Phase jump method for efficiency enhancement in free-electron lasers

The efficiency of a free-electron laser can be enhanced by the phase jump method. The method utilizes the phase-shifting chicanes in the drift sections between the undulator segments. By applying appropriate phase jumps, the microbunched electron beam can decelerate and radiate coherently beyond the initial saturation, enabling further energy transfer to the optical beam. This article presents a new physics model for the phase jump method, and supports it with numerical simulations. Based on the electron dynamics in the longitudinal phase space, the model describes the energy extraction mechanism, and addresses the selection criteria for the phase jump magnitude. While the ponderomotive bucket is stationary, energy can be extracted from electrons outside the bucket. With the aid of the new model, a comparison is made between the phase jump method and undulator tapering. The model also explores the potential of the phase jump method to suppress the growth of synchrotron sidebands in the optical spectrum.

Figure 1

Schematic diagram showing two of the undulator segments and the drift section in between. The phase shifter in the drift section can increase the electron path length, thus adjusting the phase angle between the electron beam and the optical wave. Focusing magnets, corrector magnets and diagnostics instruments are also commonly installed in drift sections, but are not shown in this diagram.

Figure 2

The longitudinal phase space $(\psi ,\eta )$, with electron trajectories shown by the blue curves. The red curve is the separatrix, and the region enclosed by it is the ponderomotive bucket. The straight lines $\eta =0$ and $\psi =0$ divide the space into four quadrants, as indicated by the Roman numerals.

Figure 3

The microbunch deceleration cycle as illustrated by the movement of the average particle within the ponderomotive bucket. Position 1 corresponds to the starting point of a drift section, position 2 the end point of the same drift section, and position 3 the end point of the subsequent undulator segment.

Figure 4

The microbunch deceleration cycle as illustrated by the movement of the average particle outside the bucket. Position 1 corresponds to the starting point of a drift section, position 2 the end point of the same drift section, and position 3 the end point of the subsequent undulator segment.

Figure 5

Result of steady-state simulation. The following quantities are plotted as functions of the distance $z$ along the undulator line: (a) the radiation power, (b) the relative energy deviation $\overline{\eta }$ of the average particle, and (c) the ponderomotive phase $\overline{\psi }$ of the average particle (in blue), together with the lower bound ${\psi }_{\min }$ (in red) and the upper bound ${\psi }_{\max }$ (in yellow) for the target phase ${\psi }_{\mathrm{targ}}$ in each drift section. The dashed vertical lines mark the beginning of the in-bucket, out-of-bucket, and final saturation regimes.

Figure 6

Result of steady-state simulation. Snapshots in the longitudinal phase space $(\psi ,\eta )$ showing a microbunch deceleration cycle in the in-bucket regime. The red dot represents the average particle within the microbunch.

Figure 7

Result of steady-state simulation. Snapshots in the longitudinal phase space $(\psi ,\eta )$ showing a microbunch deceleration cycle during the transition from the in-bucket regime to the out-of-bucket regime.

Figure 8

Result of steady-state simulation. Snapshots in the longitudinal phase space $(\psi ,\eta )$ showing a microbunch deceleration cycle at the onset of the final saturation regime.

Figure 9

Result of steady-state simulation. The trace of the average particle in the longitudinal phase space $(\psi ,\eta )$ over the entire undulator line.

Figure 10

Result of time-dependent simulation. The optical pulse energy is plotted as a function of the distance $z$ along the undulator line for the optimal phase jumps (blue) and the optimal taper (red). The dashed vertical line indicates the common starting point for the phase jump method and the taper. The vertical axis is on a logarithmic scale.

Figure 11

Result of time-dependent simulation. The evolution of the optical spectrum for the optimal taper is illustrated with the snapshots at six positions along the undulator line.

Figure 12

Result of time-dependent simulation. The evolution of the optical spectrum for the optimal phase jumps is illustrated with the snapshots at six positions along the undulator line.