Ginzburg-Landau model for a free-electron laser: From single mode to spikes

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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 languageEnglish (US)
Pages (from-to)34-39
Number of pages6
JournalNuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
Issue number1-3
StatePublished - Apr 21 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Instrumentation


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