The linearized theory of two-stream free electron lasers (FELs) consisting of a relativistic electron beam transported along the axis of a planar wiggler in the presence of an axial guiding magnetic field is proposed and investigated. The dispersion relation is derived employing linear fluid theory. The characteristics of the dispersion relation are analyzed by numerical solutions. The results show that the growth rate is considerably enhanced on suitable ranges of normalized axial guiding magnetic field and normalized wave number. The effect of the difference between the velocities of the two beams, Δv=v1−v2, in this configuration of FELs is also considered and found that the growth rate is remarkably affected by velocity differences. It is also shown that the effect on the electrostatic mode is stronger than electromagnetic.
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.
A theory of a two-stream free-electron laser in a combined electromagnetic wiggler (EMW) is developed, in which we use an axial-guide magnetic field and take into account the effects of the self-fields. The electron trajectories and the small signal gain are derived. The stability of the trajectories, the characteristics of the linear-gain, and the normalised maximum gain are studied numerically. The results show that there are nine stable groups of orbits in the presence of self-fields instead of seven groups reported in the absence of the self-field. It is also shown that the normalised gains of four groups of the orbits are decreasing and those for the rest of them are increasing with growing Ω0 . Furthermore, it is found that the two-stream laser with self-field enhances the maximum gain in comparison with the single stream case.
The effects of self-fields on electron trajectories and gain in planar wiggler free-electron lasers with two-stream and ion-channel guiding are investigated. An analysis of the two-stream quasi-steady-state electron trajectories is given by solving the equation of motion in the presence of ion-channel guiding and the planar wiggler. The electron trajectories and the gain are derived. The stability of the trajectories, the characteristics of the linear gain, and the normalized maximum gain are studied numerically. The numerical calculations show that there are eight group trajectories rather than the two groups reported in the absence of the self-fields. It is also shown that the normalized gain group seven (G7) decreases while the rest increases with the increase in normalized ion-channel frequency. The two-stream instability and the self-field lead to a decrease in the maximum gain, except for G7.
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