Emission mechanism for the silicon He-α lines in a photoionization experiment Download: 727次
1 Introduction
The concept of photoionizing plasmas[1–5] was first introduced by Tarter, Tucker and Salpeter (1969)[6] to explain X-ray spectra from highly ionized but low-temperature celestial objects. Since then, more astronomical sources with similar spectral properties have been observed[7–9]. These are either diffuse sources (interstellar gas, supernova remnants, etc.) or high-mass X-ray binary systems (HMXBs) around compact objects (black holes, neutron stars, white dwarfs)[7–11].
In recent years there have also been a few attempts to produce photoionizing plasmas in the laboratory under controlled experimental conditions[12,13]. Several problems make such experiments extremely difficult. The first one is, of course, the generation of a high-intensity X-ray beam that can ionize high-Z material to He- and H-like species. This requires extreme technology such as the Z machine[12] or high-intensity lasers[13,14]. A second difficulty is the analysis of such experiments: while astrophysical photoionizing plasmas are stable, time-independent objects, laboratory plasmas vary on timescales of nanoseconds and spatial extents of micrometers. Nevertheless, both kinds of plasmas produce He-
The main aim of this paper is a new analysis of the experiment of Fujioka et al., which was carried out on the GEKKO-XII laser facility. In this experiment a black-body (BB) radiation source with temperature of
Fig. 1. Black line: the experimental spectrum of Fujioka et al .[13]. Blue line: the theoretical result of an optically thin model. f, Li, i and r denote the position of the forbidden line, satellite lines, the intercombination line and the resonance line, respectively.
Several studies tried to overcome the mismatch between the simulated and measured spectra. Hill and Rose used a detailed configuration for recording atomic data in a time-dependent model. They also added opacity effects into the simulation. They correctly predicted the resonance line, but the time-dependent relative intensities were always different from those in the experimental results. Later, Bao et al. simulated the spectrum with a steady-state model. While their simulated peaks around 1864 eV and 1840 eV fitted the experimental peaks, the peak at 1855 eV was weaker than the experimental value. Wu et al. developed a time-dependent model, but, similarly, their central peak was still too low. As a matter of fact, all these papers report results that are not significantly different from those of Wang et al. in Figure 1.
In this study we reanalyzed the results obtained by Fujioka et al.[13,14]. Based on assumed very high accuracy atomic data, this work focuses on the detailed contributions of every atomic process to investigate the line emission mechanism under experimental conditions. Our analysis also takes the opacity effect into account. The line emission mechanism is investigated with three models: (i) a steady-state optically thin model; (ii) a time-dependent optically thin model; and finally (iii) a steady-state optically thick model. With all these elements in our simulations, we finally succeeded to obtain reasonably good agreement between our third model and the experiment.
A brief description of the theoretical model and comparisons of atomic data are given in Section 2. In Section 3, the line emission mechanism is investigated under experimental conditions, and the reason for the weak central peak in previous studies is explained. Finally, a summary is given in Section 4.
2 Theoretical model
In the computations presented in this paper, we use radiative-collisional code based on FAC (RCF)[21,22] to calculate the spectrum emitted from a photoionizing plasma. RCF is collisional-radiative code that simulates plasma under nonlocal thermodynamic equilibrium conditions. RCF takes into account ten atomic processes in the rate equations to calculate the charge state distribution, the level distribution and the corresponding spectrum. The atomic processes are divided into five mutually inverse groups[21,23]. Two of these groups are (i) free electron collisional ionization (CI) and three-body recombination (TR); and (ii) electron collisional excitation (CE) and collisional deexcitation (CD). The other three groups include the photon-induced processes that take place when a plasma is irradiated by a strong radiation field, which may turn out to become the dominant processes: (iii) photoionization (PI) and radiative recombination (RR); (iv) photoexcitation (PE) of ionic levels and subsequent spontaneous radiative decay (A); and (v) autoionization (AI) and dielectronic capture (DC) – doubly excited states can ionize spontaneously by AI or be produced through DC, which eventually decay to ground state through emission of the corresponding satellite lines.
