[en] 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 < E(z,r,t) E*(z',r',t)> of the electric field averaged over the stochastic ansemble describing the initial shot noise in the beam, we compute the longitudinal and transverse correlation lengths sigma/sub L/ and sigma/sub T/. The radiated power S per unit cross-sectional area of the the electron beam is determined. Our analysis is applicable for wiggler length L = N/sub w/lambda/sub w/ long enough for the exponential regime to be researched, but short enough so that L sigma/sub theta/ less than or equal to a, the electron beam radius. 6 refs