Plasma diagnostics using spectral lines from transitions in oxygen-like argon

.I. Qum. Spectmsc. Rndiot. F’rinted in Great Britain

PLASMA

Tmmfer

Vol. 39,

No. I,

pp. 57455,

1988

DIAGNOSTICS USING SPECTRAL LINES TRANSITIONS IN OXYGEN-LIKE ARGON

0022~4073/88 $3.00 + 0.00

Pergamon Journals Ltd

FROM

Y. T. LEE and K. J. REED University of California, Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.A. (Received 25 March 1987)

Abstraet-We have calculated spectral line intensities for transitions among the n = 2 and 3 states of oxygen-like argon ions. Detailed atomic structure data, including transition energies and rates for electric dipole, electric quadrupole and magnetic dipole transitions, were calculated using configuration interaction wavefunctions. A distorted wave approximation was used to determine elelctron collision excitation rates for transitions from levels in the 2p4 ground state configuration to levels in the n = 2 and 3 excited state configurations. We have identified density-sensitive line-intensity ratios for some of the transitions from the 3s, 3p, and 3d levels.

1. INTRODUCTION

Many laboratories are actively investigating radiation spectra emitted from high temperature/high density plasma such as those produced in gas-puff z-pinch machines and high-power laser experiments. I-’ Sp ectral lines from these plasmas can be useful temperature and density diagnostics. In a well-diagnosed plasma, information on the emission spectrum can also be used to test the accuracy of theoretical rate coefficients. Recently, time-resolved spectra from an oxygen-like argon plasma produced in a gas-puff z-pinch were measured in the wavelength range 15&2OOA.’ Over this wavelength range, the spectrum contains mostly the An = 0 (L-shell) transitions in ArX-ArXIV and some weak transitions for n = 34 of ArVI-ArVIII. The measured spectra show the predominance of oxygen-like Ar L-shell transitions. At the shorter wavelength region (A < 50 A), the emission spectrum also shows n = 3-2 transitions of oxygen-like Ar. In a recent experiment using a pulsed-power generator, the emission spectrum also shows significant L-shell emission from oxygen-like Kr ions.* Emission spectra from plasmas produced by laser irradiation of micro-dot targets also contain strong transitions from oxygen-like ions.g We have calculated intensities for spectral lines arising from transitions among the n = 2 and n = 3 states of oxygen-like Ar ions. The intensities of spectral lines from some of the transitions from the 3p levels relative to those from 3s and 3d levels are strongly dependent on electron density. Therefore, these line ratios are potential density diagnostics for plasmas. Calculations of spectral line intensities for some oxygen-like ions have been reported,‘&12 and other authors have discussed density-sensitive lines arising from transitions in oxygen-like ions. I3514 These studies, however, have been limited to transitions among n = 2 levels of oxygen-like ions. In the following sections, we discuss the calculation of transition energies and collisional and radiative rates. Comparison of our results with measurements will be presented. We use the collisional and radiative data to compute ion level populations and spectral line intensities. We also discuss spectral line-intensity ratios which are useful density diagnostics. 2. PROCEDURE

The ground state of an oxygen-like ion is a 2s22p4 configuration. The n = 2 complex also includes a 2s2p5 configuration and a 2p6 configuration. We have calculated energy levels for all of the terms arising from the configurations of the n = 2 complex. We have also calculated energy levels for all of the fine-structure terms associated with the 2s22p3 31, 2~2~~31 and 2~~31 configurations. Some of these are shown in Fig. 1. These were calculated with configuration interaction wavefunctions constructed with orbitals generated in a modified Thomas-Fermi potential. All of the atomic 57

Y. T. LEE and K. J.

REED

Fig. 1.Energy levels of oxygen-like argon ion. The numerical keys assigned to the levels are also indicated. Not all of the 86 levels used in the calculation are shown here.

structure data were calculated using the University College London code SUPERSTRUCTURE.‘6 With this code, we have also computed rates for electric dipole, electric quadrupole and magnetic dipole transitions. These rates are used with electron collisional rates to determine the excited state populations in the plasma. Cross sections for electron collisional excitation of the transitions from the ground state configuration to the 2~~31 excited state configurations were obtained using the University College London distorted wave code DSW.” Configuration interaction wavefunctions for the target were (4

