- Email: [email protected]
Radiation field effects on the spectroscopic properties of seeded plasmas
J. Qtuvtt. Spectrosc. Rodiat. Transfer Vol. 50, No. 1, pp. 91-101, 1993 Printed in Great Britain. All rights resewed
0022-4073/93 $6.00 + 0.00 Copyright 0 1993 Pergamon PESSLtd
RADIATION FIELD EFFECTS ON THE SPECTROSCOPIC PROPERTIES OF SEEDED PLASMAS J. ABDALLAHJR.~$, R. E. H. CLARK?,
C. J. KJZANE$, T. D. SHEPARD$, and L. J. SUTER~
tLos AlamosNational Laboratory, Theoretical Division, T-4, Mail Stop B212, Los Alamos, NM 87545 and &awrence
Livermore National Laboratory, University of California P.O. Box 808, Livermore, CA 94551, U.S.A. (Received 22 July 1992; received for publication
29 January
1993)
Abstract-The presence of an external radiation field can affect the level populations that occur in a high-temperature plasma. The level populations determine, in part, the emissivity of the medium. Hence, processes induced by the radiation field must be included in spectral simulations. In the present paper, the effect of black body radiation with temperatures of several hundred eV on mid-2 seeded plasmas, with electron temperature between 100 and 4000 eV, and electron densities between 10” and lo*’ cm-’ is studied. Particular attention is focused on line ratios which are commonly used for diagnostics. It is shown that the radiation field can have significant impact on the spectroscopic properties of plasmas under these conditions. A possible electron temperature diagnostic using iron is suggested for moderate radiation temperatures.
1. INTRODUCTION Comparisons often provide
actual experimental of theoretical spectral simulations and useful information concerning the state of a laboratory plasma.
observations The electron
temperature and density can be estimated from various spectral features, i.e., line ratios, line widths, background continuum, comparison with synthetic spectra, etc. These techniques are useful for a variety of applications including magnetic fusion, inertial confinement fusion, opacity determination, x-ray lasers, and astrophysics. These methods are discussed at length in several articles. ld The calculation of accurate ionization balance and level populations is of fundamental importance to any spectral simulation. Populations can be calculated using a variety of methods whose validity depends upon plasma conditions. Coronal equilibrium, in which ions exist in ground states only, is valid at low electron densities depending on the element.3 Local thermodynamic equilibrium (LTE) is valid at high electron densities, or when radiation is in equilibrium with thermal electrons. Collisional-radiative steady-state models which include excited states explicitly bridge the gap between coronal equilibrium and LTE. Time dependent kinetics is required for transient plasmas. The calculation of level populations is also directly dependent on the energy levels and cross sections that are used to describe the atomic processes which occur. These control the rate of population and depopulation of individual atomic levels. In principle, the coronal and collisional-radiative treatments should include radiation effects when fields are present. Photon induced processes should be accounted for in the rate equations. However, usually only electron collisions and spontaneous processes are considered. The radiation field introduces an additional mechanism for atomic excitation and ionization. The competition between electrons and photons varies as a function of electron density, electron temperature, and the applied radiation field strength. The purpose of the current work is to assess the effect of an intense background radiation field on the spectroscopic properties of a plasma as a function of electron temperature, density, and radiation temperature. A steady-state kinetics approach is used. Plasma conditions are chosen such $To whom all correspondence should be addressed. 91
J. ABDALLAH JR. et al
92
Table 1. Configurations used to generate the level structure for each of the ion stages included in the atomic model. The notation [ 1” means all possible distributions of w electrons in the shells specified inside the brackets. All possible allowed values of the orbital angular momentum quantum 1 are included. Be-like
w.r2PP ls[2s2p]3
Li-like
lsynr] [email protected]]‘nI
He-like
IS[?rl]’ D2P12
H-like
WI’
that K-shell emissions from ions with l-3 bound electrons are prevalent. The radiation field is taken to be black body with temperatures of several hundred electron volts. The plasma is considered to be optically thin for the present application. That is, plasma ions interact only with radiation from the applied field. Photons which are created through various atomic processes are assumed to escape the plasma without further interaction. The effect of radiation on various line ratios will be studied. Line ratios are intensity ratios of one line to another at a given electron density and temperature. Their behavior as a function of density and temperature can provide a rough diagnostic of plasma conditions without a complete analysis of a complicated spectrum. They also provide insight into the various processes which drive transitions. The computational method will be discussed in Sec. 2, results will be discussed in Sec. 3, and conclusions will be presented in Sec. 4.
1.0
0.8
2 ‘F;
0.6
: 2 5 ._
0.4
4 --.
