A 3-D Frequency-Domain Nonlinear Theory of the BWO With an Inclined Rectangular Electron Beam

A 3-D frequency-domain nonlinear theory of the backward wave oscillator (BWO) with an inclined rectangular electron beam (IRB) is presented in this article. The ohmic losses, space-charge effects, and full 3-D motion of electrons are considered in the nonlinear theory. A set of self-consistent differential equations that describe the nonlinear beam-wave interaction in the BWO with an IRB (IRB BWO) is given, and a calculation code called IRB BWO-3-D is written. Particle-in-cell (PIC) simulations verify the nonlinear theory of the IRB BWO. The effects of the width of the electron beam, the thickness of the electron beam, and the inclination angle on the output power and efficiency of the IRB BWO are also discussed.