Evidence of coherent synchrotron radiation has been reported recently at the electron storage rings of several light source facilities. The main features of the observations are (i) a radiation wavelength short compared to the nominal bunch length, and (ii) a coherent signal showing recurrent bursts of duration much shorter than the radiation damping time, but with spacing equal to a substantial fraction of the damping time. We present a model of beam longitudinal dynamics that reproduces these features.

We study longitudinal coherent motion of a stored electron beam by a time domain integration of the nonlinear Vlasov-Fokker-Planck equation. For the present SLAC damping rings we found several features in agreement with experiment. This report emphasizes the earlier vacuum chamber of the rings, replaced in 1992-93. Nonlinear e ects are much stronger for the old chamber, and the computed phenomena more various.

We study the microbunching instability in a bunch compressor by a parallel code with some improved numerical algorithms. The two-dimensional charge/current distribution is represented by a Fourier series, with coefficients determined through Monte Carlo sampling over an ensemble of tracked points. This gives a globally smooth distribution with low noise. The field equations are solved accurately in the lab frame using retarded potentials and a novel choice of integration variables that eliminates singularities. We apply the scheme with parameters for the first bunch compressor system of FERMI@Elettra, with emphasis on the amplification of a perturbation at a particular wavelength and the associated longitudinal bunch spectrum. Gain curves are in rough agreement with those of the linearized Vlasov system at intermediate wavelengths, but show some deviation at the smallest wavelengths treated and show the breakdown of a coasting beam assumption at long wavelengths. The linearized Vlasov system is discussed in some detail. A new 2D integral equation is derived which reduces to a well-known 1D integral equation in the coasting beam case.