0.2
3
0.0
0
600
1000
1600
2000
2600
electron temperature ( eV
3000
3600
4000
1
Fig. 1. Ion fractions (unitless) as a function of electron temperature for an electron density of 10r9.(-) correspondsto T’,=OeV,(. . . . . . ..) corresponds to T, = 200 eV. and (- - - -) corresponds to T, = 300 eV. The curves labeled by FS correspond to the fully stripped bare nucleus.
Radiation field effects on spectroscopic properties of plasmas
93
1,,~.1~.~11~~1~1~..~~~~~~I~.‘~‘~..~~..”~””
16.0 0
60
100
200
160
260
300
360
radiation temperature
400
460
600
( eV 1
Fig. 2. The mean ion charge Z as a function of radiation temperature for various electron densities at T, = IOOOeV. Each curve is labeled by the log,&. 2.
COMPUTATIONAL
METHOD
The atomic physics and kinetics programs used for this study have been described elsewhere.’ The net production rate of level p of ion stage i is given by
dN = dt
ip
&p((Njq},N,, T,, T,),
where Nip is the number density of ions in level p of ionicity i, (i = 1 represents the neutral atom, i = 2 represents the singly charged species, etc.) t is time, {Njq) represents the set of all levels that are involved in reactions with level ip, N, is the electron density, T, is the temperature which describes the electron energy distribution through the Maxwellian function, and T, is the radiation temperature that describes the photon energy distribution through the Plan&an black body function. Electron and photon distributions are restricted to Maxwellians and Planckians, respectively, for the purpose of this paper. The function F has the form
4p = C NhQpljqip - C NipQNipi4 3
@kl
(2)
(J4
where the first sum contains the contributions from all processes which populate level ip, and the second sum contains the contribution from all processes which depopulate level ip. QeiP. represents the rate coefficient for process c1which act on ion in level ip and leaves it in a final level jq. The rate coefficient is essentially the integrated cross section for a process weighted by the appropriate electron or photon distribution function. The coefficients Q include the appropriate factors of N, for processes initiated by electron collisions. They also depend on T, for processes initiated by electron collisions, T, for processes initiated by photon collisions, and on both T, and T, for processes like stimulated radiative recombination which involve both photons and free electrons. Rate coefficients are independent of distribution functions for spontaneous processes such as autoionization and spontaneous emission. Other processes, such as ion-ion collisions are beyond the scope of the present paper.
J. ABDALLAHJR. et al
94
The steady-state, or large time solution of Eq. (1) is given by Fip= 0.
(3)
If the free electron density N. is specified then Eq. (3) forms a system of linear algebraic equations which is solved assuming charge conservation, that is, ;(_+
l)N,=N,.
(4)
The resulting set of N,,rmay then be renormalized to any desired total ion density N. The solution of Eq. (3) provides level populations for given N,, T, and T,. These level populations may then be used to predict the spectroscopic properties of the plasma. For example, the intensity of a spectral line may be expressed as’ IM = N,A,E&,
(5)
where N&represents the population of level ip, A, is the Einstein A coefficient foi spontaneous emission from level ip to level iq, and Eb is the energy separation between levels ip and Q. The quantities A, and Eh are readily available from the atomic physics data and they are independent of N,, T,, and T,. It is often useful to form line ratios, (6) &W = &q/$&w~ which gives the intensity of one line relative to another at a given N,, T,, and T,. Hence, a line ratio can be extracted from an experimental measurement and compared to theoretical predictions to estimate the plasma conditions. A ratio which is approximately independent of electron density is a good temperature indicator, and vice versa. The processes included in Eq. (3) for the present study are photoexcitation, spontaneous decay, stimulated decay, electron collisional excitation, and de-excitation, photoionization, radiative
16.0L”“““““““““““‘.‘..‘....‘.‘l.’....’....J 100 0 60
160
200
260
300
radiation temperature
360
400
460
600
( eV )
Fig. 3. The mean ion charge Z as a function of radiation temperature for N, = 10’9cm-3 includea both photoionization and radiative excitation, (- - --) includes and T,=lOOOeV. ( -) photoionization without radiative excktion, and (. . . . . . . . . .) includes radiative excitation without photoionization.
