Transverse Electron Beam Waves in Varying Magnetic Fields

Abstract

The properties of electron cyclotron and synchronous waves in varying magnetic fields are discussed. Magnetic field variations in space and time are considered. The problem is treated by establishing the wave excitation from knowledge of the macroscopic beam motion. It is shown that the cyclotron wave is coupled to the synchronous wave and that both waves are always amplified in a changing field. Unless the charge density is an appreciable fraction of the full Brillouin value, however, the individual electron orbits will be amplified along with the waves causing beam expansion. The phase velocity of the waves is shown to be approximately independent of space charge. In the case of a spatially varying field, one of the waves must be fast, carrying positive kinetic power, and the other slow, carrying negative kinetic power. The total kinetic power carried by the two waves is conserved. When the magnetic field varies in time, the kinetic power of the two waves is not conserved hut the Manley-Rowe relation is satisfied. When the field varies at a rate greater than the signal frequency, both modes may carry positive kinetic power.