Free-electron lasers with variable parameter wigglers, a strictly nonlinear oscillator with slowly varying parameters
The first part of this dissertation gives a detailed mathematical modeling of free-electron lasers (FEL), and the second part is a study of a number of general perturbation methods for solving FEL and other systems. The author derives a dimensionless model of the motion of electrons in FEL and systematically accounts for secular effects due to slow variations in the magnetic-field amplitude of the wiggler, and the effect of the density of electrons on the rate of evolution of the signal field. The mathematical problem reduces to the analysis of a strictly nonlinear oscillator with slowly varying parameters and small perturbation terms. Two distinguished limits governing the rate of variation of the wiggler and three distinguished limits governing the evolution of the signal field are identified. To analyze solutions of FEL and other strictly nonlinear systems the author reviews and extends the method of Kuzmak-Luke and the method of averaging, then shows that both methods are equivalent. In order to implement the calculation of explicit solutions, he develops two approximation schemes.
- Research Organization:
- Washington Univ., Seattle (USA)
- OSTI ID:
- 6876831
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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