A quantum model of the orotron free-electron laser

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Abstract
A quantum model of the orotron (Smith–Purcell) free-electron laser is formulated in which the classical electron current density derived from a linearization of the equation of motion exhibits hybrid properties between the current densities of the Čerenkov and the wiggler free-electron lasers. Here, consistent with the (four-dimensional) current-density conservation law, the current density is proportional to the average change of the electron velocity Δv in the interaction region. From the interaction of the electron current with the quantized radiation field in an interaction volume of finite extent, we arrive at the multiphoton distribution function, which in turn yields the full ‘‘quantum-mechanical’’ gain after quantum recoil is taken into account. In an example where the radiation wavelength is 0.4 cm and the electron beam velocity is 0.1 c [corresponding to the Harry Diamond Laboratories (HDL) orotron experiment], we estimate that the maximum gain can easily be 8% or larger although the interaction length is chosen to be only 4 cm.

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