Stocuastic 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 = X0 27/k 0) and constant-amplitude, circularly polarized primary electromagnetic wave (6B , ,k) propagating in the z-direction. For particle velocity near the beat wave phase velocity w/(k + k0) of the primary wave, it is shown that the presence of a second, moderate-amplitude longitudinal wave (EL,w,k) or transverse electromagnetic wave (6B2 'W2,k2) 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 FEL application is discussed. For development of long-pulse or steadystate 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 -/(k + k 0) may lead to a degradation of beam quality and concommitant modification of FEL emission properties.