Narrow Results

A general method for quick and accurate evaluation of escape factor is presented, for any optical depths and any line profiles, using least square procedure. The principle of the least square procedure is discussed. As an example, the parameters are fitted when the optical depth is in the region of 0–1000, and the escape factors we obtained are in accordance with the theoretical formula.

In this paper, the concepts of the photon escape probability and the transmission factor are reviewed and the photon escape probabilities for infinite plane-parallel slab and spherical geometries are discussed. The photon escape probabilities using the transmission factor, for Lorentzian profile and Holtsmarkian profile, are discussed. Finally, the photon escape probabilities we calculated are compared with that calculated using before method for Lorentzian profile and Holtsmarkian profile, and some useful conclusions are drawn.

In this letter, self-absorption is discussed using the concept of escape factor. The calculation method of the escape factor for spherical geometry plasma is discussed. For the spherical geometry, the escape factors Λ(r) at any position r in a spherical geometry plasma (with the radius R) for Lorentzian and Holtsmarkian profiles are calculated, and a general expression is obtained. As an example, for the sodium 330.3 nm resonance line, the total radiance and the real radiance are calculated, and the self-absorption for the resonance line is discussed. This discussion will be useful for the study of the relationship of escape factor and the self-absorption of spectral lines for any geometries.

For accurate electron temperature and density diagnostics in laser high-temperature plasma implosion, opacity of Krypton (Kr) helium-$\beta$ and Balmer-$\alpha$ lines are discussed, and ratio of escape factor of the two X-rays are calculated, both for Gaussian and Holtzmarkian profiles. Finally, the line ratios of the two X-ray lines are analyzed for optically thin and thick plasmas. Results indicate that for the Gaussian profile, the line ratio varies greatly with the opacity of the Kr helium-$\beta$ line, which provides excellent source for temperature and electron density diagnostics; while for the Holtzmarkian profile, the line ratio varies less with the opacity of the Kr helium-$\beta$ line, which can be used for escape factor diagnostics. This method is significant in accurate plasma diagnostics using X-rays under the condition of optically thick.