 24, 223–230.CrossRefGoogle Scholar
Rasband, S.N. (1983). Dynamics. New York: John Wiley & Sons.Google Scholar
Rax, J.M. (1992). Compton harmonic resonances, stochastic instabilities, quasilinear diffusion, and collisionless damping with ultra-high-intensity laser waves. Phys. Fluids B 4, 3962–3972.CrossRefGoogle Scholar
Roberts, C.S. & Buchsbaum, S.J. (1964). Motion of a charged particle in a constant magnetic field and a transverse electromagnetic wave propagating along the field. Phys. Rev. 135, A381–A389.CrossRefGoogle Scholar
Romeiras, F.J. (1989). Stochasticity of Nonlinear waves in Plasmas. Proc. Int. Conf. Plasma Physics, New Delhi, India.Google Scholar
Sheng, Z.-M., Mima, K., Sentoku, Y., Jovanovic, M.S., Taguchi, T., Zhang, J. & Meyer-Ter-Vehn, J. (2002). Stochastic heating and acceleration of electrons in colliding laser fields in plasma. Phys. Rev. Lett 88, 055004/1–4.CrossRefGoogle ScholarPubMed
Sheng, Z.-M., Mima, K., Zhang, J. & Meyer-Ter-Vehn, J. (2004). Efficient acceleration of electrons with counter propagating intense laser pulses in vacuum and underdense plasma. Phys. Rev. E 69, 016407.CrossRefGoogle Scholar
Swanson, D.G. (1989). Plasma Waves. Boston: Academic Press, Inc.CrossRefGoogle Scholar
Tabor, M. (1989). Chaos and Integrability in Nonlinear Dynamics. New York: John Wiley & Sons.Google Scholar
Tajima, T., Kishimoto, Y. & Masaki, T. (2001). Cluster fusion. Phys. Scripta T89, 45–48.Google Scholar
Van Der Weele, J.P., Capel, H.W., Valkering, T.P. & Post, T. (1998). The squeeze effect in non-integrable hamiltonian systems. Phys. 147a, 499–532.Google Scholar
Walker, G.H. & Ford, J. (1969). Amplitude instability and ergodic behavior for conservative nonlinear oscillator systems. Phys. Rev. 188, 416–431.CrossRefGoogle Scholar
Winkles, B.B. & Eldridge, O. (1972). Self-consistent electromagnetic waves in relativistic vlasov plasmas. Phys. Fluids 15, 1790–1800.CrossRefGoogle Scholar
Ziaja, B., Weckert, E. & Moller, T. (2007). Statistical model of radiation damage within an atomic cluster irradiated by photons from free-electron-laser. Laser Part Beams 25, 407–414.CrossRefGoogle Scholar