J. Plasma Fusion Res. SERIES, Vol.7 (2006) 131-134

Satellite Line Spectra of H-Like Mg Ions for
Plasma Diagnostics and Atomic Data
YAMAMOTO Norimasa∗ , KATO Takako1 and ROSMEJ Flank B.2
Rikkyo University, Tokyo 171-8501, Japan
1 National Institute for Fusion Science, Toki 509-5292, Japan
2 Universite de Provence et CNRS, Centre de Saint Jerome, PIIM, UMR 6633, 13397 Marseille cedex 20, France（Received: 30 October 2004 / Accepted: 10 January 2006）

Abstract
Electron temperatures have been determined using the ratio of satellite line intensities relative to the resonance line for various plasmas. In order to diagnose precisely, atomic data, wavelengths, radiative transition
rates, and autoionization rates, have been calculated. In this paper we have developed a new method to infer plasma temperature and density using only satellite lines, since Ly α lines are easily aﬀected by opacity.
Atomic data for satellite lines of H-like Mg are calculated using four diﬀerent codes and all four data sets arecompared with each other. We derived the electron temperature and density by analyzing spectra observed
from a laser-produced plasma using a high resolution spectrometer and comparing the observed spectra withthe theoretical spectra calculated with the four diﬀerent atomic data sets.
Keywords:
Satellite line, H-like Mg ion, radiative transition, autoionization, laser-produced plasma
1．Introduction
Dielectronic satellite lines are produced through adielectronic recombination process which strongly affects ion abundances of plasmas. The satellite lines produced by dielectronic recombination can be used to estimate the electron temperature and density of a plasma.
Previously, we analyzed observed satellite line spectra measured with a high resolution spectrometer [1,2].
In Ref. [1,2], we showed a new method to estimate
electron temperature and density by using only satellite
lines which are opacity free. In this paper, we compare
atomic data for satellite lines calculated by diﬀerent
four methods. We estimate the electron temperature anddensity from the measured spectra of laser-produced
plasma by using four diﬀerent data sets. The spectra
were measured using a high resolution spectrometer.

graph [3,4]. Figure 1 shows the measured X-ray spectra with Lyα and many satellite lines of H-like Mg. Toidentify the various satellite lines, we used data from
the MZ code [5,6]. Most of the strong satellite lines
are from 1s2l − 2l 2l transitions. Satellite lines for1s3l−2l 3l and 1s4l−2l 4l transitions were also measured. In this paper, we used following labels for thevarious satellite lines considered; A: 1s2p 3 P2 –2p2 3 P2 ,B: 1s2p 3 P1 –2p23 P2 , T: 1s2s 1 S0 –2s2p 1 P1 , Q: 1s2s 3 S1 –2s2p 3 P2 , R: 1s2s 3 S1 –2s2p 3 P1 , S: 1s2s 3 S1 –2s2p 3 P0 ,J: 1s2p 1 P1 –2p2 1 D2 , and f: 1s3d 1 D2 –2p3d 1 F3 [7].
3．Comparison of intensity factor Qd
In order to interpret the satellite line intensities in themeasured spectra, the precise values of intensity factors
Qd are necessary. The Qdij for satellite lines from state ito state j is defined by

2．Measured satellite line sapectra
High resolved X-ray spectra were measured at thenhelix-laser facility in GSI-Darmstadt. The laser used isa 100 J Nd-Glass Laser with a wavelength of 1.046 µm,a pulse width of 15 ns and energy of 17 J. Plasmas wereproduced by laser irradiated onto a massive Mg target at normal incidence with a focal spot diameter of
500 µm. X-ray spectra from the laser-produced plasma
were spatially resolved using a high resolution spectro-Qdij = 

gi Arij Aaik
 q,rp Aip + q Aiq(1)

where Arij is radiative transition probability from statei to state j, Aaik is autoionization rate from state i tostate k, and gi is statistical weight of state i. The
Qd value is proportional to the intensity of the satellite line at the low density limit. We compared four
diﬀerent theoretical data sets for Aa and Ar ; (1) MZ:Corresponding author’s e-mail: n-yamamoto@esi.nagoya-u.ac.jp∗ Present address: EcoTopia Science Institute, Nagoya University, Nagoya 464-8603, Japan131

