Space-charge effects and gain in Cherenkov free-electron lasers

This paper presents a quantum mechanical treatment to study the growth rate characteristics of Cherenkov free-electron laser. For this purpose, we basically use the single-particle model in which the dynamics of a single electron in the presence of the laser field is analyzed. The inclusions of the space-charge (collective) effects are considered by taking into account the static electric field of neighboring electrons in the dynamics formulations. An analytical expression for the gain per pass in the Cherenkov laser is derived. It is shown that the space-charge effects depend mainly on the operating wavelength, the electron density, and the electron beam neutralization due to the possible presence of positive ions. We discuss the validity boundaries of the interaction mode evolved from the single-particle regime to the collective regime. Using quantum mechanical concepts, we finally present a formula for calculating the inclusion of the spontaneous emission power.