Jin Feng-Tao

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

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-transition-array 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 view-point 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].

Temperature diagnostics for iron plasmas by means of transmission spectrum obtained by accurate atomic data

Accurate atomic data such as fine-structure energy levels and oscillator strengths are calculated to obtain the radiative opacity and transmission of iron plasmas. At a temperature of 22 eV and a density of 0.01 g/cm3, the calculated transmission spectrum is in better agreement with the experiment than that by other opacity codes such as OPAL. The transmission spectrum is very sensitive to the temperature of plasmas, meaning that it is an ideal diagnostic tool for the temperature of plasmas. Practical calculations show that the uncertainty of the temperature diagnostics obtained by theoretical predictions is better than ±2 eV.

Time-Resolved Measurement of Radiatively Heated Iron 2p−3d Transmission Spectra

An experimental measurement of radiatively heated iron plasma transmission spectra was performed on Shenguang II laser facility. In the measurement, the self-emission spectrum, the backlighting spectrum, and the absorption spectrum were imaged with a flat filed grating and recorded on a gated micro channel plate detector to obtain the time-resolved transmission spectra in the range 10–20 A (approximately 0.6–1.3keV). Experimental results are compared with the calculation results of an unsolved transition array (UTA) code. The time-dependent relative shift in the positions of the 2p−3d transmission array is interpreted in terms of the plasma temperature variations.

Orbital Relaxation Effects in the Calculation of Aluminum K α Absorptions

A recent experimental Kα transmission spectrum of an aluminum plasma is theoretically studied by a detailed level accounting model. It is found that the orbital relaxation effects of the K- and L-shell orbitals should be considered to calculate accurate line positions and strengths. To do this the initial and the final radial wave functions of Kα lines are respectively optimized by solving the full relativistic Dirac–Fock equation. Extensive configuration interaction calculations are performed to obtain the energy levels and the oscillator strengths. It is shown that both the line positions and the line strengths agree quite well with experiment when the orbital relaxations are considered.

Population Diagnostics of a Hot NaBr Plasma by Detailed Simulation of Absorption Spectra

The experimental absorption spectra of a hot NaBr plasma are theoretically studied by using a detailed level accounting model. The sodium and bromine absorption spectra have been well reproduced respectively in the approach of local thermodynamic equilibrium, in which the populations between and within ions are obtained by solving the Saha–Boltzmann equation. The temperature of bromine however is found to be much lower than the one of sodium. Such discrepancy indicates that thermodynamic equilibrium is not reached between the sodium and bromine atoms during the measurement.

Open M-shell Opacity of Bromine Plasma in Comparison of the Detailed Level Accounting Model with the Average Atom Model

The open M-shell opacity of a hot bromine plasma has been calculated by using a detailed level accounting (DLA) model. One-electron orbitals obtained by solving the fully relativistic Dirac–Fock equations are used to obtain the atomic levels and the radiative transition oscillator strengths. Only the level mixing within the same electron configuration is considered to reduce the complexity of the calculations. Detailed comparisons have been made between the results of the DLA and average atom (AA) models. Good agreements are found for both the M-shell transition arrays and the Planck mean opacity but there are differences for the line positions in the 2p→3d absorption region due to the statistical treatment for the one-electron orbitals in the AA model.

Electron Temperature Measurement of Radiation-Heated CH Foam on Shenguang II Laser Facility

A spectroscopic diagnostic method, to measure electron temperature of radiation-heated CH foam on Shenguang II laser facility, is described. A tracer layer of aluminum was embedded in the middle of the CH foam and a point-projection method used in the opacity experiment was induced to measure the transmission spectrum of the embedded A1 foil. The electron temperature, of about 80 eV, was deduced through a comparison of the experimental absorption spectrum with the calculated one with a detailed level accounting opacity code. The results of hydrodynamic simulation show that its reasonable to determine the CH foam temperature by measuring the embedded Al absorption spectrum. Thus, the electron temperature of radiation-heated CH foam was obtained.

Multipole effects to the opacity of hot dense gold plasma

The contributions of the multipole transitions to the opacity of hot dense gold plasma are taken into account by using an average-atom model. The influences of the E2, E3 and E4 transitions on the Rosseland opacity are studied, respectively. Comparisons with Miao’s calculation have been made. It shows that using the Taylor series to account for the multipole transitions is no longer valid since ik · r is not much smaller than the unit when the photon energy goes very high.

Detailed Spectral Line Effects on the Radiative Opacity of Laser-Produced Al Plasmas

The detailed term accounting (DTA) approximation for the line absorption and the average atom (AA) model for bound-free and free-free absorption are used to calculate the radiative opacity of high-power laser-produced plasmas in local thermodynamic equilibrium (LTE). The spectral resolved opacities of Al plasmas are calculated at the temperatures and densities of 40 eV and 0.0135 g/cm3, and 58 eV and 0.02 g/cm3. Rosseland and Planck mean opacities are obtained by integrating the spectral resolved opacities with Rosseland and Planck weighting functions. The results show that the Rosseland mean opacity is very sensitive to the detailed profile. Radiative opacities under the same plasma conditions are also obtained by using a completely pure AA model. The results from the DTA and pure AA models are then compared.