Stochastic modeling of x-ray superfluorescence

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Abstract
An approach to modeling the dynamics of x-ray amplified spontaneous emission and superfluorescence -- the phenomenon of collective x-ray emission initiated by intense pulses of X-ray Free Electron Lasers -- is developed based on stochastic partial differential equations. The equations are derived from first principles, and the relevant approximations, derivation steps, and extensions specific to stimulated x-ray emission are presented. The resulting equations have a form of three-dimensional generalized Maxwell-Bloch equations augmented with noise terms for both field and atomic variables. The derived noise terms possess specific correlation properties that enable the correct reconstruction of spontaneous emission. As a result, the developed formalism is universally suitable for the description of all stages of stimulated x-ray emission: spontaneous emission, amplified spontaneous emission, and superfluorescence. Numerical examples illustrating multiple properties of the emitted field -- e.g., spatio-temporal coherence -- are presented. We expect that the developed formalism will form a solid base for interpreting stimulated x-ray emission spectroscopy measurements, modeling x-ray laser oscillators, and describing other experiments that employ x-ray superfluorescence.

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