胡燕飛, 李青陽, 奚松國, 鄧邦林

(1.四川輕化工大學物理與電子工程學院， 四川 自貢 643000；2.成都理工大學地球物理學院物理系， 成都 610059)

Introduction

The temperature dependence of the ratio of the intensities of Li-like spectral lines from ions of various plasmas was a considerable theoretical subject[1-2]in recent several decades. For some hard to diagnose plasmas, such as some laser plasma[3]and for astrophysical plasma[4], the ratio is a very useful or even only diagnostic tool for determining their electron temperatures[5]. The kinetics processes are the origin of spectra lines of plasma, hence, the study of rate coefficients of kinetics processes is the groundwork of spectroscopic analysis[6]. Spectroscopic analysis is also an immediate, firsthand and more efficient method for diagnostics of temperature and density of astrophysical and lab plasma[7-9].

Neon is an abundant element on the Sun and other stars[10-12], and is also often used as carrier gas in laboratory experiments[13]. The theoretical study of neon spectra, especially Li-like neon, is very important and powerful for some laboratory and astrophysical works[14-17]. Ionization balance calculations and correct spectra of plasma are based on reliable rate coefficients of kinetics processes[18], such as collisional excitation (CE), dielectronic recombination (DR), resonance excitation (RE), radiative recombination (RR), and collisional ionization (CI). Moreover, the lineshape and intensity of plasma spectra are depend upon the density of plasma[19].

The aims of this paper are to provide some accurate theoretical parameters of the atomic kinetics processes and to calculate the ratios of the intensities of Li-like neon spectral lines. The present work is also a companion effort to studies of the relationship between the intensity of Li-like neon plasma spectra and the electron temperature as well as density of the plasma.

1 Theory

The interaction among the ions and atomic in the plasmas includes intricate processes of atomic physics and dynamics processes, which is the primary cause of X-ray radiation spectrum of plasma being produced[20-21]. In this letter, we use the flexible atomic code (FAC)[23]to simulate X-ray spectrum emission from Li-like neon plasma. FAC is an integrated software package to calculate various atomic radiative and collisional processes, and this package also includes a collisional radiative model (CRM) to construct synthetic spectra for plasmas under different physical conditions. First of all, we must establish a rate equation to calculate the rate of different atomic processes before simulating the X-ray spectra.

In low-density plasma, coronal models for collisionally ionized only includes CE from the ground state of each ion and the subsequent radiative cascades. Then, we can treat the spectra for different charge states separately. Several main collisional and radiative processes (CE, CI, RR, DR, and RE) are considered in the model. For simulating spectrum exactly, some indirect processes in the multi-ions model should involve the neighboring charge states (Ne6+and Ne8+, in this letter) of the target ion (Ne7+, in this letter). Hereby, the rate equations, involving statistical equilibrium and taking multi-ions atomic states into account, can be written minutely as:

(1)

wherenpjis the population of leveljin ionp,neis the electronic density. It also can be written simply as

(2)

(3)

Because Eq.(1) and Eq.(2) are the same equation just different form, it does not provide a unique solution. The usual way to solve the rate equations is to replace the Eq.(2) with the normalization condition. The normalization condition is:

(4)

In the actual operation, it is impractical and unnecessary that all important ionization and recombination channels of all charge states are included in Eq.(2). Namely, instead of all ions of the atomic elements, the normalization condition can be applied for each ion. The way is replacing the Eq.(2) within each ion with:

(5)

wherenqis the fractional abundance of ionqobtained from a separate ionization balance calculation, or equivalently, one can set

forq≠p, and replace the right side on Eq.(2) with a vector:

b=[n0,0,...,nq,0...]T

(6)

It turn the Eq.(2) into inhomogeneous, therefore, the Eq.(2) have a unique solution. Then, we can obtain the intensity of a emission line produced by radiative decay from statepitopj:

(7)

The number of double-excited states producing DR and resonance excitation (RE) far exceeds those directly responsible for line emission. Hence, we can not use a standard way which is easy and saving time to gain the solution of the rate equations. As Lucy (2001) proposed[23], a reduced atomic mode is introduced, which is constructed by grouping a large number of atomic states in a so-called superlevel. The density of the superlevel is defined as:

(8)

where the summation is over the all statesjto form the superlelvelJ.

(9)

where the summation overiandjincludes all the states forming superlevelsIandJ, respectively. If the original rate equations are satisfied with these definitions, the similar equations content the reduced atomic model and the solution of Eq.(2) also can be achieved iteratively. As described in Lucy(2001)[23], each iteration consists of four steps, and the iteration is terminated when the difference between the level populations in two consecutive steps is within 10-4.

Before simulating the spectra of neon plasma, we need analyze the total recombination and ionization rate coefficients obtained in this work and discuss the contributions of each process to the spectral lines.

2 Total rate coefficients

Before simulating the theoretical spectra of Li-like neon plasmas at different electron temperature and density, we should obtain the rate coefficients of the correlative atomic dynamics processes. The present total rate coefficients and some previous results of DR, RR, and CI are shown in Fig.1～Fig.3 respectively.

In Fig.1, we compare the present DR rate coefficients with the results of B?hm (2005) (B?hm05 in Fig. 1)[24]and Colgan (2004) (Colgan04 in Fig. 1)[25]. The present DR rates are consistent with those of Bohm05, and the difference between them is less than 20%. The present DR rates also agree with those of Colgan04 in a temperature range (T=106～106.7K).

Fig.1 The total DR rate coefficients of Ne VIII

Fig.2 shows the total present RR rate coefficients together with the results of Sultana (2006) (Sultana06 in Fig. 2)[26]and Badnell (2006) (Badnell06 in Fig. 2)[27]. The present rates are consistent with two previous results, and the results between present rates and Badnell06 are only a very small difference as shown in Fig.2.

Fig.2 The total RR rate coefficients of Ne VIII

The present total CI rate coefficients and the results of Rowan (1979) (Rowan79 in Fig.3)[28]as well as Wolfgang (1967) (Wolfgang67 in Fig.3)[29]are shown in Fig.3. The data of those are excellent in agree with very well, and there are only a minute difference among them. Especially, the difference between the present data and the Wolfgang66 can be ignored.

Fig.3 The total CI rate coefficients of Ne VIII

The present total rate coefficients (DR, RR, and CI), overall, are content with previous results, and the correct synthetic spectra are based on these reliable data.

3 The contributions of indirect processes

As mentioned before, lots of rate coefficients data for simulating spectra have been obtained. The next, we should consider the contributions of indirect processes to the spectral line. Fig.4 shows some ratios of the collective effects of DR+RR and RE to 3 s, 3 p, and 3 d excited states relative to direct CE. From the figure, one can easily find that the contributions of these indirect processes to the line emission and ionization balance are also very important and can’t be ignored. Obviously, the RE of 3 s, 3 p, and 3 d has more contributions than DR+RR. Relative to CE in lower temperature (T=105.4～106K), the RE contributions reaches 25% and DR+RR reaches 15%.

Fig.4 Rate coefficients of indirect processes relative to
direct CE for 3s, 3p, and 3d states

Besides the indirect processes, the contributions of cascade should be considered, as listed in Table 1. The contributions of all cascade are very important and can’t be neglected, in particularly, cascade is as important as or even more important than “CE”, “RE”, and “RR” for the lower levels (I=0, 1, and 2). “CS3” has more contributions than the cascades of other states for these lower levels. In addition, RR has more contributions than DR for the recombination effects in the low density neon plasmas, especially for the higher levels (I=3～7), and the contributions of cascades for the recombination are more important than DR and RR.

