Plasma and Fusion Research

Volume 3, 057 (2008)

Regular Articles

The Conjugate Variable Method in Hamilton-Lie Perturbation Theory - Applications to Plasma Physics -
Shinji TOKUDA
Japan Atomic Energy Agency, Naka, Ibaraki, 311-0193 Japan
(Received 21 February 2008 / Accepted 29 July 2008 / Published 2 October 2008)

Abstract

The conjugate variable method, an essential ingredient in the path-integral formalism of classical statistical dynamics, is used to apply the Hamilton-Lie perturbation theory to a system of ordinary differential equations that does not have the Hamiltonian dynamic structure. The method endows the system with this structure by doubling the unknown variables; hence, the canonical Hamilton-Lie perturbation theory becomes applicable to the system. The method is applied to two classical problems of plasma physics to demonstrate its effectiveness and study its properties: a non-linear oscillator that can explode and the guiding center motion of a charged particle in a magnetic field.

Keywords

one-form, Hamilton-Lie perturbation method, conjugate variable, non-linear oscillator, guiding center motion, plasma physics

DOI: 10.1585/pfr.3.057

Full Text

PDF format (147Kbytes) PDF Download

References

  • [1] E.C.G. Sudarshan and N. Mukunda, Classical Dynamics: A Modern Perspective (Rober E. Krieger Publishing Company, Florida, U.S.A, 1983).
  • [2] J.R. Cary and R.G. Littlejohn, Ann. Phys. 151, 1 (1983).
  • [3] C.M. Bender and S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, U.S.A, 1978) Chap.11.
  • [4] B. Jouvet and R. Phytian, Phys. Rev. A 19, 1350 (1979).
  • [5] T.G. Northrop, The Adiabatic Motion of Charged Particles (Interscience, New York, U.S.A, 1963).
  • [6] A.I. Morozov and L.S. Solov'ev, Motion of Charged Particles in Electromagnetic Fields, in Reviews of Plasma Physics Vol.2, 201-297, Edited by M.A. Leontovich, Consultants Bureau, New York (1966).
  • [7] R.G. Littlejohn, J. Plasma Phys. 29, 111 (1983).
  • [8] T.S. Hahm, W.W. Lee and A. Brizard, Phys. Fluids 31, 1940 (1988).

This paper may be cited as follows:

Shinji TOKUDA, Plasma Fusion Res. 3, 057 (2008).