There is always some ambient gas in electron beam devices and background ionization is ubiquitous. For long pulse times, the electrostatic potentials associated with this ionization can reach significant levels and give rise to such observed phenomena as phase noise in microwave tubes. Observations of noise in microwave tubes such as coupled-cavity traveling wave tubes and klystrons have been discussed in the literature and will be briefly reviewed. In order to explain this phenomenon, a 1D hybrid model of the ion effects in microwave tubes has been developed in which the electron beam is treated as a fluid using the beam envelope equation, and the ions generated by beam ionization are treated as discrete particles. The effect of secondary electrons is neglected. The ionization rate depends on the ambient gas pressure and species as well as on the electron beam current and energy. Based on this rate, ions are created and distributed on an axial grid on each time step. The ion charge is then mapped onto the grid, and Poisson's equation is then solved in 1D under the assumption that the transverse scale lengths are less than the betatron wavelength of the electron beam. The ion charge distribution is then used to integrate the beam envelope equation that updates the beam equilibrium. The ion motion is then integrated subject to the wall potential, the space-charge potential of the electron beam, and the self-consistent ion potential. This process is iterated over any desired pulse time. The coupling between the ionization and the electron beam equilibrium is responsible for the phase noise. In effect, the ion motion between and within the different wells as well as ion draining to the cathode and collector results in a dynamic retuning of the electron beam equilibrium. Oscillations are observed on many time scales. The fastest time scale oscillation is related to the bounce motion of ions in the axial potential wells formed by the scalloping of the electron beam. Slower oscillations are observed to correlate with the well-to-well interactions induced by the ion coupling to the electron equilibrium. These oscillations have observable effects on ion dumping to the cathode or collector.

*Work supported by the Office of Naval Research.