Abstract

Linearized Vlasov-Maxwell equations are used to derive a partial differential equation determining the 3-dimensional slowly varying envelope function of the radiated electric field. The equation is solved analytically. From the correlation function $〈\text{E}\left(\text{ξ},\overrightarrow{\text{r}},\text{t}\right)\text{E}*\left(\text{ξ}\prime ,\overrightarrow{\text{r}\prime },\text{t}\right)〉$ of the electric field averaged over the stochastic ensemble describing the initial shot noise in the beam, we compute the longitudinal and transverse correlation lengths σ_||, and σ_⊥.

© 1986 Optical Society of America