Nonlinear gain computation for the sheet beam crossed-field amplifier

When the RF amplitude in a crossed field device is much smaller than the external DC voltage, the energy exchange between an electron and the wave is given by the change in the potential energy of the electron guiding center. The shift of the beam center of charge follows the space bunching into “spokes” caused by the RF-induced drift. A nonlinear estimate for the gain is derived and applied to the linear format crossed-field amplifier fed by a continuous sheet beam. The adiabatic approximation for the guiding center trajectories in the low gain regime determines the fraction of trapped/streaming particles and the energy exchange for each group. The radiation gain equals the change in the electron potential energy resulting from the shift in the beam center of charge across the anode-cathode voltage. The drift kinetic energy is approximately conserved, opposed to other microwave devices converting kinetic energy into radiation. The theory accounts for the symmetry of the response curve relative to the frequency detuning ω-ω₀, and the flat top near resonance. The analytic predictions agree with the experimental measurements of the gain versus frequency response