Beam quality requirements for the Ion-Channel Laser

In this paper, we determine the electron beam quality requirements to obtain exponential radiation amplification in the ion-channel laser, where a relativistic electron beam wiggles in a focusing ion-channel that can be created in a wakefield accelerator. The beam energy and wiggler parameter spreads should be limited. Those spread limits are functions of the Pierce parameter, which is calculated here without neglecting the radiation diffraction. Two dimensional and three dimensional simulations of the self-consistent ion-channel laser confirm our theoretical predictions.