Fig. 1. Black line: the experimental spectrum of Fujioka et al .[13]. Blue line: the theoretical result of an optically thin model. f, Li, i and r denote the position of the forbidden line, satellite lines, the intercombination line and the resonance line, respectively.
3 Results and discussion
Three models were used in our study.
- Model 1: The plasma is assumed to be in a steady state, having constant density and temperature throughout the period of the irradiation. It is assumed also to be optically thin.
- Model 2: The time dependence of the charge state distribution in the plasma is taken into account, but the model still assumes an optically thin plasma.
- Model 3: A steady-state but optically thick plasma is assumed that accounts for the reabsorption of the emerging radiation inside the irradiated plasma.
- Photoexcitation produces a strong resonance line and some nearby Li-like lines because of large photoexcitation rates and lower-level densities. Consequently, these lines are much stronger than the forbidden line and intercombination line in the optically thin models (Model 1 and Model 2).
- The resonance line and some satellite lines are easily absorbed as the photons travel to the detector. As a result, the experimental spectrum is successfully simulated by an optically thick model, where the intercombination lines become more visible than in previous studies.
- The
and$G$ ratios of He-$R$ lines are influenced by the satellite lines, optical effect and plasma ionization structure. Therefore, one needs to be careful when using these line ratios in plasma diagnosis.$\mathrm{\alpha}$
The line emission mechanism is investigated with all three models, and the differences between the results, in particular the opacity effects, are explained and discussed.
3.1 Model 1: steady-state optically thin model
For the steady-state model, the rate equations used to calculate the charge state distribution are written in a shortened form,
In this model the irradiated plasma and the BB source have the same values as in the experiment of Fujioka et al. The input parameters are radiation temperature
Fig. 2. Comparison of the collisional excitation cross-section with the results of Refs. [26–29]. The transitions include 1s2s 3S 1s2p 1P1, 1s2s 3S 1s2s 1S1, 1s2p 3P 1s2p 1P1 and 1s2s 1S 1s2p 1P1 of He-like Si.
In Figure 3, the
At the electron temperature of
Altogether, this simulation shows that the main excitation of the He-like
3.2 Model 2: time-dependent optically thin model
Next we tried to investigate the influence of a time-varying radiation pulse on the emission spectrum. For this purpose BB radiation having a Gaussian temporal profile was used,
Fig. 4. Evolution of fractions of charge states from C-like ion to bare nuclei in the time-dependent model with a Gaussian radiation pulse (red line). The radiation pulse is adapted as a Gaussian distribution with FWHM of 160 ps and =80 ps[13,16,20].
3.3 Model 3: steady-state optically thick model
Finally, the opacity effects were added into Model 3. Recently, in the experiment of Loisel et al. on photoionized silicon plasma, optical depth up to 60 was measured for the He-like resonance line. This indicates that reabsorption along the line between the point of emission and the measuring device in the photoionization experiment has to be taken into account. As the assumption of time dependence of the incident pulse could not account for the difference between the experimental and simulated spectra, in Model 3 a steady-state plasma was used, as in Model 1.
To account for the opacity effect, i.e., photon reabsorption (PR) on the way to the spectrometer, we used the escape probability[31] method, i.e.,
As the Einstein A coefficient is proportional to
Model 3 uses the same input parameters as Model 1. The red line in Figure 6 is the simulation result of Model 3. Compared with the optically thin model, the resonance line and the satellite line of the Li-like ion are reduced by PR so much that they are comparable to the intercombination line. It turns out that the result of Model 3 is much closer to the experimental spectrum than the previous results.
In Model 3, the column density of the He-like ion is
3.4 Line ratios
Now that the experimental spectrum is successfully explained by an optically thick model, the line ratios of He-
4 Conclusion
In this paper, the X-ray spectrum of photoionized silicon plasmas under the conditions of the Fujioka et al. photoionization experiment was investigated with a steady-state optically thin model, a time-dependent optically thin model and a steady-state optically thick model, respectively.
The following was found.
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Article Outline
Bo Han, Feilu Wang, David Salzmann, Jiayong Zhong, Gang Zhao. Emission mechanism for the silicon He-α lines in a photoionization experiment[J]. High Power Laser Science and Engineering, 2021, 9(1): 010000e9.