Modeling of population kinetics of plasmas that are not in local thermodynamic equilibrium, using a versatile collisional-radiative model based on analytical rates

We discuss the modeling of population kinetics of nonequilibrium steady-state plasmas using a collisional-radiative model and code based on analytical rates (ABAKO). ABAKO can be applied to low-to-high $Z$ ions for a wide range of laboratory plasma conditions: coronal, local thermodynamic equilibrium or nonlocal thermodynamic equilibrium, and optically thin or thick plasmas. ABAKO combines a set of analytical approximations to atomic rates, which yield substantial savings in computer running time, still comparing well with more elaborate codes and experimental data. A simple approximation to calculate the electron capture cross section in terms of the collisional excitation cross section has been adapted to work in a detailed-configuration-accounting approach, thus allowing autoionizing states to be explicitly included in the kinetics in a fast and efficient way. Radiation transport effects in the atomic kinetics due to line trapping in the plasma are taken into account via geometry-dependent escape factors. Since the kinetics problem often involves very large sparse matrices, an iterative method is used to perform the matrix inversion. In order to illustrate the capabilities of the model, we present a number of results which show that the ABAKO compares well with customized models and simulations of ion population distribution. The utility of ABAKO for plasma spectroscopic applications is also outlined.

Figure 1

Average ionization of a carbon plasma at $T_e=10\text{eV}$ over a wide range of electron densities. As it is expected the CR model tends asymptotically to the results obtained with the CE and Saha-Boltzmann equations in the low and high electron density regimes, respectively.

Figure 2

Average ionization of a carbon plasma at several temperatures and densities. In order to stress the role of autoionizing states, we used ABAKO to compare different calculations: DR does not include autoionizing states explicitly, instead the Burgess-Merts formalism is used to carry out a direct evaluation of the dielectronic recombination rate; AU-EC denotes here the same ABAKO-DCA results shown in Table , which include autoionizing states explicitly and the rate coefficients of autoionization and electron capture computed as described in the previous section.

Figure 3

(Color online) Fractional populations of carbon ion stages calculated with ATOMIC [88] and ABAKO over a wide range of temperatures for a density $n_e={10}^{13}{\text{cm}}^{-3}$.

Figure 4

(Color online) Comparison of charge state distributions simulated by different models and the measurements for the Au experiment with $n_e={10}^{12}{\text{cm}}^{-3}$ and $T_e=2500\text{eV}$ performed at LLNL EBIT-II.

Figure 5

(Color online) Comparison of charge state distributions simulated by different models and the measurements for the Au experiment with $n_e=6\times {10}^{20}{\text{cm}}^{-3}$ and $T_e=2200\text{eV}$ performed at NOVA.

Figure 6

(Color online) Comparison of charge state distributions simulated by different models for the Xe experiment performed at LULI.

Figure 7

Comparison between an Al $K$-shell spectrum recorded at LULI and the ABAKO best fit. Two examples are shown corresponding to different recorded measurements along the laser-target axis. The analysis gives (top) $n_e=2.26\times {10}^{22}{\text{cm}}^{-3}$ and $T_e=469\text{eV}$ and (bottom) $n_e=1.52\times {10}^{22}{\text{cm}}^{-3}$ and $T_e=417\text{eV}$.

Figure 8

Comparison between a time-resolved Ar $K$-shell spectrum and the ABAKO best fit: (top) OMEGA shot 49952, the extracted conditions are $T_e=1412\text{eV}$ and $n_e=2.81\times {10}^{23}{\text{cm}}^{-3}$; (bottom) OMEGA shot 49954, the extracted conditions are $T_e=1518\text{eV}$ and $n_e=1.51\times {10}^{24}{\text{cm}}^{-3}$.