Hybrid atomic models for spectroscopic plasma diagnostics

TLDR: In this article, a hybrid approach is proposed to treat atomic structure and rates in collisional-radiative models, combining the completeness of highly averaged models with the accuracy of detailed models.

About: This article is published in High Energy Density Physics.The article was published on 2007-05-01 and is currently open access. It has received 159 citations till now. The article focuses on the topics: Configuration interaction.

Figures

Fig. 3. Comparison of average ion charge calculations for Ge at ne = 1017cm−3 from the hybrid model of the present work, a model based on relativistic configurations, and other codes (from Ref. [22])

Fig. 1. Number of fine structure levels, coronal fine structure levels, configurations, and hybrid-model levels in the configuration sets described in the text for ions from H-like to Ar-like.

Fig. 2. Comparison of fE1 factors for Rate(p2d4αJ → p3d3 ). The analytic formulation given in Eqn.(8) matches the fully relativistic level-to-level factors very well.

Fig. 5. Comparison of detailed fine structure model emission spectra of Li-like Ge at Te=8 keV and ne = 1014cm−3 with the predictions of the hybrid model with and without approximate configuration interaction corrections to its relativistic configurations. Transitions among the coronal configurations are given by the dashed lines.

Fig. 4. (a) shows the charge state distribution of Ge ions at Te=600 eV and ne = 1017cm−3 as calculated by the hybrid model and models based on relativistic configurations and detailed fine structure levels. (b) shows that the hybrid model agrees with the detailed models, in its predictions for the populations of metastable states in the (2`)7(3`) configurations, which the RC model underpredicts.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Hybrid atomic models for spectroscopic plasma diagnostics" ?

The authors propose a hybrid approach to treating atomic structure and rates in collisionalradiative models, combining the completeness of highly averaged models with the accuracy of detailed models. The authors present results from a trial hybrid model of germanium which demonstrate the accuracy of the hybrid model for charge state distributions and spectra. 

Q2. Why can't configuration interaction be included in the RC levels?

Because configuration interaction can have significant effects on both transition energies and strengths [19–21], its absence in transitions among the RC levels could degrade the diagnostic utility of spectra from the hybrid model. 

Q3. What are the main caveats of coronal models?

reliable coronal models must include configurations up to a sufficiently large quantum number2(usually n = nvalence+ ≈ 5 is sufficient [2]) to adequately describe radiative cascades into metastable levels, which give rise to the familiar density-sensitive diagnostic emission lines [3]. 

Q4. What is the main reason for the inclusion of dielectronic recombination channels?

accurate calculations of charge state distributions in the coronal regime require the inclusion of many dielectronic recombination channels, often through doubly excited levels not accessible from the ground configuration. 

Q5. What is the main reason why coronal models are unreliable?

Coronal models become unreliable at moderate or high densities or in the presence of a thermal radiation field, where collisional excitation from the ground level is no longer the dominant excitation mechanism and excited configurations can have populations that approach or exceed (because of their large statistical weights) the population of the ground configuration. 

Q6. What is the number of configurations in the M shell?

Since the authors must solve a system of N ×N coupled rate equations, where N is the total number of levels, it is clear that the number of fine structure levels becomes intractable as soon as the authors have more than two or three electrons in the M shell, The number of configurations, however, remains tractable, as does the number of coronal fine structure levels defined above. 

Q7. What is the way to describe the atomic structure of a valence shell?

FAC can operate in two modes, giving atomic structure and rate data for either fine structure levels or relativistic configuration averages. 

Q8. What is the skeleton of the hybrid model?

Since any model which makes claims of spectroscopic accuracy must be able to describe high resolution spectra from well characterized, low-density plasma sources, the authors set as the skeleton of their hybrid model a fairly restricted set of fine structure levels belonging to configurations which are directly accessible via single-electron transitions from the ground state. 

Q9. What is the reason for the failure of the relativistic configuration model?

The reason for the failure of the relativistic configuration model is shown in Fig. 4(b): since the RC model averages over the metastable levels in the (2`)7(3`) configurations, it underpredicts their populations and cannot account properly for ladder ionization from Ne-like to F-like Ge. 

Q10. What are the main caveats of such models?

Such models work well whenever collisional excitation from the ground state is the dominant population mechanism and spontaneous decay is the dominant depopulation mechanism, with two important caveats: 

Q11. How many excitations from the first inner shell to n nvalence?

2 1s22s22p63s 3p41s22s22p63s23p23d 1s22s22p63s23p24` 1s22s22p63s23p25` 1s22s22p63s 3p33d 1s22s22p63s 3p34` 1s22s22p63s 3p35`• single excitations from the first inner shell to n ≤ nvalence + 

Q12. What is the way to solve the hybrid level structure?

Thus the authors arrive at their proposal for the hybrid level structure: from a set of SCs with sufficient completeness to describe the general non-LTE problem, the authors replace a subset of coronal configurations with fine structure levels. 

Q13. What is the second approach to obtaining FS C ′ rates?

The second approach is to obtain approximate FS → C ′ rates by statistically decomposing the available C → C ′ rates from Eq. (3), ensuring that on reversal the authors regain C → C ′ rates which are averages over the initial levels and sums of the final levels of the FS → FS ′ rates:Ratestat(FS → C ′) = Rate(C → C ′) (6)andRatestat(C → FS ′) = gFS ′∑ FS ′ gFS ′Rate(C → C ′) (7)with FS ′ running over all fine structure levels in C ′.