Explicit approximations for strictly nonlinear oscillators with slowly varying parameters with applications to free electron lasers

Technical Report · Sat Aug 01 04:00:00 EDT 1987

OSTI ID:5734055

Kevorkian, J; Li, Y P

The first part of this paper summarizes the mathematical modeling of free electron lasers (FEL), and the remainder concerns general perturbation methods for solving FEL and other strictly nonlinear oscillatory problems with slowly varying parameters and small perturbations. We review and compare the methods of Kuzmak-Luke and of near-identity averaging transformations. In order to implement the calculation of explicit solutions we develop two approximation schemes. The first involves use of finite Fourier series to present either the leading approximation of the solution or the transformation of the governing equations to a standard form appropriate for the method of averaging. In the second scheme we fit a cubic poly-nomial to the potential such that the leading approximation is expressible in terms of elliptic functions. The ideas are illustrated with a number of examples which are also solved numerically to assess the accuracy of the various approximations.

• Research Organization: Washington Univ., Seattle (USA). Dept. of Applied Mathematics
• DOE Contract Number: AI05-86ER25016
• OSTI ID: 5734055
• Report Number(s): DOE/ER/25016-6; TR-87-8; ON: DE88004116
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300* -- Engineering-- Lasers-- (-1989)
99 GENERAL AND MISCELLANEOUS
990230 -- Mathematics & Mathematical Models-- (1987-1989)
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FOURIER TRANSFORMATION
FREE ELECTRON LASERS
HAMILTONIANS
INTEGRAL TRANSFORMATIONS
LASERS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
QUANTUM OPERATORS
TRANSFORMATIONS