<RESEARCH REPORT>Canonical Formalism of the Motion of a Charged Particle in a Magnetic Field
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概要
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The motion of a charged particle in a static magnetic field with axial symmetry is formulated by introducing a set of canonical variables, thus ambiguities in intuitive theory being avoided. It is shown to be possible to choose these variables as describing three modes of motion, the gyration about a line of force, the drift along the line of force and the azimuthal drift about the symmetry axis. The Hamiltonian expressed in terms of these variables is expanded in power of a small parameter that is of the same order of magnitude as the ratios of the gyration radius to the radii of curvature of a line of force and of a magnetic equipotential line and also to the distance from the axis. The zeroth order Hamiltonian thus obtained describes the motion in the first order orbit theory, whereby the magnetic moment is taken as equal to the action variable of the gyration mode at a line of force at which the kinetic angular momentum vanishes. The mirror point migration is obtained in a higher order approximation. This effect results, when applied to geomagnetically trapped particles, in the increase of the thickness of matter traversed by the particles, because of a steep altitude dependence of air density, and may be responsible for the absence of high energy protons in the outer radiation belt. Through this application it is illustrated that the present method provides a good approximation in the case of large γ, where γ is Stφrmer's constant of integral proportional to the angular momentum about the symmetry axis.
- 核融合科学研究所の論文
著者
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Obayashi Haruo
Information Center Institute Of Plasma Physics Nagoya University:permanently At Physical Institute N
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HAYAKAWA Satio
information center Institute of Plasma Physics, Nagoya University
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Hayakawa Satio
Information Center Institute Of Plasma Physics Nagoya University:permanently At Physical Institute Nagoya University