Forward Space Charge Wave Amplifiers Using Lossy Backward Circuit Waves

Previous studies of the metamaterial-enhanced resistive wall amplifier (MERWA) predicted gain and bandwidth properties attractive for high-power microwave (HPM) applications. The MERWA theory used a transverse admittance matching (AM) technique at the boundary between the beam and a lossy negative-permittivity metamaterial (MTM) slab to predict that forward slow space charge wave growth should occur if the wall presents a resistive-inductive admittance to the beam. We show that the growth and bandwidth of the MERWA can be equivalently predicted via wave-coupling theory. The main interaction occurs between two coupled waves (CWs) that correspond to the beam slow space charge wave and a lossy backward propagating circuit wave in the limit of weak coupling. We present a two-wave-coupling model to build intuition and discuss two modes of operation, oscillation and amplification, in terms of a damped feedback system. We compare the two-wave-coupling solutions against four-wave model solutions. We further demonstrate and discuss equivalency between the AM model and the wave-coupling model for an infinite parallel plate geometry. Finally, we validate the AM method predictions using particle-in-cell (PIC) simulations.