Study the Integro-Differential Equation in a Lorentzian Energy Spread Case

Abstract

The fundamentals of free electron laser (FEL) theory are now well–establishedand can provide a sophisticated description of experiments over a wide rangeof parameters. While new technology is being developed for systems workingfrom 1mm to 10nm wavelengths, the theory remains the same. In this work,the final consequences of Lorentzian energy distribution in FEL amplifier willbe found by solving of Integro-differential equation using symbolic toolboxservices in MATLAB software v. 6.5 and the relation between severalparameters will be delimited and plotted in order to extract and present thecomplex relations between the FEL parameters.

Keywords

• evolutionary programming and symbolic analysis
• mathematical modeling
• fel amplifier process