C 2006 by The Japan Society of Plasma

Science and Nuclear Fusion ResearchSatellite Line Spectra of H-Like Mg Ions for Plasma Diagnostics and Atomic DataFig. 1 The measured spectra from our laser-produced plasma observed with a high resolution spectrometer

MZ code by Vainshtein and Safronova [5,6], (2) MBS:RMBPT (Relativistic Many Body Perturbation Theory)code by Safronova [8], (3) MBL: data based on the
many body theory by Lindroth [9], and (4) Hullac : Hullac code [10].
Figure 2 shows the comparison of Qd × P(λ) calculated using diﬀerent four data sets, where P(λ) is theVoigt profile. Figures 2(a), (b), (c), and (d) are the
1s2l−2l 2l , 1s3l−2l 3l , 1s4l−2l 4l , and 1s5l−2l 5lsatellite lines, respectively. Almost all of the Q d values
for the 1s2l − 2l2l satellite lines show good agreements
each other. The Qd values by MBS and MBL for line
A, which is a useful line for estimating the electron density, are 30 % smaller than that of MZ. Hullac is 43 %smaller than that of MZ. The intensity ratio of line A toline J (A / J) increases strongly with increasing electrondensity. Therefore the electron density estimated using
MBL data sets gives larger values than that using MZdata set. The various theoretical Qd values for strong
1s3l−2l 3l satellite lines agree to within 15 % with one
another except for the Hullac results which are smallerthat the other three calculation. This is because the Hullac Aa value for several of the Qd values is smaller thanthe other calculations. Line f is useful for estimating theelectron temperature. The MBS Qd value for this line is
7 % larger than the MZ result, The MBL value is 13 %smaller than the MZ result, and the HULLAC value is
25 % smaller than the MZ result. A smaller Qd value
for line f results in higher inferred temperatures whenthe electron temperature is estimated using the intensity
ratio of a line f to a line J (f / J). The diﬀerences between
the MBS, MBL, and HULLAC results are small for Qdfor the 1s4l − 2l 4l transitions. However, the MZ Qdvalues are larger than that of the other calculations. TheMZ Aa values for the 2p4f 3 P states are larger by 1-4orders of magnitude than those from the other calculations. For the 1s5l − 2l 5l transitions similar results ton = 4 are found.
4．Collisional-radiative model
We constructed a collisional-radiative model including doubly excited states for two-electron ions [11].
Our model includes singly excited 1snl states and doubly excited 2snl, 2pnl, 3snl, 3pnl, and 3dnl states. In
our model, excitation / de-excitation by electron impact,radiative transition, ionization / three-body recombination, radiative recombination, and autoionization / dielectronic capture are all included. We solved the following rate equations
dNi=−Wi j Ni +W ji N j ,dtjj(2)where Wi j is a total transition rate from i to j. The population density is calculated assuming quasi-steady state.
5．Estimation of Te and Ne used four data sets
We compared the measured spectra shown in Fig. 1
with the theoretical spectra calculated with the four different atomic data sets and estimated the electron temperature and density of laser-produced plasma. The
electron temperature is estimated by using the temperature dependence of the intensity ratio of line f to line
J [1,2]. This method uses only satellite lines which are
opacity free and can estimate the temperature more accurately than the method of using the intensity ratio of asatellite line to Lyα . For estimation of the electron den132

Satellite Line Spectra of H-Like Mg Ions for Plasma Diagnostics and Atomic Data

Fig. 2 Comparison of different four data sets for the predicted Q d × P (λ) values for (a) 1s2l – 2l’2l”, (b) 1s3l – 2l’3l”, (c)1s4l – 2l’4l”, (d) 1s5l – 2l’5l”. Solid, dotted, dot-dashed, and dot-dot-dashed line indicates those of MZ, MBS, MBL,and Hullac, respectively.

