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)|
|Number of pages||6|
|Journal||Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment|
|State||Published - Apr 21 1998|
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics