This paper is an extension of an earlier work by the author to include the electron motion. The problem is quite similar to that considered by tonksb; the essential differences being that we allow the particles a component of velocity in the direction of the magnetic field and that the solution is exact.

Briefly the problem may be described as follows. All quantities are assumed to depend only on a single variable, x. The magnetic field is directed everywhere in the z-direction, and is uniform from x w to x=. O. As we cross the plane x z 0 we enter into the plasma domain, where the field decreases and eventually becomes uniform again at x -w. The paths of the plasma constituents are determined by the fields (magnetic and electric) in which they move. The fields are in turn determined by the paths of the particles. Our problem then is to solve>self consistently, Maxwell's equations and the equations of motion of the particles.

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