10-14

10-15

1

0.6

0.8

0.6

1.0 Temperature

ild

0.8

Temperature

W

Fig. 2 (a and b)

I

I 1.0

2.0 (10’

4.0 eV)

Plasma diagnostics using spectral lines

‘II2

0.6 Temperature

(lo*

0.6

1.0 Temperature

2.0 (ld

1.0 Temperature

4.0 eV)

2.0 (10’

(2 P33P)

4.0

eV)

lo-l2 I!_0.6

0.6

0.6

eV)

(2 P4, - 3s,

0.8

1.0

Temperaturn

2.0

4.0

1

1102 eV)

Fig. 2. Electron collisional rate coefficient as a function of electron temperature.

calculated with SUPERSTRUCTURE as described above. Term coupling coefficients calculated with SUPERSTRUCTURE were used with the computer program JAJOM” to transform the DSW results from LS coupling to collision strengths in intermediate coupling. In Fig. 2 we show plots of some collision rate coefficients for oxygen-like argon. The major limitation of the distorted wave approximation is the neglect of couplings between the various channels for collisional excitation. These couplings can result in resonances which may enhance the cross sections for some transitions. While these effects may be important for some transitions among the n = 2 levels,

60

Y. T. LEE and K.

J.

REED

recent studies of electron impact excitation of oxygen-like krypton show that for n = 2-3 transitions, a simple two-state approximation should be adequate for calculating reliable cross sections.” We calculate ion-level populations in the plasma using the collisional-radiative model. In this model, the level populations are given by the solution of the following equations. 1 n,Ci + 1 n, CTk+ c AIk N’ = c n,C;, Nk + c n,C$Nk + c &Nk, (1) k>l kc/ k-z/ k>l k>l ( kc/ > where n, = electron density, N’ = population of level I, CL = coefficient for collisional excitation from level 1 to level k, Ci = coefficient for collisional deexcitation from level 1 to level k, A,k = radiative spontaneous emission rates from level 1 to level k. In this model, we assume that the plasma is optically thin and neglect the contributions to the level populations due to ionization and recombination processes. The last approximation is reasonable for the n = 3 levels since the electron collisional excitation rates from the ground state and the radiative spontaneous emission rates are larger than both the ionization and recombination rates by a factor of approx. 102. In some situations where the dielectronic recombination rate coefficients for the excited states are large, the model presented here is still useful for a plasma with nitrogen-like ion populations much less than the oxygen-like ion populations. This happens when these ionization stages are at the tail of the charge-state distribution. We also assume the plasma is at steady-state equilibrium. Although many laboratory plasmas are time-dependent, at the time of maximum emission, most of them are approximately at steady-state. Therefore, the model is useful in providing a reasonable population estimate. We calculate the populations of 80 levels belonging to the configurations 2s22p4, 2s2p5, 2p6, 2s22p33s, 2s22p33p, and 2s22p33d. We neglect the contributions to the population of these levels due to electron collisional deexcitation and radiative cascade from the upper levels of other configurations. Using a more detailed kinetic model, we have estimated the cascade contribution to these level populations to be < 30%. The electron collisional excitation rate coefficient for a transition from level I to level k is given in terIIIS of the collision strength R/k as ChZ

2.113 x 10p8cm3sIIlk

exp(

-

ElkOWlkTh

(2)

gi

where AElk = the transition energy, In = ionization energy of hydrogen and g, = statistical weight for level 1. The deexcitation rate coefficient Ci, is obtained using the detailed balance relation C:, =

(dgk)

c?k.

(3)

The accuracy of radiative spontaneous emission rates given by the code SUPERSTRUCTURE is better than 10%. We estimate the electron collisional rates to be generally accurate within 20%, although the accuracy for some of the dipole forbidden transitions may be more affected by neglect of resonance contributions. In general, we expect our results for the level populations to be accurate within a factor of 2. The collisional excitation rates for all the An = 1 transitions are computed using the collision strengths discussed above. The collisional excitation rates for transitions between the n = 2 states are also computed using collision strengths from a distorted wave calculation.lg We estimate the collisional excitation rates for the transitions among n = 3 states using a formula of Regemorter2’ with the effective Gaunt factor taken to be 1. 3. RESULTS

AND DISCUSSION

In Tables l(a)-(c) we list some of the strong transitions from the levels in the 2s22p33s, 2s22p33p, and 2s22p33d configurations to the levels in the ground state configuration 2s22p4. Also included in the tables are the wavelength (A) and oscillator strength associated with the transitions. Alphabetical keys for the transitions are also included. In these tables, we compare our calculated wavelengths to their experimentally determined values. The comparison shows our calculated wavelengths agree with measured values better than 1%.