Radiation field effects on spectroscopic properties of plasmas
95
E I E, Fig. 4. The cross section for ionization of the ground state of He-like chlorine as a function of energ); a: in thresholdunits. The curve labeledPI is the cross section for photoionization,and the curve labeled CI is the cross section for direct electron impact ionization.
recombination, stimulated radiative recombination, collisional ionization, three body recombination, autoionization, and dielectronic recombination. The cross sections for excitation and ionization are evaluated from the detailed atomic physics calculations discussed below. The rate coefficients for the reverse reactions are calculated using the principle of detailed balance. For T, = 0, the rate coefficients for photoexcitation, photoionization, and the contributions due to stimulated decay and stimulated radiative recombination are zero. All processes are followed individually, therefore, no net effective rate coefficients are introduced. For example, inner shell excitation, autoionization, dielectronic capture, and radiative decay are all included as separate processes. Table 1 summarizes the electron configurations which were used to model each of the ion stages included in the kinetics. Note that the calculations have been restricted to the Be-like, Li-like, He-like, and H-like ion stages, since those are the ions of interest for the density and temperature domain of the current study. Detailed atomic structure calculations using the method of Cowana” were performed to generate the set of fine structure energy levels corresponding to the configurations of Table 1. The structure calculations include intermediate coupling and configuration interaction. Each resulting level is denoted by total orbital angular momentum L, total spin S, and total angular momentum .I. The energy levels and wave functions produced by these calculations are used consistently to generate the required cross sections. Oscillator strengths were calculated for all possible level-to-level dipole allowed transitions. The oscillator strengths are used to evaluate the radiative excitation and de-excitation rate coefficients. Plane-Wave-Born (PWB) collision strengths8 were calculated for all possible pairs of level-to-level transitions for all ion stages considered. These strengths are used to calculate rate coefficients for electron collisional excitation and de-excitation. Distorted wave (DW) collision strengths’O were used for the most important transitions. These include all ls+nl in the H-like ion, all 1s2+ lsnl and ls21+ls21’ in the He-like ion and all ls22Z-+ls221’, ls221+ls2121’, and ls212l’+ls2121” in the L&like ion. DW cross sections were not used for the Be-like ion because transitions belonging QSRT Jo/l--o
J. ABDALLAH JR. et al
96
to this ion stage were not studied. The more accurate DW cross sections are required to yield more spectroscopically accurate results. Photoionization and autoionization cross sections were calculated for all possible level-to-level transitions between adjacent ion stages using the atomic structure wave functions discussed above with distorted wave type continuum wave functions. Level-to-level collisional ionization cross sections were calculated using the calculated fine structure energies and fits to scaled hydrogenic theory. ’ ’ 3. RESULTS
AND COMPARISONS
The methods described in the previous section were applied to chlorine and iron seeded plasmas. However, results are presented mainly for chlorine. The effect of radiation on level populations was studied. Ionization balance and line ratios were calculated as functions of radiation temperature, electron density, and electron temperature. Only several of the many possible choices of line ratios are presented here for the sake of brevity. Results were checked at random using the RATION coden which uses somewhat less detailed atomic physics. Both methods are in general agreement. 3.1. Ionization balance Figure 1 shows the ionization balance for chlorine as a function of electron temperature for an electron density of 10”. The figure shows the ionization balance for T, = 0, 200, and 300 eV. The fraction for an ion species i is given by
The figure shows that the ion distribution for T, = 200 eV is slightly more ionized than the T, = 0 results as expected. However, the T, = 300 eV radiation field produces dramatic change in the ionization state by stripping most nuclei of all bound electrons, even at very low electron 0.36
I”“I”“I”“I”“!““I”“I”“I”“I”“_
0.30
0.25
._0 !!
0.20
0.15
0.10
0.05
,,,,I,,~lI~~~~I~,~~I~~~~I,I,,I~~~~I~~~~I',,,I~~~~
0.00 0
50
100
150
200
250
300
radiation temperature
350
( eV
400
450
1
Fig. 5. The 3-1/2-l line ratio of He-like as a function of radiation temperature for various electron densities at an electron temperature of 1OOOeV.The curves are labeled by log,,N,.
500
Radiation field effects on spectroscopic properties of plasmas
97
10’
10"
._0
5
10-l
-----a__
16'
---___
--.__
----____
---_
--__
-__,_
I/ 19:
1O-3
0
( 500
I I I I I I I I I I I I I I I I I I I I I I I I * I I I I I 1000
1500
2000
2500
electron temperature
3000
( eV
3500
4000
1
Fig. 6. The chlorine #/He 2-1 line ratio as a function of electron. temperature at various electron densities. The solid curves correspond to T, = 0 at N. = 1019, Ido, I@‘, and 1022cme3. The curves are difficult to distinguish and are unlabeled. The dashed curves correspond to T, = 200 eV and are labeled by the log,,N,.
