### Abstract

Mode competition of a free-electron laser is modeled by the Ginzburg-Landau equation. The stability of a single-mode solution is analyzed, and connections are established with known instabilities of the Ginzburg-Landau equation. It is found that the principal mode with the largest gain is always stable and hence there is no Benjamin-Feir instability. However, the Eckhaus (or phase) instability generally occurs if the frequency of a mode lies outside of a designated range centered on the principal mode. Under certain conditions, the Eckhaus instability can cause a sudden chaotization and spikiness in the radiation field. Analytical criteria and scaling for single-mode operation are given and tested by numerical simulations. A theoretical controversy on single-mode operation of the free-electron laser at the University of California at Santa Barbara is resolved.

Original language | English (US) |
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Pages (from-to) | 3826-3832 |

Number of pages | 7 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 58 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1998 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics