Simplified model for fast optimization of a free-electron laser oscillator

A simplified one-dimensional theoretical model for free-electron laser oscillator (FELO) calculation which reserves the main physics is proposed. Instead of using traditional macroparticles sampling method, the theoretical model takes advantage of low gain theory to calculate the optical power single-pass gain in the undulator analytically, and some reasonable approximations are made to simplify the calculation of power growth in the cavity. The theoretical analysis of single-pass gain, power growth, time-dependent laser profile evolution and cavity desynchronism are accomplished more efficiently. We present the results of infrared wavelength FELO and X-ray FELO with the new model. The results are validated by simulation with GENESIS and OPC.

Figure 1

The complex reflectivity of Bragg crystal at various incident photon energy deviation from Bragg energy.

Figure 2

The electron density distribution function in phase space of one slice.

Figure 3

The gain as a function of electric field intensity. (The dash line is the expected constant gain function curve in the low-gain theory at small electric field intensity.)

Figure 4

The enhancement of output laser peak power with various passes $N_{\text{pass}}$.

Figure 5

Snapshots of output radiation pulse for a typical infrared FELO at $1.6\mu \mathrm{m}$. The top and the bottom row show the longitudinal pulse temporal profile and corresponding spectrum respectively [33].

Figure 6

The output laser energy as a function of desynchronism.

Figure 7

The laser profile at $0.6\lambda$ cavity desynchronism.

Figure 8

The electron density distribution in the phase space of one slice.

Figure 9

The enhancement of output laser peak power with various passes $N_{\text{pass}}$.

Figure 10

Snapshots of output radiation pulse for a typical X-ray FELO at $1.0\AA$. The top and the bottom row show the longitudinal pulse temporal profile and corresponding spectrum respectively [33].

Figure 11

The output laser energy as a function of electron beam shift distance in each pass.