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

The relativistic motion of an electron is calculated in the combined fields of a transverse helical wiggler field (axial wavelength is ${\lambda }_0=\frac{2\pi }{k_0}$) and the constant-amplitude, circularly polarized primary electromagnetic wave ($\hat{\delta }{B}_T,\omega ,k$) propagating in the $z$ direction. For particle velocity near the beat-wave phase velocity $\frac{\omega }{(k+k_0)}$ of the primary wave, it is shown that the presence of a second, moderate-amplitude longitudinal wave ($\hat{\delta }{E}_L,\omega ,k$) or transverse electromagnetic wave ($\hat{\delta }{B}_2,{\omega }_2,k_2$) 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 $\frac{\omega }{(k+k_0)}$ may lead to a degradation of beam quality and concomitant modification of FEL emission properties.