temperatures. The ion distribution has only a slight dependence on electron temperature indicating the dominance of photon collisions at T, = 300 eV and low electron density. Figure 2 is a plot of mean ion charge (Z) as a function of radiation temperature for various electron densities at T,= 1000 eV. The figure shows that low levels of radiation have little effect on the ionization state and gives an estimate of the radiation temperature required to alter the ionization state for a given density. It also illustrates how the effect of radiation decreases with increasing electron density. For example, at N, = 1022cmb3, the T,= 300 eV result differs only slightly from the T,= 0 result, in comparison to the large difference for N, = 10” noted above. Figure 3 is a plot of the mean ion charge as a function of radiation temperature for different models at N, - 10” cmd3 and T,= 1000eV. The solid line is the full model, the dashed line is the full model excluding radiative excitation, and the dotted line is the full model excluding photoionization. Hence the dashed line represents the role of photoionization while the dotted line represents the role of the radiative excitation in producing the plasma charge state. The full model and the photoionization model are in general agreement indicating that photoionization is more important than radiative excitation in establishing the ionization balance. It is also interesting to note that radiative excitation can actually retard rather than enhance plasma ionization. This occurs in Fig. 3 for relatively low radiation temperatures between about 100 and 200 eV. Here the radiative excitation of He-like metastables becomes important. The mechanism depletes metastable 1~2s levels via excitations to the 1~2~ levels which can undergo spontaneous decay to the ground state, resulting in decreased ionization. As the radiation temperature is increased, radiative excitation tends to enhance ionization, Note that all three models approach the fully stripped limit at large radiation temperature. Figure 4 is a comparison of the calculated photoionization and the electron collisional ionization cross sections for ionization from the ground state of He-like chlorine. The figure shows that photons are more effective “ionizers” if they have energies of less than about 3 in threshold units.
J.
98
ABDALLAH
JR. et al
However, the figure also shows that high-energy electrons are more effective than high-energy photons for producing ionization. Therefore, the dominating processes will be sensitive to the nature of the electron and photon distributions with respect to the relevant atomic ionization energies. 3.2. Line ratios Figure 5 shows the effect of radiation on the ls3p ‘P,-ls2’S,,/ls2P ‘PI-ls2’$ (3-1/2-l) line ratio of He-like chlorine (Cl XVI) for various densities at T, = 1000 eV. This ratio is mildly sensitive to electron temperature and provides useful information about the populations of different n levels for the same ion stage if optical depth effects are small. The ratios start out constant at values of T, near zero. At low electron density, as the radiation temperature is increased, the manifold of 2s-+3p transitions are pumped by photons and cause the ratio to increase by a factor of 3. The ratio begins to drop as 1s +2p transitions from the ground state become energetically possible. As the radiation temperature increases even further, the ratio begins to increase again due to direct excitation from ls+3p. As electron density increases, higher radiation temperatures must be attained to obtain these excitations because of increased photon-electron competition, and the curves are dispiaced toward the right. Also note that the variation of the curves decreases with increasing density. At N, = 1022cme3, the effect of 2s+3p photo-pumping becomes negligible. Figure 6 shows how an apparently good temperature diagnostic4 is affected by a radiation field. For this example, thejkZ/ls2p’P, - ls2’S,(jkZ/He 2-l) line ratio of Cl is considered. The notation jkl is used to specify the ls2p2*D-ls22p2P transition of the Li-like ion. The four solid curves represent the line ratios at 10“, 1O2O,102’, and 102’cme3 with T, = 0. Note that these curves are essentially independent of electron density, all of them practically lay on top of each other and hence provide an excellent temperature diagnostic. When a 200-eV radiation field (dashed curves) is applied the curves become nondegenerate. This is caused by photo-pumping of the n = 2 level by the radiation field. The effect is greatest for low electron densities and temperature. As electron density is increased, electron collisions become more dominant, and the effect of radiation 0.16
0.14 0.12 0.10 .;0
5
0.08 0.06 0.04 0.02 0.00 0
50
100
150
200
250
300
radiation temperature
350
( eV
400
450
)
Fig. 7. The chlorine &l/He 2-l line ratio as a function of radiation temperature for various densities at T, = 1000 eV. The curves are labeled by the log,&.
electron
500
Radiation field effects on spectroscopic properties of plasmas
99
ld 10’ 10"
0
ld
‘E;
2 lo'
10"
10-l
10"
0
500
1000
1500
2000
2500' 3000
electron temperature ( eV
3500
4000
1
Fig. 8. The chlorine He 2-l/H 2-I line ratio as a function of electron temperature for various values of radiation temperature at N, = 1019cm-3. The curves are labeled by radiation tempexature in eV.
