### Abstract

Single-mode operation of a free-electron laser is modeled by the Ginzburg-Landau equation. The linear stability of a single-mode solution is analyzed, and connections are established with known instabilities of the Ginzburg-Landau equation. It is found that there is no Benjamin-Feir instability and hence, the principal mode with the largest gain is always stable. However, the Eckhaus (or the phase) instability generally exists for a mode with frequency outside a range centered on the principal mode. This gives rise to two distinct possibilities: either there is spontaneous frequency shifting to the stable mode with the largest growth rate and a consequent tendency to approach single-mode operation, or there is a sudden chaotization and spikiness in the radiation field. Analytical criteria and scaling are given and tested by numerical simulations.

Original language | English (US) |
---|---|

Pages (from-to) | 34-39 |

Number of pages | 6 |

Journal | Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment |

Volume | 407 |

Issue number | 1-3 |

DOIs | |

State | Published - Apr 21 1998 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Instrumentation

## Fingerprint Dive into the research topics of 'Ginzburg-Landau model for a free-electron laser: From single mode to spikes'. Together they form a unique fingerprint.

## Cite this

*Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment*,

*407*(1-3), 34-39. https://doi.org/10.1016/S0168-9002(97)01363-6