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The plasma undulator

On the basis of the theory of magnetic undulator for free electron laser (FEL) we analyze the use of a large amplitude plasma wave as an electrostatic undulator. We review the original idea of the plasma undulator and consider some particular plasma undulator configurations. By using low energy electron beams we show the possibility to generate very small wavelength electromagnetic radiation. The fluid theory for the FEL with a plasma undulator, in complete analogy with the ordinary ones, is presented and the thresholds for the FEL action are discussed. An analysis for the intrinsic efficiency, with respect to the emittance and the plasma wake field effects, is presented and applied to some new configurations.