Radiative opacity of plasmas studied by detailed term (level) accounting approaches

Abstract

Detailed term and level accounting (DTA and DLA) schemes have been developed to calculate the spectrally resolved and Rosseland and Planck mean opacities of plasmas in local thermodynamic equilibrium. Various physical effects, such as configuration interaction effect (including core-valence electron correlations effect and relativistic effect), detailed line width effect (including the line saturation effect), etc., on the opacity of plasmas have been investigated in detail. Some of these physical effects are less capable or even impossible to be taken into account by statistical models such as unresolved transition arrays, super-transitionarray or average atom models. Our detailed model can obtain accurate opacity of plasmas. Using this model, we have systematically investigated the radiative opacities of low, medium and high-Z plasmas under different conditions of temperature and density. For example, for aluminum plasma, in the X-ray region, we demonstrated the effects of autoionization resonance broadening on the opacity for the first time. Furthermore, the relativistic effects play an important role on the opacity as well. Our results are in good agreement with other theoretical ones although better agreement can be obtained after the effects of autoionization resonance broadening and relativity have been considered. Our results also show that the modelling of the opacity is very complicated, since too many physical effects influence the accuracy of opacity.For medium and high-Z plasmas, however, there are systematic discrepancies unexplained so far between the theoretical and experimental opacities. Here, the theoretical opacities are mainly obtained by statistical models. To clarify the discrepancies, efforts from both sides are needed. From the viewpoint of theory, however, a DLA method, in which various physical effects can be taken into account, should be useful in resolving the difference. Taking gold plasma as an example, we studied in detail the effects of core-valence electron correlation and line width on the opacity. Our DLA results correctly explained, for the first time, the relative intensity of the two strong absorption peaks located near the photon energy of 70 and 80 eV, which was experimentally observed by Eidmann et al. [Europhys. Lett., 1998, 44: 459].

Ionization competition effects on population distribution and radiative opacity of mixture plasmas

“…The theoretical background for calculating the radiative opacity of pure plasmas can be found in our previous work. [23][24][25][26][27][28][29] The procedure for mixtures is similar to pure matters, although new features have to be taken into account. For a mixture plasma in LTE with mass density q consisting of n different elements with atomic number Z 1 , Z 2 ,…, Z n and atomic mass A 1 , A 2 ,…, A n , we define the normalized number fraction v j for element j which satisfies the condition of…”

“…and r j;i;ll 0 is the photo-excitation cross section from level l to l 0 of ionization stage i of element j, r j,i,l is the photoionization cross section of level l for ionization stage i of element j, r j,i,f is total free-free cross section of ionization stage i of element j which is approximated by Kramers formula, 23 and l scatt (h) is the absorption coefficients contributed by scattering processes which is obtained using the Thomson scattering formula. For the bound-bound process, r j;i;ll 0 ðhÞ can be obtained from the absorption oscillator strength f j;i;ll 0 for the transition from level l to l 0 of ionization stage i of element j…”

“…The detailed expression of electron-impact broadening and Doppler broadening can be found in Ref. 23. For autoionized levels, the broadening due to single Auger decay is included, whereas the contribution of direct double Auger decay is neglected.…”

“…where u ¼ h/kT and j scatt (u) is the opacity contributed by scattering processes, W P and W R are, respectively, the Planck and Rosseland weighting functions, definitions for which can be found in Ref. 23. The fraction of radiation transmitted F at photon energy h with respect to some incident source of arbitrary intensity is given by…”

<title>Calculation of the radiative opacity for some low Z plasmas produced by high power pulsed lasers</title>

“…Up to now DTA and DLA have achieved great success in predicting the opacity of low-z plasma. 16 In this work, the opacity has been calculated by using of DLA model which is described in the following section.…”