Design theory of relativistic magnetron resonant structure

This paper proposes a novel reverse-design framework for designing resonant structures in relativistic magnetrons (RMs), addressing the limitations of conventional approaches that derive electrical parameters (voltage and magnetic field) from fixed structural parameters. Traditional methods based on Buneman-Hartree and Hull conditions are constrained to forward calculations, whereas our study enables the extraction of key structural parameters (anode radius ra, cathode radius rc) from predetermined operational requirements, including voltage V, magnetic field Bz, resonant frequency fn, and mode number n. By establishing constraints, basic, and additional conditions through monotonicity analysis of value functions, this theory delineates feasible ranges for ra and rc. Case studies involving five distinct RM configurations validate the framework, demonstrating alignment with particle-in-cell simulations from the literature. This method significantly streamlines RM design, reduces empirical trial-and-error, and enhances adaptability to diverse high-power microwave applications.