Numerical Simulation of Smith-purcell Free Electron Lasers

We present a one-dimensional time-dependent analysis and simulation of Smith-Purcell (SP) free-electron lasers (FELs). The coupled Maxwell-Lorentz equations are set up, and the details of numerical simulation are presented. At low electron beam energy, a SP-FEL is a backward wave oscillator (BWO), and oscillations can be achieved without the need for feedback mirrors. In the linear regime, we show that the optical power grows exponentially if the current is larger than a certain value, the start current. Results of our numerical calculation compare well with the analytic calculation in the linear regime and show saturation behavior in the nonlinear regime.