Two-stream instability in free electron lasers with a planar wiggler and an axial guide magnetic field

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.