decreases. Hence, it is difficult to infer a temperature from this line ratio when the plasma is in the presence of a radiation field. Figure 7 shows this line ratio as a function of radiation temperature at various densities. The electron temperature is fixed at T,= 1000eV. The figures predict the radiation temperatures where the Is+2p photopumping begins to have an effect on the line ratio. This occurs when the ratio begins to fall off rapidly. Note at low density, at JV,N lOi cm-‘, a bump occurs before the 13-2~ falloff. This enhancement is due to 2s+2P photoexcitation in the Li-like ion. Figure 8 shows the 1s2P’P1-1S*‘& 2p2P - ls2S
(8)
(He 2-l/H 2-l) line ratio for Cl as a function of electron temperature at N, = lOI cm-j. This ratio is a strong function of temperature because it depends mostly on the relative amounts of He-like ions to H-like ions through the ionization balance. The T,= 0 and T,= 100eV results are similar because the ionization balance is essentially unchanged by the radiation field. As T,is increased, the ionization balance is affected and these differences become apparent in the line ratio. The result for the line ratio involving the 3P upper level in the numerator and denominator of Eq. (8) is nearly identical to these results, since the ionization balance is the determining factor. It is sometimes advantageous to use the 3p line ratios as a diagnostic because of smaller optical depth effects. Note the line ratio has little practical diagnostic value at temperatures below 1000eV where it has very large values. Figure 9 shows the ls2P3P,-lS*‘S, lS2P ‘P,-lS*‘S, (IC/He 2-l) line ratio for He-like Cl as a function of electron density at T,= 1000eV. The
J.
100
AE~DALLAH
JR. et al
transition in the numerator is often referred to as the intercombination (IC) line. The ratio is normally considered to be density sensitive for T,= 0. Since the oscillator strength from the ls2P 3P,to the ground level is small (the transition is spin forbidden), population builds up in the 3Pmultiplet through electron collisions at low density. As the electron density is increased, further electron collisions depopulate the 'P,causing the line ratio to fall. The T,= 0 curve in Fig. 9 shows this behavior and the T,= 100eV case shows little difference. However, for T,= 200 eV, the line ratio at low density is significantly decreased because of strong photoexcitations from the ground state to the 'P,level. As electron density is increased from 10” cme3, the line ratio gets larger because the 3P state population increases due to electron collisions. At about N, = 10” cm-’ collisional depopulation occurs and the line ratio decreases causing a maximum in the curve. At T,= 300 eV, the line ratio is almost completely independent of electron density. Note that all curves approach the same limit as N, gets large because electron collision processes become dominant. The ratios of certain satellite lines of Li-like and He-like ions have been used to determine electron density.4 Usually, the upper level of one line is mainly populated by collisional excitation, and the other is fed by dielectronic capture, making the ratio sensitive to electron density. However, these ratios were found to have a small variation (less than a factor of 2) in the density range studied here, even in the presence of radiation. These ratios become better diagnostics at electron densities somewhat higher than those considered here. Similar calculations were also performed for iron. In general, the effect of radiation is greater for Cl than Fe due to the larger energy separations in Fe. For example, the 300 eV radiation field which can fully strip Cl, leaves iron mostly in the He-like ion stage. Lines from the H-like iron ion are impractical to use except at the highest electron temperatures. However, the abed/He 2-l line ratio in iron was found to exhibit reasonably good properties as an electron temperature diagnostic for moderate black body radiation fields with T,< 300 eV. The notation abed is the standard designation for the ls22p(2P)-ls2P2(2P) manifold of transitions in Li-like ions. Figure 10 shows this line ratio for T,= 200 eV and T,= 300 eV at various densities. This ratio appears to be a good diagnostic above T,= 500eV for T,= 200 eV. Unfortunately, there is a slight spread 0.6
I
I
I I
IIll]
I
I
llllll~
I
I
,
Illil-
0.4
0.3 .-0 + 2 0.2
0.1
0.0
10"
IO’”
electron
density
( cd’
)
Fig. 9. The chlorine He IC/H 2-l line ratio as a function of electron density for various of radiation temperatures at T, = lOI9cm-‘. The curves are labeled by radiation temperature in eV.
101
Radiation field effects on spectroscopic properties of plasmas
"oJ."""'."."""""'."'.*'."'
-
600
1000
1600
2000
2500
electron temperature
3000
3600
4000
( eV 1
Fig. 10. The abed/He 2-1 line ratio for iron as a function of electron temperature for various electron densities between 1OL9and ld* cmw3. (-) corresponds to T,=200 eV, and (----) corresponds to T, = 300 eV. The dashed curves are labeled by the log,&, while the solid curves are too close to be distinguishable.
in the ratio at high temperature due to density effects. At T, = 300 eV, it is a reasonable diagnostic for T, 2 1000 eV and N, 2 1020cmM3.This ratio is effective because both the abed and He 2-1 upper levels are pumped by radiation, and the ionization state varies slowly with electron temperature. 4.
