Abstract
A theoretical and phenomenological consideration is given to higher order, strong field effects in electron/laser interactions. A consistent strong field theory is the Furry interaction picture of intense field quantum field theory. In this theory, fermions are embedded in the strong laser field and the Volkov wavefunction solutions that result, are exact with respect to the strong field. When these Volkov fermions interact with individual photons from other sources, the transition probability is enhanced in a series of resonances when the kinematics allow the virtual fermion to go on-shell. An experiment is proposed in which, for the first time, resonances could be used to generate high energy photons from relativistic electrons at rates orders of magnitude in excess of usual mechanisms.
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