61

Plasma diagnostics using spectral lines Table l(a). Transitions between 2.~~2~’ and 2.~~2~~3~configurations. Term

ey

Wavelength (A) (calculated)

Wavelength (A) (measured)

gf

0.073

3P*-3P2

31.68

3P2-3D3

38.41

38.6221

0.255

'D2-'P2

38.56

38.3322

0.148

3PO-3D,

38.64

38.8721

0.055

3P1-3D2

38.65

38. Jg2’

0.098

'D2-'02

39.30

39.492’

0.45

3P2-35,

39.50

39.752’

0.22

'SO-lP,

39.66

40.0421

0.143

3P,-35,

39.71

39.9E2'

0.12

3P0-3s1

39.73

40.0221

0.04

In Fig. 1, we show the energy levels for the terms of the oxygen-like argon ion. Also included in the figure are the numerical keys assigned to the energy levels. Not all of the energy levels used in the calculation are included in the figure. In Figs. 3(a)-(c), we plot the level populations as a function of electron density at an electron temperature of 160 eV. The populations associated with the levels in the configurations 2s22p33s, 2s22p33p and 2s22p33d are plotted separately. In these figures the populations are normalized such that the sum of all the level populations is unity. The electron temperature used in the calculation was chosen in order for the plasma to have appreciable population of oxygen-like ions. From these figures, we see some of the level populations in the 2s22p33p configuration are approximately independent of electron density between 10” and 1020cm-3. However, at these electron densities the level populations of the 2s22p33d configuration are approximately linearly dependent on electron density. This is also true for some of the levels in the 2s *3p 33s configuration. The reason for the different dependence on electron density is as follows. For the electron densities of interest here, the excited state level populations are approximately given by Table l(b). Transitions between 2.~~2~’ and 2.~~2~~3~configurations. Key

I

Term

Wavelength

I

(R)

Wavelength (A) (measured)

gf I

3P,-3P.

44.13

0.004

3P2-3D3

44.35

0.014

3P2-3P2

44.39

0.021

3P,-3Do

44.73

0.006

3P2-3D,

44.74

0.021

E

3P2-3F3

45.39

0.014

F

3P2-3D3

45.58

0.003

D

62

Y. T. LEE and K. J.

REED

Table l(c). Transitions between 2s22p4 and 2s22p43d configurations.

J

I

'D2-'P,

35.09

3P2-3D3

35.15

35.372'

1.12

3Po-3D,

35.32

35.702'

0.26

3P,-3D2

35.33

35.5a2'

0.533

'so-'P,

36.00

35.9621

2.15

0.532

1

I

IC

N’ = (N’n,C;; + SF)

C(A,k+ 4Cii) k

I

1 3

(4)

where ST represents the cascade contribution to the level populations. The cascade contribution to the levels in 2s22p3 3dconfiguration is < 20% and has been neglected in our calculation. However, the cascade contribution to the levels in the 2~~2~~3.9and 2s22p33p configurations is usually much larger and has been included in the calculation. The terms ST for these levels are approximately linear with electron density. For electron densities from lOI* to 1020cm-3, the radiative emission rates of the levels in the 2s22p3 3d configuration are much larger than the electron collisional deexcitation rates. Therefore, the level populations are approximately proportional to electron density. This is also true for some of the levels in the 2s22p33s configuration. In general, the levels which can go to levels in the ground configuration by a dipole transition are linearly dependent on electron density. However, for the levels in the 2s22p33p configuration, the radiative emission rates are much smaller and approximately equal to the electron collisional deexcitation rates at the electron densities of interest here. Therefore, the level populations are approximately independent of electron density. In Fig. 4, we plot the spectral line intensity arising from the transitions from the levels in the 2s22p33p, 2s22p33p, and 2s22p33d configurations to the levels in the ground state configuration. The alphabetical keys for the transitions are defined in Tables l(a)-(c). From these figures, we see that spectral line intensities from the levels in the 2s23p33s and 2s22p33d configurations are strongly dependent on the electron density, while the line intensities from the levels in the 2s2 3p33p configuration are relatively insensitive to the electron densities from 10” to 1020cm-3. Therefore, the line-intensity ratio for the transitions from 2s22p33s and 2s22p33d relative to the transition from 2s22p33p will be strongly dependent on electron density.

