We have used Monte Carlo calculations to verify the classical electrodynamics result describing the multiparticle coherent enhancement at long wavelengths for synchrotron-radiation emission. In addition we show the derivation of the result that, for a bunch of electrons in a storage ring, the synchrotron-radiation emission has a multiparticle coherent enhancement that is given by the square of the Fourier transform of the longitudinal spatial distribution function of the electrons. The result has been verified for Gaussian and sinusoidal distributions. For a Gaussian distribution of particles in a bunch, this is seen to have an effect only at wavelengths close to the bunch length. For a sinusoidal distribution as in the transverse optical klystron, the enhancement can easily be seen to occur at one specific wavelength.

• Received 29 March 1991

DOI:https://doi.org/10.1103/PhysRevA.44.1316