It is shown via theory and simulation that the resonant frequency of a Free Electron Laser may be modulated to obtain an FEL interaction with a frequency bandwidth which is at least an order of magnitude greater than normal FEL operation. The system is described in the linear regime by a summation over exponential gain modes, allowing the amplification of multiple light frequencies simultaneously. Simulation in 3D demonstrates the process for parameters of the UKs CLARA FEL test facility currently under construction. This new mode of FEL operation has close analogies to Frequency Modulation in a conventional cavity laser. This new, wide bandwidth mode of FEL operation scales well for X-ray generation and offers users a new form of high-power FEL output.
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