  The efficiency of a free-electron laser can be enhanced by sustaining the
growth of the radiation power beyond the initial saturation. One notable method
is undulator tapering, which involves the variation of the gap height and/or
the period along the undulator. Another method is the introduction of phase
jumps, using phase-shifting chicanes in the drift sections separating the
undulator segments. In this article, we develop a physics model of this phase
jump method, and verify it with numerical simulations. The model elucidates the
energy extraction process in the longitudinal phase space. The main ingredient
is the microbunch deceleration cycle, which enables the microbunched electron
beam to decelerate and radiate coherently beyond the initial saturation. The
ponderomotive bucket is stationary, and energy can even be extracted from
electrons outside the bucket. The model addresses the selection criteria for
the phase jump values, and the requirement on the undulator segment length. It
also describes the mechanism of the final saturation. In addition, we discuss
the similarities and differences between the phase jump method and undulator
tapering, by comparing our phase jump model to the classic
Kroll-Morton-Rosenbluth model.
