Free electron lasers (FELs) are considered, typically, as fast wave devices. The normal FEL interaction satisfies the tuning condition oDðkz þ kWÞVz , where o and kz are the em-wave angular frequency and longitudinal wave number, respectively, Vz is the electron axial speed, and kW is the wiggler periodicity. This paper presents an anomalous FEL interaction, which may occur in slow-wave FELs (i...

We present a numerically exact study of polaron with quadratic coupling to the oscillator displacement, or ${X}^{2}$ polaron, using two alternative methodological developments. Our results cover both antiadiabatic and adiabatic regimes entire range electron-phonon ${g}_{2}$, from system's stability threshold at attractive ${g}_{2}=\ensuremath{-}1$ arbitrary strong repulsion ${g}_{2}\ensuremath{...