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Space Charge Wave Growth Via Coupling To Lossy Backward Circuit Wave: Two Wave Theory*

With the focus on increasing instantaneous bandwidth capabilities of high-power microwave (HPM) devices, the Metamaterial Enhanced Resistive Wall Amplifier (MERWA) is being investigated for potential use as an HPM amplifier 1 , 2 , 3 . Rather than growth of a circuit wave, the MERWA operates via growth of the beam’s slow space charge wave. MERWA theory uses a 2D impedance matching technique at the boundary of the beam to show that growing wave solutions exist if a nearby metamaterial wall presents a resistive-inductive admittance to the beam 1 . Although the theory never expects or requires that an axially propagating cold circuit wave would exist, a low power experimental prototype was found to support a lossy backward wave in the vicinity of growth 2 , 3 . Using a two-wave coupling theory, we show that the space charge wave growth (of this specific prototype) can alternatively be explained in terms of coupling between the beam’s slow space charge wave and the lossy backward circuit wave. In contrast to the coupling with a lossless backward wave, which is known to produce a pair of non-growing waves, the interaction with the lossy backward wave produces a region of stable exponential space charge wave growth below an oscillation threshold. This two-wave coupling perspective provides insight into performance capabilities, limitations, and tradeoffs. Among these insights, we discuss how the amount of cold circuit loss affects the maximum stable growth rate, oscillation threshold, and gain-bandwidth product. We will compare analytical predictions against simulation results for validation.