Analytical model for the transition to superradiance in seeded free-electron lasers

Free-electron lasers (FEL) seeded by short radiation pulses can exhibit superradiant behavior. In the superradiant regime, the pulse simultaneously compresses and amplifies as it propagates through the FEL, making superradiance very promising for pushing the performance limits of attosecond x-ray FELs. To date, this regime has been studied in asymptotic limits, but there is no model for how the initially linear dynamics of the seeded FEL transition into the nonlinear superradiant behavior. We derive an analytical model for the 1D FEL seeded by a short pulse which accurately captures the linear dynamics, the nonlinear superradiant evolution, and the smooth transition between them. Our model fills a critical gap in our understanding of FEL superradiance and nonlinear time-dependent FEL physics more broadly, and may provide a bridge to the corresponding problem in three-dimensions, and analogous problems in other fields exhibiting soliton behavior.