CONCLUSIONS
An externally applied black body radiation field with temperatures of a few hundred electron volts can have a significant effect on the spectroscopic properties of low to mid-Z plasmas in the electron temperature and density range considered here. Radiation fields can have adverse effects on line ratios which are generally considered to be diagnostics of electron temperature and density in the absence of radiation. A possible diagnostic for electron temperature in a known radiation field is suggested. The authors would like to thank R. W. Lee for useful discussions and for making the RATION program available. This work was performed under the auspices of the U.S. Department of Energy. REFERENCES 1. 2. 3. 4.
5. 6. 7. 8. 9.
10. 11. 12. 13.
A. H. Gabriel and C. Jordan, Case Stud. Atom. Collision Phys. II, 211 (1972). R. Mewe and J. Schrijver, Astron. Astrophys. 65, 99 (1978). M. H. Key and R. J. Hutcheon, A& Atom. Molec. Phys. 16, 201 (1980). C. DeMichelis and M. Mattioli, Nucl. Fusion 21, 677 (1981). T. F. Stratton, Plasma Diagnostic Techniques, R. H. Huddlestone and L. L. Leonard, eds., p. 359, Academic Press. New York. NY (1965). R. W. Lee, B. i. Whitten, &d R: E. Stout, JQSRT 32, 91 (1984). J. Abdallah Jr., R. E. H. Clark and J. M. Peek, Phys. Rev. A 45, 3980 (1992). R. D. Cowan, Theory of Atomic Spectra, Univ. of California Press, Berkeley, CA (1981). J. Abdallah Jr., R. E. H. Clark, and R. D. Cowan, Los Alamos Manual No. LA-11436-M-1, 1988 (unpublished). R. E. H. Clark, J. Abdallah Jr., G. Csanak, J. B. Mann, and R. D. Cowan, Los Alamos Manual, LA-1 1436-M-11, 1988 (unpublished). R. E. H. Clark, J. Abdallah Jr., and J. B. Mann, Astrophys J. 381, 597 (1991). R. W. Lee, “User Manual for Ration,” Lawrence Livermore National Laboratory report, 1990. J. F. Seely, Atom. Data Nucl. Data Tables 26, 137 (1981).
0022-4073/93 $6.00 + 0.00 Copyright 0 1993 Pergamon PESSLtd
RADIATION FIELD EFFECTS ON THE SPECTROSCOPIC PROPERTIES OF SEEDED PLASMAS J. ABDALLAHJR.~$, R. E. H. CLARK?,
C. J. KJZANE$, T. D. SHEPARD$, and L. J. SUTER~
tLos AlamosNational Laboratory, Theoretical Division, T-4, Mail Stop B212, Los Alamos, NM 87545 and &awrence
Livermore National Laboratory, University of California P.O. Box 808, Livermore, CA 94551, U.S.A. (Received 22 July 1992; received for publication
29 January
1993)
Abstract-The presence of an external radiation field can affect the level populations that occur in a high-temperature plasma. The level populations determine, in part, the emissivity of the medium. Hence, processes induced by the radiation field must be included in spectral simulations. In the present paper, the effect of black body radiation with temperatures of several hundred eV on mid-2 seeded plasmas, with electron temperature between 100 and 4000 eV, and electron densities between 10” and lo*’ cm-’ is studied. Particular attention is focused on line ratios which are commonly used for diagnostics. It is shown that the radiation field can have significant impact on the spectroscopic properties of plasmas under these conditions. A possible electron temperature diagnostic using iron is suggested for moderate radiation temperatures.
1. INTRODUCTION Comparisons often provide
actual experimental of theoretical spectral simulations and useful information concerning the state of a laboratory plasma.
