Focusing of a Long Cylindrical Electron Stream by Means of Periodic Electrostatic Fields

This paper presents a theory of focusing long cylindrical electron streams by means of electric fields which vary periodically along the stream. The use of a bifilar helix or a series of annular rings to produce periodic electric fields is considered.The potential distribution at the position of the electrons is expanded in a power series, and an equation of electron motion is written. The solutions obtained indicate that the flow of electrons is essentially parallel, provided that the electrons enter the focusing structure practically without transverse velocities and are distributed across the stream such that the space charge fields decrease radially toward the axis in a manner similar to that of the periodic electric fields.The method of periodic electrostatic focusing is of particular interest in connection with traveling wave tubes. The possibility of using a bifilar helix as both the slow wave and the focusing structure is discussed.