Stochastic particle instability for electron motion in combined helical wiggler, radiation, and longitudinal wave fields

Abstract

The relativistic motion of an electron is calculated in the combined fields of a transverse helical wiggler field (axial wavelength is ${\ensuremath{\lambda}}_{0}=\frac{2\ensuremath{\pi}}{{k}_{0}}$) and the constant-amplitude, circularly polarized primary electromagnetic wave ($\stackrel{^}{\ensuremath{\delta}}{B}_{T},\ensuremath{\omega},k$) propagating in the $z$ direction. For particle velocity near the beat-wave phase velocity $\frac{\ensuremath{\omega}}{(k+{k}_{0})}$ of the primary wave, it is shown that the presence of a second, moderate-amplitude longitudinal wave ($\stackrel{^}{\ensuremath{\delta}}{E}_{L},\ensuremath{\omega},k$) or transverse electromagnetic wave ($\stackrel{^}{\ensuremath{\delta}}{B}_{2},{\ensuremath{\omega}}_{2},{k}_{2}$) can lead to stochastic particle instability in which particles trapped near the separatrix of the primary wave undergo a systematic departure from the potential well. The condition for onset of instability is calculated, and the importance of these results for free-electron-laser (FEL) application is discussed. For development of long-pulse or steady-state free-electron lasers, the maintenance of beam integrity for an extended period of time will be of considerable practical importance. The fact that the presence of secondary, moderate-amplitude longitudinal or transverse electromagnetic waves can destroy coherent motion for certain classes of beam particles moving with velocity near $\frac{\ensuremath{\omega}}{(k+{k}_{0})}$ may lead to a degradation of beam quality and concomitant modification of FEL emission properties.