The Water-bag Model of a Sheet Electron Beamy

Abstract

A shoot electron beam in a fictitious focusing field regarded as purely electric in a frame moving with the electron is analysed in terms of a model in which the phase space density changes in discrete steps at certain contour lines in the phase plane. The equilibria and the eigenvalues for small perturbations in the case of a single contour are worked out. The advantage of this technique is that the only significant motions are those of the contour itself, the phase fluid inside being incompressible and homogeneous.