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  • New method of deriving local energy and momentum-conserving Maxwell-collisionless drift-kinetic and gyrokinetic theories: conservation laws and their structures


In this paper we describe a relatively simple and transparent method of obtaining collisionless drift-kinetic, gyrokinetic and more general theories, including local charge, energy and momentum conservation laws. An important feature of the new formalism is, contrary to present-day theories, the exact gauge invariance, thus avoiding certain inconsistencies. The present paper starts with the introduction and proof of the correctness of a Lagrangian for combined Maxwell-kinetic theories in general coordinates as concerns the particle motion. The kinetic part of it is formulated in Eulerian form by means of the equations of motion in the form of Hamilton�Jacobi's equation, used only as a tool, and Dirac's constraint theory. Charge and current densities automatically distinguish between �particle-like� (guiding-centre), polarization and magnetization contributions. This formalism is applied to averaging coordinates derived by a method similar to Kruskal's. Certain properties of the averaging coordinates, according to the basic requirements imposed on them, can be used to obtain a gyroangle independent Lagrangian, from which one can obtain a Lagrangian for the combined Maxwell-kinetic theories in a reduced phase space that is applicable to situations in which one is not interested in the dependence on some kind of gyroangle describing the gyromotion, whose treatment can, however, easily be added. The basic perturbation theory, which aims at obtaining averaging phase-space coordinates, is done solely within the Kruskal formalism in which only the electric and magnetic fields appear, but not the corresponding potentials. This formalism provides, in particular, information about the allowed amplitudes of fluctuations. The results are later used to obtain approximate expressions for the Lagrange functions in the drift-kinetic and the gyrokinetic ordering.

Additional information

Authors: PFIRSCH D, Max-Planck-Institut für Plasmaphysik, IPP-EURATOM Association, Garching (DE);CORREA-RESTREPO D, Max-Planck-Institut für Plasmaphysik, IPP-EURATOM Association, Garching (DE)
Bibliographic Reference: Garching: Max-Planck-Institut für Plasmaphysik, 2004. 48 pp Free of charge
Availability: The document can be downloaded at:
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