A model of ion noise in microwave tubes

Summary form only given. A hybrid model has been developed in which the electron beam is treated as a 2D fluid using the beam envelope equation, and the ions generated by beam ionization are treated as discrete particles in 1D. The effect of secondary electrons is neglected in the present analysis. 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 introduce oscillations 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. A specific example relating to ion noise in a coupled-cavity TWT is discussed.