Abstract
Rate equations are proposed which describe the operation of a crystal as a resonant cavity for x rays. The formalism, which applies equally well to two-beam or multibeam diffraction cases, is not restricted to any particular mechanism of x-ray emission. It automatically takes into account dynamical diffraction effects on energy flow (group velocity) and absorption (the Borrmann effect) which are shown to be instrumental in increasing gain and lowering the lasing threshold. The resonant x-ray modes are those for which the group velocity vanishes (the resonant diffraction condition).
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