sity we use the density dependence of intensity ratio ofline A to line J.
Figure 3 (a) shows the measured spectra and Fig.
3 (b) shows the theoretical spectra with best fit parameters T e and Ne obtained using the MZ data set.
The best fit parameters for T e and Ne are 200 eV and5 × 1020 cm−3 , respectively. The T e and Ne derived byfitting spectra with the MZ data are lower than the value
obtained by other atomic data sets. Figure 3 (c) shows
the theoretical spectra with best fit parameter, T e andNe , obtained using MBS data set. Best fit parameters forT e and Ne are 200 eV and 6 × 1020 cm−3 , respectively.
The theoretical spectra with best fit parameters, T e andNe , obtained using the MBL data set are shown in Fig.
3 (d). Best fit parameters for T e and Ne are 230 eV and7 × 1020 cm−3 , respectively. These parameters are relatively higher than the results obtained using other different atomic data. Figure 3 (e) shows the theoretical
spectra with best fit parameters, T e and Ne , obtained using the Hullac data. Best fit parameters for T e and Ne
are 240 eV and 8 × 1020 cm−3 , respectively. We founda better spectral fit with MZ data than MBL, and MBSin 8.43 ∼ 8.44 Å (2l4l lines). However MBL and MBS
are better than MZ near 8.415 Å (2l4l and 2l5l lines).

produced plasma using our collisional-radiative modelusing four atomic data sets. When the measured spectra
are fitted by the theoretical spectra by MBL and Hullac
data, higher temperature and density are fitted using thetheoretical spectrafrom the MBL and HULLAC data,higher temperatures and densities are obtained from theintensity ratios of line f to line J and from line A to line
J than are those obtained using the MZ or MBS data.
We find that the structure of the theoretical spectra in
the wavelength range of 8.41 ∼ 8.46 Å is diﬀerent between the four data sets. This is due to the diﬀerence of
the atomic data for the 2l4l and 2l5l satellite lines

6．Results
We have used a new method for plasma diagnostics
involving intensity line ratios using only satellite lines.
We have compared four diﬀerent theoretical atomic data
sets for satellite line spectra of H-like Mg ions. We estimated T e and Ne from high resolution spectra of laser-[3]

Acknowledgements
The authers thank Drs. U. I. Safronova and E. Lindroth for providing their atomic data for our use. N.
Y. is partially supported by Grant-in-Aid for Scientific
Research (C) of Japan Society for the Promotion of Science, 16540221, 2004.

[1]
[2]

[4]
[5]

133

References
N. Yamamoto, T. Kato and F.B. Rosmej, NIFSDATA-88.
N. Yamamoto, T. Kato and F.B. Rosmej, J. Quant.
Spectrosc. Radiat. Transf. 96, 343 (2005).
F.B. Rosmej et al., J. Exp. Theor. Phys. Lett. 70,270 (1999).
F.B. Rosmej et al., Phys. Rev. A 63, 032716(2001).
L.A. Vainshtein and U.I. Safronova, At. Data
Nucl. Data Tables 25, 311 (1978).

Satellite Line Spectra of H-Like Mg Ions for Plasma Diagnostics and Atomic Data

Fig. 3 The measured and theoretical spectra with best ﬁt parameters using different data sets. (a) The measured spectra,(b) theoretical spectra with MZ atomic data, (c) with MBS, (d) with MBL, and (e) with Hullac. From (b) to (e), solid,
dotted and dot-dashed are sum of all lines, only satellite lines, and Lyα , respectively.

[6]
[7]
[8]
[9]

U.I. Safronova, private communications.
S.A. Pikuz et al., Phys. Rev. A 49, 3450 (1994).
U.I. Safronova, private communications.
M. Tokman et al., Phys. Rev. A 66, 012703(2002).

[10] A. Bar-Shalom, M. Klapisch and J. Oreg, Phys.
Rev. A 38, 1773 (1988).
[11] N. Yamamoto, T. Kato and T. Fujimoto, J. Plasma
Fusion Res. 78, 151 (2002).

134