| A computer based method for computing the structure of electromagnetic fields produced by electrons in a Free Electron Laser is presented. The driving equations for this time based method are the vector wave equation and the Lorentz force equations. The electric and magnetic fields are computed via the Liénard-Wiechert fields, which are solutions of the vector wave equation for a point charge. Data is analyzed in the time domain and, by means of a discrete Fourier transform, in the frequency domain. Solutions in both domains contain all three vector components of the electric field associated with single electron radiation in an undulator. When all terms of the Liénard-Wiechert fields are retained, the solution is valid even in the vicinity of the electron, making this method an excellent tool for studying the electromagnetic fields near to or even inside an undulator.; As an application of this method, the fields generated inside a planar undulator and a parallel plate waveguide will be studied. The output radiation of this system is analyzed in terms of time and frequency at any specific point in space. The results reveal insights into how the presence of the waveguide acts to change the nature of undulator radiation. Data is also computed detailing the spatial distribution of the electric component of radiation at a set time. This data is used to compute the curvature of the electromagnetic field in the vicinity of an output resonator mirror. |
