Noise-figure calculations for crossed-field forward-wave amplifiers

The problem of finding an adequate model for derivation of noise-figure expressions for crossed-field forward-wave amplifiers is investigated. The modified Llewellyn-Peterson equations are used for the portion of the beam near the cathode. Four waves, two cyclotron waves and two space-charge waves, are used for the space connecting the gun and interaction region. Noise-figures are found by considering five waves in the interaction region. The results are very close to those found when only the space-charge waves are considered in the development of the equations for both drift and interaction regions. A matrix, like the space-charge-wave matrix for O-type beams, giving the transformation of beam fluctuations along a drifting, crossed-field stream including the effects of four waves is presented. Expressions for fluctuations of transverse velocity and beam center of gravity are derived to account for all the excitation quantities which are believed to be important in crossed-field amplifiers. The transformation of fluctuations of beam position, or center of gravity, along an accelerating stream is derived. Calculated values of noise figures are far in excess of experimental values. The reasons for the discrepancies are discussed.