Quantum statistical properties of free-electron laser with ion-channel guiding

The operation of the quantum free-electron lasers (QFELs) with a helical wiggler and in the presence of ion-channel guiding is considered. The quantum Hamiltonian of single particle has been derived in the Bambini-Renieri (BR) frame. Time dependent wave function and three constants of motion are obtained. The Raman-Nath equation (RNE) and its approximation solution have been calculated, and then the resulted solution has been employed to obtain the quantum gain, photon statistics parameter and squeezing parameter. A quantum approach has been used to get quantum statistical properties of the FEL and the photon gain formula for the small signal gain limit. It is found that the ion-channel guiding decreases the squeezing. Also, the conditions for positive (bunching) and negative (antibunching) gain have been studied numerically.