Free-electron laser growing modes and their bandwidths

The behavior of free-electron laser amplification in the small signal linear regime can be understood by studying the dispersion relation derived from the electron energy distribution. A thorough understanding of the growth modes in this regime is of great value in understanding numerical results obtained using simulations. In this paper we show that for a typical bell-shape energy distribution in the electron beam there is not more than one growing mode. We also derive an analytical expression, which determines the bandwidth of the free-electron laser. We also discuss the limitation on the number of growing modes for the case of beam energy distributions with multiple peaks. Published by the American Physical Society under the terms of the http://creativecommons. org/licenses/by/3.0/ Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.