Analytical treatment of the linear stability of a thin, dilute rotating electron layer propagating in a rippled waveguide is presented. The vacuum properties of the rippled conducting walled waveguide are approximated by the disc loaded waveguide dispersion relation. An expression of the growth rate for TM mode of the waveguide is obtained. Results are plotted for TM,, and TM,, modes as a function of beam azimuthal mode number 1 of the beam space charge mode. As the mode number I increases, the growth rate for TM,, and TM,, modes takes a minimum value for a certain 1 and then it shows an increase. This can be understood by noting that the beam waveguide resonant backward wave oscillator interaction is highly azimuthal mode dependent.
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