The general velocity and current modulation linear transfer matrix of FEL and control over SASE power in the collective regime

We present the general linear transfer matrix of FEL in the collective regime in terms of a single-mode radiation field amplitude and e-beam current and velocity modulation parameters. The formulation is useful to account for composite configurations of the FEL, including non-radiating sections, and is employed to demonstrate the possibility to control the SASE radiation power (including its substantial reduction for facilitating coherent emission with seed radiation amplification) by varying the space-charge parameter in a drift section.