Space charge electrostatic fields and focusing of a sheet electron beam with diffused edges

An analytical and numerical study of the stability of sheet electron beams in periodically cusped magnetic fields (PCM ) is made. The beam has been considered as having edges with a prescribed density variation. In estimating the electrostatic fields, we have considered the density variation of both the edges along the width and thickness of the sheet beam. The conditions for beam focusing and beam matching are discussed.