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The self‐consistent interaction of an electron beam with an electromagnetic wiggler and a radiation field is analyzed. Equations are derived for the depletion and diffraction of the wiggler wave. The formalism yields local conservation laws for the system energy flux and photon flux. Using a one‐dimensional approximation, pump depletion is examined for pulsed and steady‐state electron beams. A three‐dimensional analysis shows that the wiggler diffraction is dominated by the nonresonant interaction of the electrons with the wiggler wave. This is studied in detail for a specific electron pulse shape. It is concluded that wiggler depletion and diffraction should not substantially degrade the free electron laser interaction for experimentally obtainable system parameters.

Depletion and diffraction of an electromagnetic wiggler field during the free electron laser interaction