Table 1 Line-formation rate coefficients of neon L-shell ions

NEaIblogTcCoefficient/(10-10 cm3s-1)RTdCEeREeRReCE+CS3fCE+CSgRE+CSgDR+RR+CS3fDR+RR+CSg335.455.81E+103.76E-028.21E-039.66E-043.76E-023.79E-028.22E-039.72E-041.98E-03336.205.82E+101.68E+008.93E-024.02E-041.69E+001.81E+009.09E-024.04E-048.33E-04336.955.79E+101.73E+001.92E-021.37E-041.73E+002.04E+001.97E-021.40E-041.73E-03345.459.37E+106.18E-031.85E-031.03E-036.18E-036.59E-031.85E-031.03E-031.85E-03346.209.33E+104.90E-012.80E-023.41E-044.90E-016.04E-012.94E-023.41E-046.20E-04346.959.40E+101.11E+007.13E-037.19E-051.11E+001.29E+007.28E-037.19E-051.02E-03355.459.33E+101.22E-023.66E-032.06E-031.22E-021.30E-023.66E-032.06E-033.70E-03356.209.29E+109.69E-015.56E-026.79E-049.69E-011.20E+005.84E-026.79E-041.24E-03356.959.36E+102.20E+001.41E-021.43E-042.20E+002.56E+001.44E-021.43E-042.06E-03365.452.82E+111.99E-022.12E-031.09E-031.99E-022.03E-022.12E-031.09E-033.16E-03366.202.81E+111.18E+004.16E-022.44E-041.18E+001.30E+004.53E-022.44E-046.22E-04366.952.80E+111.49E+008.91E-033.18E-051.49E+001.68E+008.97E-033.18E-057.98E-04375.452.81E+112.98E-023.16E-031.64E-032.98E-023.05E-023.16E-031.64E-034.74E-03376.202.80E+111.76E+006.18E-023.65E-041.76E+001.95E+006.73E-023.65E-049.33E-04376.952.80E+112.24E+001.33E-024.77E-052.24E+002.52E+001.34E-024.77E-051.22E-03

Notes.-All rate coefficients are in units of 10-10cm3s-1.

aNumber of electrons of the ion, here NE=3.

bThe level index.

cThe base-10 logarithm of the temperature in units of kelvins. There are three types of electron temperature of neon plasma.

dThe total depletion rate of the state in units of s-1.

eThe rate coefficients without cascades.

fThe rate coefficients including only the cascade contributions from n=3 states.

gThe rate coefficients with all cascade contributions included

4 The spectra of Li-like Ne plasma

Based on these reliable rate coefficients, the synthetic spectra emitted from Ne VIII L-shell ions at different temperature are simulated and shown in Fig.5, the electron densityneof neon plasma is given as 1010cm-3, and used the Lorentz lineshape.

To illustrate the contributions of the indirect processes, in the Fig.5, three columns spectra correspond to different processes, the same column have the same type of processes, indicated by the label “Nion”, and the same row have the same electron temperature, indicated by the label “Te” in units of keV. The first column includes only CE and the subsequent radiative cascades, corresponding to the model including only one type of ion (Ne7+, “Nion=1” in Fig.5). The second column includes DR and RR as well, corresponding to two types of ions (Ne6+and Ne8+, “Nion=2”). The third column also includes the RE and CI, corresponding to three types of ions (Ne6+, Ne7+and Ne8+, “Nion=3”). From the first row to fourth row, the electron temperatureTeof neon plasma are 0.3 keV, 0.4 keV, 0.5 keV, 0.6 keV respectively.

The spectral lineshapes of the second and third columns are more refined than the first column as shown in Fig.5，in other words, DR, RR, RE, CI and cascade are as important or even more important than CE in spectra simulation of neon plasma. The intensities of spectral lines are very sensitive to the temperature of plasma, and they decrease as the temperature of plasma going up. The intensities of spectral lines at “Te=0.3 keV” are about 2 times of “Te= 0.4 keV”, and 5 times of “Te=0.5 keV”, as well as 10 times of “Te= 0.6 keV”.

Fig.5 Simulated spectra of neon L-shell ions

We expect that these conclusions could be used to diagnose the temperature of some thin neon plasma[26-27].

5 Conclusions

In this paper, the synthetic spectra of neon L-shell ions are simulated by FAC. It is found that DR, RR, RE, CI and cascade are as important as CE process, and can’t be ignored. The intensities of spectral lines are very sensitive to the temperature and density of neon plasma. We expect that the above-mentioned conclusions could be used to diagnose the temperature of some thin neon plasma, for example astrophysical sources, laser plasma and so on, and also could be used to provide theoretical forward-looking forecasts for some future experimental researches.