observations The electron
temperature and density can be estimated from various spectral features, i.e., line ratios, line widths, background continuum, comparison with synthetic spectra, etc. These techniques are useful for a variety of applications including magnetic fusion, inertial confinement fusion, opacity determination, x-ray lasers, and astrophysics. These methods are discussed at length in several articles. ld The calculation of accurate ionization balance and level populations is of fundamental importance to any spectral simulation. Populations can be calculated using a variety of methods whose validity depends upon plasma conditions. Coronal equilibrium, in which ions exist in ground states only, is valid at low electron densities depending on the element.3 Local thermodynamic equilibrium (LTE) is valid at high electron densities, or when radiation is in equilibrium with thermal electrons. Collisional-radiative steady-state models which include excited states explicitly bridge the gap between coronal equilibrium and LTE. Time dependent kinetics is required for transient plasmas. The calculation of level populations is also directly dependent on the energy levels and cross sections that are used to describe the atomic processes which occur. These control the rate of population and depopulation of individual atomic levels. In principle, the coronal and collisional-radiative treatments should include radiation effects when fields are present. Photon induced processes should be accounted for in the rate equations. However, usually only electron collisions and spontaneous processes are considered. The radiation field introduces an additional mechanism for atomic excitation and ionization. The competition between electrons and photons varies as a function of electron density, electron temperature, and the applied radiation field strength. The purpose of the current work is to assess the effect of an intense background radiation field on the spectroscopic properties of a plasma as a function of electron temperature, density, and radiation temperature. A steady-state kinetics approach is used. Plasma conditions are chosen such $To whom all correspondence should be addressed. 91
J. ABDALLAH JR. et al
92
Table 1. Configurations used to generate the level structure for each of the ion stages included in the atomic model. The notation [ 1” means all possible distributions of w electrons in the shells specified inside the brackets. All possible allowed values of the orbital angular momentum quantum 1 are included. Be-like
w.r2PP ls[2s2p]3
Li-like
lsynr] [email protected]]‘nI
He-like
IS[?rl]’ D2P12
H-like
WI’
that K-shell emissions from ions with l-3 bound electrons are prevalent. The radiation field is taken to be black body with temperatures of several hundred electron volts. The plasma is considered to be optically thin for the present application. That is, plasma ions interact only with radiation from the applied field. Photons which are created through various atomic processes are assumed to escape the plasma without further interaction. The effect of radiation on various line ratios will be studied. Line ratios are intensity ratios of one line to another at a given electron density and temperature. Their behavior as a function of density and temperature can provide a rough diagnostic of plasma conditions without a complete analysis of a complicated spectrum. They also provide insight into the various processes which drive transitions. The computational method will be discussed in Sec. 2, results will be discussed in Sec. 3, and conclusions will be presented in Sec. 4.
1.0
0.8
2 ‘F;
0.6
: 2 5 ._
0.4
4 --.
0.2
3
0.0
0
600
1000
1600
2000
2600
electron temperature ( eV
3000
3600
4000
1
Fig. 1. Ion fractions (unitless) as a function of electron temperature for an electron density of 10r9.(-) correspondsto T’,=OeV,(. . . . . . ..) corresponds to T, = 200 eV. and (- - - -) corresponds to T, = 300 eV. The curves labeled by FS correspond to the fully stripped bare nucleus.
Radiation field effects on spectroscopic properties of plasmas
93
1,,~.1~.~11~~1~1~..~~~~~~I~.‘~‘~..~~..”~””
16.0 0
60
100
200
160
260
300
360
radiation temperature
400
460
600
( eV 1
Fig. 2. The mean ion charge Z as a function of radiation temperature for various electron densities at T, = IOOOeV. Each curve is labeled by the log,&. 2.
COMPUTATIONAL
METHOD
The atomic physics and kinetics programs used for this study have been described elsewhere.’ The net production rate of level p of ion stage i is given by
dN = dt
ip
&p((Njq},N,, T,, T,),
where Nip is the number density of ions in level p of ionicity i, (i = 1 represents the neutral atom, i = 2 represents the singly charged species, etc.) t is time, {Njq) represents the set of all levels that are involved in reactions with level ip, N, is the electron density, T, is the temperature which describes the electron energy distribution through the Maxwellian function, and T, is the radiation temperature that describes the photon energy distribution through the Plan&an black body function. Electron and photon distributions are restricted to Maxwellians and Planckians, respectively, for the purpose of this paper. The function F has the form
4p = C NhQpljqip - C NipQNipi4 3
@kl
(2)
(J4
where the first sum contains the contributions from all processes which populate level ip, and the second sum contains the contribution from all processes which depopulate level ip. QeiP. represents the rate coefficient for process c1which act on ion in level ip and leaves it in a final level jq. The rate coefficient is essentially the integrated cross section for a process weighted by the appropriate electron or photon distribution function. The coefficients Q include the appropriate factors of N, for processes initiated by electron collisions. They also depend on T, for processes initiated by electron collisions, T, for processes initiated by photon collisions, and on both T, and T, for processes like stimulated radiative recombination which involve both photons and free electrons. Rate coefficients are independent of distribution functions for spontaneous processes such as autoionization and spontaneous emission. Other processes, such as ion-ion collisions are beyond the scope of the present paper.
J. ABDALLAHJR. et al
94
The steady-state, or large time solution of Eq. (1) is given by Fip= 0.
(3)
If the free electron density N. is specified then Eq. (3) forms a system of linear algebraic equations which is solved assuming charge conservation, that is, ;(_+
l)N,=N,.
