Linear gain of a free-electron laser with an electromagnetic wiggler and an axial-guide magnetic field

The small-signal gain for an electromagnetically pumped free-electron laser is calculated for an amplifier configuration which includes an axial-guide magnetic field. The large-amplitude electromagnetic wave acts like the magnetostatic wiggler in a conventional free-electron laser, and the expression for the gain is shown to reduce to the well-known result in the limit of a magnetostatic wiggler. Substantial enhancements in the gain are found when ${\Omega }_0$≃${\gamma }_0$(${\omega }_w$+$k_w$ $v_{?}$), where ${\Omega }_0$ is the axial gyrofrequency, ${\gamma }_0$ is the relativistic factor for the electron beam, $v_{?}$ is the axial velocity of the electron beam, and (${\omega }_w$,$k_w$) are the frequency and wave vector of the electromagnetic wiggler.