Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T20:04:58.701Z Has data issue: false hasContentIssue false
  • English
  • Français

Transient fields produced by a cylindrical electron beam flowing through a plasma

Published online by Cambridge University Press:  17 July 2012

Marie-Christine Firpo
Marie-Christine Firpo*
Affiliation:
Laboratoire de Physique des Plasmas, CNRS-Ecole Polytechnique, Palaiseau cedex, France
*
Address correspondence and reprint requests to: Marie-Christine Firpo, Laboratoire de Physique des Plasmas, CNRS-Ecole Polytechnique, 91128 Palaiseau cedex, France. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The out-of-equilibrium situation in which an initially sharp-edged cylindrical electron beam, that could, e.g., model electrons flowing within a wire, is injected into a plasma is considered. A detailed computation of the subsequently produced magnetic field is presented. The control parameter of the problem is shown to be the ratio of the beam radius to the electron skin depth. Two alternative ways to address analytically the problem are considered: one uses the usual Laplace transform approach, the other one involves Riemann's method in which causality conditions manifest through some integrals of triple products of Bessel functions.

Keywords

Beam/plasma interactionFast ignition studiesOut-of-equilibrium calculationsPlasma-based acceleratorsWave equations
Type
Research Article
Information
Laser and Particle Beams , Volume 30 , Issue 3 , September 2012 , pp. 497 - 507
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Borisov, V.V. (2002). On transient waves in dispersive media produced by moving point sources. J. Phys. A: Math. Gen. 35, 5403–5409.CrossRefGoogle Scholar
Borisov, V.V. & Simonenko, I. (1994). Transient waves generated by a source on a circle. J. Phys. A: Math. Gen. 27, 6243.CrossRefGoogle Scholar
Bret, A., Firpo, M.C. & Deutsch, C. (2004). Collective electromagnetic modes for beam-plasma interaction in the whole k space. Phys. Rev. E 70, 046401.CrossRefGoogle ScholarPubMed
Bret, A., Firpo, M.C. & Deutsch, C. (2005 a). Bridging the gap between two stream and filamentation instabilities. Laser Part. Beams 23, 375–383.CrossRefGoogle Scholar
Bret, A., Firpo, M.C. & Deutsch, C. (2005 b). Characterization of the initial filamentation of a relativistic electron beam passing through a plasma. Phys. Rev. Lett. 94, 115002.CrossRefGoogle ScholarPubMed
Bret, A., Firpo, M.C. & Deutsch, C. (2005 c). Transverse beam temperature effects on mixed two-stream/filamentation unstable modes. Nucl. Instr. Meth. Phys. Res. A 544, 427–429.CrossRefGoogle Scholar
Bret, A., Firpo, M.C. & Deutsch, C. (2007). About the most unstable modes encountered in beam plasma interaction physics. Laser Part. Beams 25, 117–119.CrossRefGoogle Scholar
Bret, A., Gremillet, L., Benisti, D. & Lefebvre, E. (2008). Exact relativistic kinetic theory of an electron-beam–plasma system: Hierarchy of the competing modes in the system-parameter space. Phys. Rev. Lett. 100, 205008.CrossRefGoogle ScholarPubMed
Deutsch, C. (2004). Penetration of intense charged particle beams in the outer layers of precompressed thermonuclear fuels. Laser Part. Beams 22, 115–120.CrossRefGoogle Scholar
Deutsch, C., Bret, A., Firpo, M.C., Gremillet, L., Lefebvre, E. & Lifschitz, A. (2008). Onset of coherent electromagnetic structures in the relativistic electron beam deuterium-tritium fuel interaction of fast ignition concern. Laser Part. Beams 26, 157–165.CrossRefGoogle Scholar
