Macroparticle Theory of a Standing Wave Free-Electron Laser Two-Beam Accelerator

Free-electron laser operation is formulated using a macroparticle approach based on a universal gain equation. Microwave excitation in a single cavity is derived analytically and is given in the form of analytic recursion equations for a multicavity system driven by a sequence of electron bunches. Qualitative and quantitative insights into the basic excitation and saturation mechanisms are provided. Stability analysis on a test particle moving around a macroparticle shows the importance of precise control of bunch spacing