Transverse correlations in start-up of a free electron laser from noise
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 solve analytically. From the correlation function 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 sigma/sub parallel/ and sigma/sub perpendicular/. The radiated power S per unti cross-sectional area of the electron beam is S = rhoS/sub e//9n/sub 0/V/sub c/ exp(..sqrt..3 4..pi..N/sub w/rho), where V/sub c/ = (2..pi..)/sup 3/2/ sigma/sub parallel/ sigma/sub perpendicular//sup 2/ is the coherence volume, n/sub 0/ the electron density, S/sub e/ = (..gamma../sub 0/mc/sup 2/) n/sub 0/c the power per unit area in the electron beam, N/sub w/ the number of wiggler periods and rho the Pierce parameter. The angular distribution of the radiation is characterized by the Gaussian factor exp(-theta/sup 2//2sigma/sub theta/ /sup 2/), where 2..pi..sigma/sub theta/sigma/sub perpendicular/ = lambda (radiated wavelength). Our analysis is applicable for wiggler length L = N/sub w/lambda/sub w/ long enough for the exponential regime to be reached, but short enough so that L sigma/sub theta/approx.
- Research Organization:
- National Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York 11973
- OSTI ID:
- 5226437
- Report Number(s):
- CONF-860316-
- Journal Information:
- AIP Conf. Proc.; (United States), Journal Name: AIP Conf. Proc.; (United States) Vol. 147:1; ISSN APCPC
- Country of Publication:
- United States
- Language:
- English
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