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Zur Theorie der Teilchenbewegung in zeitabhängigen elektromagnetischen Feldern
Author(s) -
Vojta Günter,
Wonn Joachim
Publication year - 1967
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.19670070608
Subject(s) - ansatz , physics , tensor (intrinsic definition) , langevin equation , differential equation , magnetohydrodynamic drive , quantum electrodynamics , classical mechanics , equations of motion , charged particle , particle velocity , magnetic field , mathematical analysis , mathematical physics , quantum mechanics , magnetohydrodynamics , mathematics , ion , geometry
The Langevin equation – i.e. the equation of motion for a charged particle including a collision term proportional to the particle velocity – is solved for arbitrary time‐dependent electric and magnetic fields by a new general method. Instead of the usual ansatz: particle velocity = cyclotron velocity + drift velocity the method given makes the ansatz: particle velocity = tensor = cyclotron velocity. The unknown tensor obeys a simple differential equation of the first order which can be generally solved at once. This method is a modification of the variation of constants method for inhomogeneous differential equations. The electromagnetic fields considered must be spatially homogeneous; for (weakly) inhomogeneous fields an iteration procedure of Pytte (1962) may be applied. Some examples are discussed shortly. The Langevin equation treated is completely equivalent to the equation of motion in a magnetohydrodynamic one‐fluid theory.