| Summary: | Approved for public release; distribution is unlimited. === A detailed exploration of free electron laser (FEL) theory has been done in two areas. An exact solution to the phase-space trajectories in a linearly-polarized undulator has been obtained using a numerical simulation. The complicated phase-space motion caused by transverse undulator deflections makes a rigorous derivation for trajectories difficult, if not impossible. The numerical solution extends the understanding of electron trajectories by quantitatively describing the fast and slow components of motion. The Bessel function coupling coefficient, describing the slow evolution is found to be valid over a broad range of parameters even though its derivation is approximate. A second program has been developed that provides a simple, quick diagnostic for accelerator designers to evaluate how well a simulated beam design will perform as an FEL. The effect of beam quality conditions like energy, angular, and positional spread are shown to depend only on the initial conditions of the beam at the entrance to the undulator. This program takes the six phase-space coordinates of the beam directly from an accelerator simulation code, like PARMELA, and predicts its performance in an FEL system. This method substitutes for more lengthy, complex integrated simulations, like INEX, that require a CRAY computer.
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