Deutsch, C., Furukawa, H., Mima, K., Murakami, M. & Nishihara, K. (1996). Interaction physics of the fast ignitor concept. Phys. Rev. Lett. 77, 2483–2486.CrossRefGoogle ScholarPubMed
Deutsch, C., Furukawa, H., Mima, K., Murakami, M. & Nishihara, K. (1997). Interaction physics of the fast ignitor concept. Laser Part. Beams 15, 557–564.CrossRefGoogle Scholar
Duffy, D. (2001). Green's Functions with Applications. New York: Chapman & Hall.CrossRefGoogle Scholar
Esarey, E., Schroeder, C. & Leemans, W. (2009). Physics of laser-driven plasma-based electron accelerators. Phys. Plasmas 81, 1229–1285.Google Scholar
Firpo, M.C. & Lifschitz, A.F. (2007). Early out-of beam-plasma evolution: Possible formation of a beam ring structure. Int. J. of Mod. Phys. B 21, 633–636.CrossRefGoogle Scholar
Firpo, M.C., Lifschitz, A.F., Lefebvre, E. & Deutsch, C. (2006). Early out-of-equilibrium beam-plasma evolution. Phys. Rev. Lett. 96, 115004.CrossRefGoogle ScholarPubMed
Gradshteyn, I.S. & Ryzhik, I.M. (2007). Table of Integrals, Series, and Products. New York.Google Scholar
Green, J.S., Lancaster, K.L., Akli, K.U., Gregory, C.D., Beg, F.N., Chen, S.N., Clark, D., Freeman, R.R., Hawkes, S., Hernandez-Gomez, C., Habara, H., Heathcote, R., Hey, D.S., Highbarger, K., Key, M.H., Kodama, R., Krushelnick, K., Musgrave, I., Nakamura, H., Nakatsutsumi, M., Patel, N., Stephens, R., Storm, M., Tampo, M., Theobald, W., Van Woerkom, L., Weber, R.L., Wei, M.S., Woolsey, N.C. & Norreys, P.A. (2007). Surface heating of wire plasmas using laser-irradiated cone geometries. Nat. Phys. 3, 853–856.CrossRefGoogle Scholar
Hoffmann, D., Blazevic, A., Ni, P., Rosmej., , Roth, M., Tahir, N.A., Tauschwitz, A., Udrea, S., Varentsov, D., Weyrich, K. & Maron, Y. (2005). Present and future perspectives for high energy density physics with intense heavy ion and laser beams. Laser Part. Beams 23, 47–53.CrossRefGoogle Scholar
Kumar, N., Pukhov, A. & Lotov, K. (2010). Self-modulation instability of a long proton bunch in plasmas. Phys. Rev. Lett. 104, 255003.CrossRefGoogle ScholarPubMed
Kuppers, G., Salat, A. & Wimmel, H.K. (1973). Current and fields induced in plasmas by relativistic electron beams with arbitrary radial and axial density profiles. Plasma Phys. 15, 429–439.CrossRefGoogle Scholar
Norreys, P.A., Beg, F.N., Sentoku, Y., Silva, L.O., Smith, R.A. & Trines, R.M.G.M. (2009). Intense laser-plasma interactions: New frontiers in high energy density physics. Phys. Plasmas 16, 041002.CrossRefGoogle Scholar
Olevsky, M.N. (1952). On the Riemann function for the differential equation u xx − u tt + [p 1 (x) + p 2 (t)]u = 0. Dokl. Akad. Nauk. 87, 337.Google Scholar
Tabak, M., Hammer, J., Glinsky, M., Kruer, W.S.C., Wilks, W., Woodworth, J., Campbell, E.M., Perry, M.D. & Mason, R.J., 1994. Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 1, 1626–1634.CrossRefGoogle Scholar
Taguchi, T., Antonsen, T.M., Liu, C.S. & Mima, K. (2001). Structure formation and tearing of an MeV cylindrical electron beam in a laser-produced plasma. Phys. Rev. Lett. 86, 5055–5058.CrossRefGoogle Scholar
Valkó, P.P. & Abate, J. (2004). Comparison of sequence accelerators for the gaver method of numerical laplace transform inversion. Comput. Math. Appl. 48, 629–636.CrossRefGoogle Scholar