Theoretical analysis of saturation and limit cycles in short pulse FEL oscillators
- Commissariat a l`Energie Atomique, Bruyeres-le-Chatel (France); and others
We derive a model for the non linear evolution of a short pulse oscillator from low signal up to saturation in the small gain regime. This system is controlled by only two independent parameters: cavity detuning and losses. Using a closure relation, this model reduces to a closed set of 5 non linear partial differential equations for the EM field and moments of the electron distribution. An analysis of the linearised system allows to define and calculate the eigenmodes characterising the small signal regime. An arbitrary solution of the complete nonlinear system can then be expanded in terms of these eigenmodes. This allows interpreting various observed nonlinear behaviours, including steady state saturation, limit cycles, and transition to chaos. The single mode approximation reduces to a Landau-Ginzburg equation. It allows to obtain gain, nonlinear frequency shift, and efficiency as functions of cavity detuning and cavity losses. A generalisation to two modes allows to obtain a simple description of the limit cycle behaviour, as a competition between these two modes. An analysis of the transitions to more complex dynamics is also given. Finally, the analytical results are compared to the experimental data from the FELIX experiment.
- Research Organization:
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- OSTI ID:
- 238619
- Report Number(s):
- BNL-61982-Absts.; CONF-9508156-Absts.; ON: DE96002729; TRN: 96:013108
- Resource Relation:
- Conference: 17. international free electron laser conference, New York, NY (United States), 21-25 Aug 1995; Other Information: PBD: [1995]; Related Information: Is Part Of 17th international free electron laser conference and 2nd international FEL users` workshop. Program and abstracts; PB: 300 p.
- Country of Publication:
- United States
- Language:
- English
Similar Records
Application of the green function formalism to nonlinear evolution of the low gain FEL oscillator
The high-gain free-electron lasers