63

Plasma diagnostics using spectral lines

Electron density kmS3)

Electron density kmS3i

(a) Levels in 292~93s configuration.

3

1o-227

f

,,25u 101’

(b) Levels in 2s22p33p configuration.

10’8

10’9

loza

102’

Electron density (cm-‘) (c)

Levels in 2s’2p33d configuration.

Fig. 3. Normalized population for some levels in the 2.~~2~~31configuration as a function of electron density at an electron temperature of 160eV. The numbers are numerical keys assigned to the levels.

In Figs. 5(a) and (b), we plot the line-intensity ratios for the transitions from the levels in the configuration relative to the transitions from the levels in the 2s22p33s and 2s22p33d configurations, respectively. From these figures, we see that the ratios are strongly sensitive to the electron densities from lOI* to 1020cm-3 and, therefore, are useful density diagnostics for high density/high temperature plasmas. These line-intensity ratios are calculated for the electron temperature of 160 eV. We have done the same calculation for the following electron temperatures; 100, 120, 140, 180 and 200 eV and have found that the line ratios do not vary significantly. Similar results have been obtained recently for Ne-like argon ions.” 2s22p’3p

Fig. 4. Spectral line intensities for some transitions from the levels in the 2s22p331 configurations to the levels in the ground state configuration as a function of electron density at an electron temperature of 160 eV. The alphabetical keys for these transitions are defined in Tables 1-3.

Y. T. LEE and K. J.

64

1101710'8 Electron

I

1

,,,I

10'9 density

I

1020

REED

I

,,I

102’

lb

kme3)

I

I1II

10’8

III1

I

10’9

Electron

density

I

III

1om

102’

kme3)

Fig. 5. (a) Intensity ratio for the lines from some transitions from 2sz2p33s configuration relative to the lines from 2s22p33p configuration as a function of electron density at an electron temperature of 160 eV. (b) Intensity ratio for the lines from some transitions from 2s22p33d configuration relative to the lines from 2s22p33p configuration as a function of electron density at an electron temperature of 160 eV.

The line-intensity ratios presented here are calculated assuming that the plasma is optically thin. These line-intensity ratios are useful density diagnostics over the range of electron densities from 10” to 10zocme3. To estimate the opacity effects on these line-intensity ratios, we present in Table 2 the optical depths for these transitions. The plasma conditions are electron temperature 160 eV, ion temperature 100 eV, ion density 10” cmm3, electron density lOI cmP3 and plasma size 50 pm. These conditions are easily produced in a gas-puff z-pinch. From Table 2, we see that the optical depths for the transitions are of the order of unity or less at the ion density 1Ou cmm3. Therefore, the line-intensity ratios presented in Fig. 5 should be useful diagnostics for plasmas with ion densities < lo’* crn3. thank R. S. Walling for use of her fitting codes. Work Performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

Acknowledgements-We

Table 2. Optical depths for same transitions between n = 2 and 3 states.

Key

Term

Doppler

width

Optical

depth

(ev)

A

3P2-3P2

0.024

0.090

El

3P2-3D3

0.024

0.320

C

'D2-'P2

0.023

0.160

D

3P,-3P.

0.021

0.005

E

3P2-3F3

0.020

0.020

F

0.020

0.025

G

0.027

1.640

H

'D2-'F3

0.026

5.000

I

'D2-'F3

0.026

0.740

J

'D2-'P,

0.026

0.520

Plasma conditions: electron density lOi cm-‘, ion density IO’*cm-‘, electron temperature 160 eV, ion temperature 100 eV, and plasma size 50 pm.

Plasma diagnostics using spectral lines

65

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