Zur Theorie der Teilchenbewegung in zeitabhängigen elektromagnetischen Feldern

Abstract

The UGMN 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 a t 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 LANOEVIN equation treated is completely equivalent. to the equation of motion in a magnetohydrodynamic one-fluid theory.Viele Probleme der Plasmaphysik lassen sich in erster und oft bereits sehr guter Naherung mit Hilfe der Theorie der Bewegung eines geladenen Einzelteilchensgegebenenfalls unter EinschluB einer Reibungskraft -behandeln ; dazu gehoren Plasmaschwingungen, Plasmainstabilitaten, Wellenfortpflanzung in Plasmen, Plasmaleitfahigkeit, Plasmahalterung, aber auch Probleme der Strahl-PlasmaWechselwirkung und der Elektronen-und Ionenoptik [ [S, 91.

Langevin equation of motion for electrons in an inhomogeneous plasma

“…Up to now, solutions of this equation were only given for constant fields and for time-dependent homogeneous fields [3]. In plasma physics, however, also spatially dependent electric fields are of importance, see, e.g.…”