In the our original paper the sign of the coefficient R 56 used in numeric calculations was wrong. It has to be changed to be consistent with the sign convention assumed in the design of a bunch compressor. The sign of R 56 depicted in Fig. 1 has to be changed from negative to positive. The sign of the chirp u related to the sign of the R 56 has to be changed as well: the chirp u in the first paragraph of Sec. VI should be positive, u 39:83 m ÿ1 . These changes do not affect the formulas of the paper but slightly modify the numeric results. The results of corrected calculations are shown in Figs. 1 and 2 given below, which should replace Figs. 3 and 4 in the paper, respectively.

The coherent synchrotron radiation of a bunch in a bunch compressor may lead to the microwave instability producing longitudinal modulation of the bunch with wavelengths small compared to the bunch length. It can also be a source of an undesirable emittance growth in the compressor. We derive and analyze the equation that describes linear evolution of the microwave modulation taking into account incoherent energy spread and finite emittance of the beam. Numerical solution of this equation for the Linac Coherent Light Source bunch compressor gives the amplification factor for different wavelengths of the beam microbunching.

A relativistic electron beam moving in a circular orbit in free space can radiate coherently if the wavelength of the synchrotron radiation exceeds the length of the bunch. In accelerators coherent synchrotron radiation of the bunch is usually suppressed by the shielding effect of the conducting walls of the vacuum chamber. However an initial density fluctuation with a characteristic length much shorter than the bunch length can radiate coherently. If the radiation reaction force results in the growth of the initial fluctuation, one can expect an instability which leads to microbunching of the beam and an increased coherent radiation at short wavelengths. Such an instability is studied theoretically in this paper.