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In this paper the operability of a Smith-Purcell free-electron laser for an arbitrary grating is considered. An arbitrary grating is described in terms of impedance matrix. The consideration is based on the self-consistent set of Maxwell-fluid equations. The dispersion relation is established for the TM mode of electromagnetic waves. The latter is studied considering amplification of the evanescent as well as radiation modes. The small signal gain in various limits is calculated and the dependence of the gain on the electron beam current is analyzed.
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G. F. Mkrtchian (2007) studied this question.
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