Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 324
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bostan, Mihai 2016. MultiScale Analysis for Linear First Order PDEs. The Finite Larmor Radius Regime. SIAM Journal on Mathematical Analysis, Vol. 48, Issue. 3, p. 2133.

    Brizard, Alain J. and Tronci, Cesare 2016. Variational formulations of guiding-center Vlasov-Maxwell theory. Physics of Plasmas, Vol. 23, Issue. 6, p. 062107.

    García-Toraño Andrés, Eduardo Mestdag, Tom and Yoshimura, Hiroaki 2016. Implicit Lagrange–Routh equations and Dirac reduction. Journal of Geometry and Physics, Vol. 104, p. 291.

    Kanno, R. Nunami, M. Satake, S. Matsuoka, S. and Takamaru, H. 2016. Development of a Drift-Kinetic Simulation Code for Estimating Collisional Transport Affected by RMPs and Radial Electric Field. Contributions to Plasma Physics,

    Kolesnichenko, Ya I Lutsenko, V V Yakovenko, Yu V Lepiavko, B S Grierson, B Heidbrink, W W and Nazikian, R 2016. Manifestations of the geodesic acoustic mode driven by energetic ions in tokamaks. Plasma Physics and Controlled Fusion, Vol. 58, Issue. 4, p. 045024.

    Li, Haochen and Wang, Yushun 2016. A discrete line integral method of order two for the Lorentz force system. Applied Mathematics and Computation, Vol. 291, p. 207.

    Miyamoto, Kenro 2016. Plasma Physics for Controlled Fusion.

    Miyamoto, Kenro 2016. Plasma Physics for Controlled Fusion.

    Miyato, N. 2016. Gyrokinetic Model beyond the Standard Ordering. Contributions to Plasma Physics,

    Pfefferlé, D. Cooper, W.A. Fasoli, A. and Graves, J.P. 2016. Effects of magnetic ripple on 3D equilibrium and alpha particle confinement in the European DEMO. Nuclear Fusion, Vol. 56, Issue. 11, p. 112002.

    Scott, B. 2016. Gyrokinetic Theory and Dynamics of the Tokamak Edge. Contributions to Plasma Physics,

    Sugama, H. Matsuoka, S. Satake, S. and Kanno, R. 2016. Radially local approximation of the drift kinetic equation. Physics of Plasmas, Vol. 23, Issue. 4, p. 042502.

    Todo, Y. Van Zeeland, M.A. and Heidbrink, W.W. 2016. Fast ion profile stiffness due to the resonance overlap of multiple Alfvén eigenmodes. Nuclear Fusion, Vol. 56, Issue. 11, p. 112008.

    Tronci, Cesare 2016. From liquid crystal models to the guiding-center theory of magnetized plasmas. Annals of Physics, Vol. 371, p. 323.

    Zestanakis, P. A. Kominis, Y. Anastassiou, G. and Hizanidis, K. 2016. Orbital spectrum analysis of non-axisymmetric perturbations of the guiding-center particle motion in axisymmetric equilibria. Physics of Plasmas, Vol. 23, Issue. 3, p. 032507.

    Zhu, Siqiang Xu, Yingfeng and Wang, Shaojie 2016. Nonlinear gyrokinetic theory and its application to computation of the gyrocenter motion in ripple field. Physics of Plasmas, Vol. 23, Issue. 6, p. 062306.

    Zhu, Beibei Hu, Zhenxuan Tang, Yifa and Zhang, Ruili 2016. Symmetric and symplectic methods for gyrocenter dynamics in time-independent magnetic fields. International Journal of Modeling, Simulation, and Scientific Computing, Vol. 07, Issue. 02, p. 1650008.

    Ellison, C Leland Finn, J M Qin, H and Tang, W M 2015. Development of variational guiding center algorithms for parallel calculations in experimental magnetic equilibria. Plasma Physics and Controlled Fusion, Vol. 57, Issue. 5, p. 054007.

    He, Yang Sun, Yajuan Liu, Jian and Qin, Hong 2015. Volume-preserving algorithms for charged particle dynamics. Journal of Computational Physics, Vol. 281, p. 135.

    Hirvijoki, E. Kurki-Suonio, T. Äkäslompolo, S. Varje, J. Koskela, T. and Miettunen, J. 2015. Monte Carlo method and High Performance Computing for solving Fokker–Planck equation of minority plasma particles. Journal of Plasma Physics, Vol. 81, Issue. 03,


Variational principles of guiding centre motion

  • Robert G. Littlejohn (a1)
  • DOI:
  • Published online: 01 March 2009

An elementary but rigorous derivation is given for a variational principle for guiding centre motion. The equations of motion resulting from the variational principle (the drift equations) possess exact conservation laws for phase volume, energy (for time-independent systems), and angular momentum (for azimuthally symmetric systems). The results of carrying the variational principle to higher order in the adiabatic parameter are displayed. The behaviour of guiding centre motion in azimuthally symmetric fields is discussed, and the role of angular momentum is clarified. The application of variational principles in the derivation and solution of gyrokinetic equations is discussed.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

V. I. Arnold 1978 Mathematical Methods of Classical Mechanics. Springer.

A. H. Boozer 1980 Phys. Fluids, 23, 904.

J. R. Cary 1981 Phys. Rep. 79, 131.

A. J. Dragt & J. M. Finn 1976 J. Math. Phys. 17, 2215.

E. A. Frieman & L. Chen 1982 Phys. Fluids, 25, 502.

R. J. Hastie , J. B. Taylor & F. A. Haas 1967 Ann. Phys. 41, 302.

R. G. Littlejohn 1979 J. Math. Phys. 20, 2445.

R. G. Littlejohn 1981 Phys. Fluids, 24, 1730.

R. G. Littlejohn 1982 aJ. Math. Phys. 23, 742.

T. G. Northrop & J. A. Rome 1978 Phys. Fluids, 21, 384.

J. B. Taylor 1964 Phys. Fluids, 7, 767.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *