Optical Escape Factors for Bound-bound and Free-bound Radiation from Plasmas. I. Constant Source Function

Optical escape factors for bound-bound and free-bound radiation have been calculated by solving the equation of radiative transfer with the assumption that the corresponding source functions are space-independent. The general expression for bound-bound transitions yields for large optical depths—within a correction factor of order unity—Holstein's asymptotic expressions for the two limiting cases of a Doppler and a dispersion profile. Application to the more general case of a Voigt profile leads to an analytical formula which permits a rapid estimate of the escape factor for any optical depth. Numerical application to the resonance lines of neutral helium-which are broadened by Stark and Doppler effects—shows that under certain plasma conditions most of the higher members of the resonance series remain optically thin.—The general expression obtained for the escape factor of free-bound radiation has been applied to the resonance continuum of neutral helium. The numerical results show that the resonance continuum remains optically thin as long as the optical depth in the center of the He resonance line (λ = 584 Å) remains smaller than 10⁴ to 10⁵. A similar result is obtained for atomic hydrogen.     

Zur spektroskopischen Temperatur- und Dichtemessung von Plasmen bei Abwesenheit thermodynamischen Gleichgewichtes

After a discussion of the ionization formulae for both a steady-state and a transient plasma with and without thermodynamic equilibrium it is shown that for the practical application of these formulae the introduction of a non-Maxwellian velocity distribution function for the electrons is necessary in special cases, because the electrons can escape from the plasma without effecting a sufficiently high number of ionizing impacts. The influence of both the “Maxwell”- and the “Druyvesteyn”-distribution on the excitation, ionization, and recombination processes is treated quantitatively. The modification of the ionization formula due to three-body collisional recombination into excited states is discussed. It is emphasized that the normally unknown velocity distribution of the electrons can be obtained by measuring the free-bound recombination continuae.     

Influence of the boundary layer of a shock-heated plasma on the stark profiles of the A1(I) resonance lines

The influence of temperature and density gradients in the boundary layer of an Al(CH₃)₃-seeded shock-heated plasma on the Stark profiles of the A1(I) resonance lines λ = 3961.5 Å and λ = 3944 Å is investigated by solving the radiative transfer equation. The thermal boundary layer thickness δ is varied from 0 to 1 cm, assuming complete local thermodynamic equilibrium (LTE) throughout the inhomogeneous region. The calculations show that the line profiles are distorted. For the plasma conditions of an experiment made recently by one of us, it is shown that reabsorption diminishes the intensity and displaces the maxima of the profiles of both resonance lines in the same relative proportions. Thus, the ratios of their half-widths and of their shifts are practically independent of the boundary-layer effect. We conclude, therefore, that the measured difference of the half-widths of the A1(I) resonance doublet must be an intrinsic plasma effect.