The Gain Equation of a Helical Wiggler Free Electron Laser with Ion-Channel Guiding and/or an Axial Magnetic Field

Electron motion in the combined ion-channel, helical wiggler and axial magnetic fields is analyzed in the absence of a radiation field. Detailed analysis of the gain equation in a free-electron laser is presented. Numerical calculations are made to illustrate the effects of the two electron-beam guiding devices on the gain when applied separately and simultaneously.