Analysis of Smith-Purcell BWO with end reflections

We present a one-dimensional time-dependent analysis and simulation of Smith-Purcell (SP) backward wave oscillator (BWO) taking end reflections and attenuation into account. In the linear regime, we obtain an analytic solution and calculate the start current. The dependence of start current on end reflections is studied taking the attenuation due to finite conductivity into account. In this paper, we have set up Maxwell-Lorentz equations for the one-dimensional time-dependent analysis of SP-BWO including end reflection and attenuation due to finite conductivity. We have obtained a solution in the linear regime and extended the analysis to the nonlinear regime by solving the Maxwell-Lorentz equations numerically. Our analysis can be used for detailed optimization of outcoupled power and start current in SP-BWO taking end reflection and attenuation into account.