The effects of wiggler taper rate and signal field gain rate in free-electron lasers
Derived is a dimensionless formulation of the motion of electrons in free electron lasers with tapered wigglers and systematically account for the cumulative effects of tapering and signal field gain. The mathematical problem involves three small parameters: epsilon, measuring the slowness of spatial variations of the wiggler field, , the ratio of signal wave length to wiggler period, and kappa, the square of the ratio of the plasma frequency to signal frequency. We identify two distinguished limits governing the relation between and epsilon, and three distinguished limits governing the relation between kappa and epsilon. The mathematical problems which result consist of the solution of strictly nonlinear oscillators with slowly varying parameters and small perturbation terms. Techniques from the asymptotic theory of nonlinear oscillations are used to derive results pertinent for FEL problems.
- Research Organization:
- Washington Univ., Seattle (USA). Dept. of Applied Mathematics
- DOE Contract Number:
- FG06-86ER25019
- OSTI ID:
- 6422906
- Report Number(s):
- DOE/ER/25019-4; ON: DE87011830
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
420300* -- Engineering-- Lasers-- (-1989)
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLIFICATION
BEAM DYNAMICS
DIFFERENTIAL EQUATIONS
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
ENERGY RANGE
EQUATIONS
EQUATIONS OF MOTION
EQUIPMENT
FREE ELECTRON LASERS
GAIN
LANGMUIR FREQUENCY
LASERS
MAGNETS
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
RELATIVISTIC RANGE
RESONANCE
SYNCHROTRON OSCILLATIONS
WIGGLER MAGNETS