Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T05:05:01.739Z Has data issue: false hasContentIssue false
  • English
  • Français

Guiding-centre transformation of the radiation–reaction force in a non-uniform magnetic field

Part of: Focus on Fusion Energetic Electrons

Published online by Cambridge University Press:  13 July 2015

E. Hirvijoki ,
J. Decker ,
A. J. Brizard  and
O. Embréus
E. Hirvijoki*
Affiliation:
Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
J. Decker
Affiliation:
Ecole Polytechnique Fédérale de Lausanne (EPFL), Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne, Switzerland
A. J. Brizard
Affiliation:
Department of Physics, Saint Michael’s College, Colchester, VT 05439, USA
O. Embréus
Affiliation:
Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
*
†Email address for correspondence: eero.hirvijoki@chalmers.se
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we present the guiding-centre transformation of the radiation–reaction force of a classical point charge travelling in a non-uniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field non-uniformity length scale, so that the guiding-centre Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation–reaction force is obtained with the Poisson-bracket formalism originally introduced by Brizard (Phys. Plasmas, vol. 11, 2004, 4429–4438), where it was used to eliminate the fast gyromotion from the Fokker–Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-centre radiation–reaction force include tracing of charged particle orbits in complex magnetic fields as well as the kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g. for runaway-electron dynamics in tokamaks.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 5 , October 2015 , 475810504
Copyright
© Cambridge University Press 2015 

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

Abraham, M. 1905 Theorie der Elektrizität, Vol II: Elektromagnetische Theorie der Strahlung. Teubner.Google Scholar
Andersson, F., Helander, P. & Eriksson, L.-G. 2001 Damping of relativistic electron beams by synchrotron radiation. Phys. Plasmas 8 (12), 5221–5229.Google Scholar
Bakhtiari, M., Kramer, G. J., Takechi, M., Tamai, H., Miura, Y., Kusama, Y. & Kamada, Y. 2005 Role of bremsstrahlung radiation in limiting the energy of runaway electrons in tokamaks. Phys. Rev. Lett. 94, 215003.Google Scholar
Brizard, A. J. 2004 A guiding-center Fokker–Planck collision operator for nonuniform magnetic fields. Phys. Plasmas 11 (9), 4429–4438.Google Scholar
Brizard, A. J., Decker, J., Peysson, Y. & Duthoit, F.-X. 2009 Orbit-averaged guiding-center Fokker–Planck operator. Phys. Plasmas 16 (10), 102304.Google Scholar
Cary, J. R. & Brizard, A. J. 2009 Hamiltonian theory of guiding-center motion. Rev. Mod. Phys. 81, 693–738.Google Scholar
Decker, J., Peysson, Y., Brizard, A. J. & Duthoit, F.-X. 2010 Orbit-averaged guiding-center Fokker–Planck operator for numerical applications. Phys. Plasmas 17 (11), 112513.Google Scholar
Dirac, P. A. M. 1938 Classical theory of radiating electrons. Proc. R. Soc. Lond. A 167 (929), 148–169.Google Scholar
Ford, G. W. & O’Connell, R. F. 1993 Relativistic form of radiation reaction. Phys. Lett. A 174 (3), 182–184.Google Scholar
Griffiths, D. J., Proctor, T. C. & Schroeter, D. F. 2010 Abraham–Lorentz versus Landau–Lifshitz. Am. J. Phys. 78 (4), 391–402.Google Scholar
Guan, X., Qin, H. & Fisch, N. J. 2010 Phase-space dynamics of runaway electrons in tokamaks. Phys. Plasmas 17 (9), 092502.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1975 The Classical Theory of Fields, 4th edn., Course of Theoretical Physics, vol. 2. Pergamon.Google Scholar
Littlejohn, R. G. 1983 Variational principles of guiding centre motion. J. Plasma Phys. 29, 111–125.CrossRefGoogle Scholar
Liu, J., Qin, H., Fisch, N. J., Teng, Q. & Wang, X. 2014 What is the fate of runaway positrons in tokamaks? Phys. Plasmas 21 (6), 064503.Google Scholar
Lorentz, H. A. 1936 La théorie électromagnétique de Maxwell et son application aux corps mouvants. In Collected Papers, pp. 164–343. Springer.Google Scholar
Pauli, W. 1958 Theory of Relativity. Pergamon.Google Scholar
Rohrlich, F. 2007 Classical Charged Particles. World Scientific.Google Scholar
Spohn, H. 2000 The critical manifold of the Lorentz-Dirac equation. Europhys. Lett. 50 (3), 287–292.Google Scholar
Stahl, A., Hirvijoki, E., Decker, J., Embréus, O. & Fülöp, T. 2015 Effective critical electric field for runaway-electron generation. Phys. Rev. Lett. 114, 115002.Google Scholar