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Zur Theorie der Bewegung geladener Teilchen in richtungskonstanten Magnetfeldern exponentieller Zeitabhängigkeit. III. Allgemeine Schaltprozesse
Author(s) -
Koch Eckhard
Publication year - 1969
Publication title -
beiträge aus der plasmaphysik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0005-8025
DOI - 10.1002/ctpp.19690090205
Subject(s) - physics , magnetic field , magnetosphere particle motion , electric field , kinetic energy , field (mathematics) , superposition principle , classical mechanics , constant (computer programming) , particle (ecology) , condensed matter physics , quantum mechanics , mathematics , pure mathematics , oceanography , computer science , programming language , geology
The motion of a charged particle in a magnetic field is calculated for the following case: the spatially homogeneous magnetic field having a constant direction is a superposition of a field constant in time and one decreasing exponentially in time; taken into account is the influence of the electric field induced by the time dependent magnetic field and a friction force proportional to the particle velocity. The higher transcendental functions appearing in the exact solutions are approximated in various ways in dependence on the values of argument and parameters. In this manner approximated formulae of a very simple form are obtained for position, velocity, kinetic energy and magnetic moment of the particle, and the domain of validity of these formulae is determined. The particle orbits are classified, and their dependence on the initial values, parameters of the magnetic field and on the magnitude of the friction force is studied. A comparison between our results and a rectangular variation of the field is given. It is shown that the electric field induced by the time dependent magnetic field has an important influence on the particle motion.