NOISE PROPAGATION IN AN ACCELERATED NONUNIFORM ELECTRON GAS.
Technical rept. no. 70,
MICHIGAN UNIV ANN ARBOR ELECTRON PHYSICS LAB
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Approximate phase-integral solutions of the differential equation for adiabatic propagation of plane compressional waves in an accelerated electron stream are studied. The adiabatic assumption excludes Landau damping, but since the conditions under which Landau damping is to be expected are well understood, this fact is not a serious disadvantage. The approximate solutions are analyzed for stop bands, phase velocities, and conditions favorable to Landau damping Previously known results are obtained as asymptotic limits. A singularity analogous to a shock wave is found at the plane where the stream velocity equals the sound velocity in the electron gas. No suggestion of a noise-reducing mechanism beyond this plane is found. This would indicate that a minimum noise temperature of about 16 of the cathode temperature would be obtainable, if a total reflection of noise occurred at the shock plane. A three-dimensional pattern of tilted shock waves could possibly reduce the noise temperature below this value. Author