Escape factors for laser-plasmas

A method of parameterizing escape factors (transmission factors and net radiative brackets) for conditions typical of laser-produced plasmas is introduced. The assumptions of planar geometry, exponentially decreasing emissivity and absorption coefficient with distance with a step rise at a particular point, and spatially constant Doppler broadened line profiles have been made. The effect of velocity gradients in spectrally shifting the absorption and emission line profiles relative to each other is taken into account assuming linear velocity gradients with distance. A parameter R representing the ratio of the spatial scale-length of the absorption coefficient to the Doppler decoupling length is introduced. Fitting formulae for transmission factors and net radiative brackets are given which are valid for all R and all optical depths. In the limit of small R (large Doppler decoupling length), the escape factors asymptotically approach formulae developed originally by, for example, Holstein assuming negligible plasma velocities. For large R (small Doppler decoupling length), the escape factors have been shown to asymptotically approach the Sobolev approximation. The parameterized net radiative bracket has been used in the hydrodynamic and atomic physics code ‘EHYBRID’ for the calculation of the effect of radiation trapping on population densities in laser-produced plasmas. The output of the modified EHYBRID code has then been post processed using the parameterised transmission factors to simulate 123 Ne-like and 399 F-like germanium resonance line intensities emitted in typical X-ray laser experiments. We obtain an agreement between the simulated and experimental spectra.