Interaction of a relativistic dense electron beam with a laser wiggler in a vacuum: self‐field effects on the electron orbits and free‐electron laser gain

Employing laser wigglers and accelerators provides the potential to dramatically cut the size and cost of X‐ray light sources. Owing to recent technological developments in the production of high‐brilliance electron beams and high‐power laser pulses, it is now conceivable to make steps toward the practical realisation of laser‐pumped X‐ray free‐electron lasers (FELs). In this regard, here the head‐on collision of a relativistic dense electron beam with a linearly polarized laser pulse as a wiggler is studied, in which the laser wiggler can be realised using a conventional quantum laser. In addition, an external guide magnetic field is employed to confine the electron beam against self‐fields, therefore improving the FEL operation. Conditions allowing such an operating regime are presented and its relevant validity checked using a set of general scaling formulae. Rigorous analytical solutions of the dynamic equations are provided. These solutions are verified by performing calculations using the derived solutions and well known Runge–Kutta procedure to simulate the electron trajectories. The effects of self‐fields on the FEL gain in this configuration are estimated. Numerical calculations indicate that in the presence of self‐fields the sensitivity of the gain increases in the vicinity of resonance regions. Besides, diamagnetic and paramagnetic effects of the wiggler‐induced self‐magnetic field cause gain decrement and enhancement for different electron orbits, while these diamagnetic and paramagnetic effects increase with increasing beam density. The results are compared with findings of planar magnetostatic wiggler FELs.