A theory of wiggler pumped ion-channel free-electron laser (WPIC-FEL) and an axial magnetic field is presented. The motion of a relativistic electron is analyzed in the field configuration consisting of a helical wiggler magnetic field, a uniform axial magnetic field, and an electrostatic electric field produced by an ion-channel. An equation for the function Φ, which determines the rate of change of axial velocity with energy, is derived. Numerical calculations are made to illustrate the effects of two electron beam guiding devices on the trajectories. By means of linear fluid theory, the sixth-degree polynomial dispersion equation for electromagnetic and space-charge waves is derived. The dependence of growth rate-frequency curves on the ion-channel frequency and axial magnetic field is studied numerically.
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.
The effects of self-fields on the free electron lasers (FELs) with a helical wiggler and ion-channel guiding are considered. The steady-state orbits for a single electron in this configuration are obtained. The rate of change of axial velocity with energy, the characteristic function , is derived and studied numerically. A kinetic approach has been used to get the effects of self-field on the FEL and betatron gain formula in the low-gain-pre-pass limit. It is shown that betatron gain is smaller than FEL gain. We also found a gain decrement (enhancement), arising from diamagnetism (paramagnetism) generated by the self-magnetic field for group I (group II) orbits. It is interesting that the gain enhancement is found for the non-relativistic part of group II orbits. The FEL gain and betatron gain have also been investigated for different relativistic factors γ .
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