Electron trajectory and growth rate in a two-stream electromagnetically pumped free electron laser and axial guide field

The effects of two-stream on electromagnetic wiggler free electron lasers (TSEMWFEL) with an axial guiding magnetic field are studied. An analysis of the two-stream steady-state electron trajectories is given by solving the equation of motion in the axial guiding magnetic field and the electromagnetic wiggler. Numerical calculations are made to illustrate the effects of the dual electron beam on the trajectories. The dispersion relation is derived employing linear fluid theory. The characteristics of the dispersion relation are analyzed numerically. The result shows that the growth rate is considerably enhanced in comparison with single-stream. The maximum growth rate is studied numerically as a function of axial guiding magnetic field for multiple electron trajectories. It is shown that the maximum growth rate of TSEMWFEL increases and decreases with respect to the axial guiding field for different trajectories.