(4)
The resulting set of N,,rmay then be renormalized to any desired total ion density N. The solution of Eq. (3) provides level populations for given N,, T, and T,. These level populations may then be used to predict the spectroscopic properties of the plasma. For example, the intensity of a spectral line may be expressed as’ IM = N,A,E&,
(5)
where N&represents the population of level ip, A, is the Einstein A coefficient foi spontaneous emission from level ip to level iq, and Eb is the energy separation between levels ip and Q. The quantities A, and Eh are readily available from the atomic physics data and they are independent of N,, T,, and T,. It is often useful to form line ratios, (6) &W = &q/$&w~ which gives the intensity of one line relative to another at a given N,, T,, and T,. Hence, a line ratio can be extracted from an experimental measurement and compared to theoretical predictions to estimate the plasma conditions. A ratio which is approximately independent of electron density is a good temperature indicator, and vice versa. The processes included in Eq. (3) for the present study are photoexcitation, spontaneous decay, stimulated decay, electron collisional excitation, and de-excitation, photoionization, radiative
16.0L”“““““““““““‘.‘..‘....‘.‘l.’....’....J 100 0 60
160
200
260
300
radiation temperature
360
400
460
600
( eV )
Fig. 3. The mean ion charge Z as a function of radiation temperature for N, = 10’9cm-3 includea both photoionization and radiative excitation, (- - --) includes and T,=lOOOeV. ( -) photoionization without radiative excktion, and (. . . . . . . . . .) includes radiative excitation without photoionization.
Radiation field effects on spectroscopic properties of plasmas
95
E I E, Fig. 4. The cross section for ionization of the ground state of He-like chlorine as a function of energ); a: in thresholdunits. The curve labeledPI is the cross section for photoionization,and the curve labeled CI is the cross section for direct electron impact ionization.
recombination, stimulated radiative recombination, collisional ionization, three body recombination, autoionization, and dielectronic recombination. The cross sections for excitation and ionization are evaluated from the detailed atomic physics calculations discussed below. The rate coefficients for the reverse reactions are calculated using the principle of detailed balance. For T, = 0, the rate coefficients for photoexcitation, photoionization, and the contributions due to stimulated decay and stimulated radiative recombination are zero. All processes are followed individually, therefore, no net effective rate coefficients are introduced. For example, inner shell excitation, autoionization, dielectronic capture, and radiative decay are all included as separate processes. Table 1 summarizes the electron configurations which were used to model each of the ion stages included in the kinetics. Note that the calculations have been restricted to the Be-like, Li-like, He-like, and H-like ion stages, since those are the ions of interest for the density and temperature domain of the current study. Detailed atomic structure calculations using the method of Cowana” were performed to generate the set of fine structure energy levels corresponding to the configurations of Table 1. The structure calculations include intermediate coupling and configuration interaction. Each resulting level is denoted by total orbital angular momentum L, total spin S, and total angular momentum .I. The energy levels and wave functions produced by these calculations are used consistently to generate the required cross sections. Oscillator strengths were calculated for all possible level-to-level dipole allowed transitions. The oscillator strengths are used to evaluate the radiative excitation and de-excitation rate coefficients. Plane-Wave-Born (PWB) collision strengths8 were calculated for all possible pairs of level-to-level transitions for all ion stages considered. These strengths are used to calculate rate coefficients for electron collisional excitation and de-excitation. Distorted wave (DW) collision strengths’O were used for the most important transitions. These include all ls+nl in the H-like ion, all 1s2+ lsnl and ls21+ls21’ in the He-like ion and all ls22Z-+ls221’, ls221+ls2121’, and ls212l’+ls2121” in the L&like ion. DW cross sections were not used for the Be-like ion because transitions belonging QSRT Jo/l--o
J. ABDALLAH JR. et al
96
to this ion stage were not studied. The more accurate DW cross sections are required to yield more spectroscopically accurate results. Photoionization and autoionization cross sections were calculated for all possible level-to-level transitions between adjacent ion stages using the atomic structure wave functions discussed above with distorted wave type continuum wave functions. Level-to-level collisional ionization cross sections were calculated using the calculated fine structure energies and fits to scaled hydrogenic theory. ’ ’ 3. RESULTS
AND COMPARISONS
The methods described in the previous section were applied to chlorine and iron seeded plasmas. However, results are presented mainly for chlorine. The effect of radiation on level populations was studied. Ionization balance and line ratios were calculated as functions of radiation temperature, electron density, and electron temperature. Only several of the many possible choices of line ratios are presented here for the sake of brevity. Results were checked at random using the RATION coden which uses somewhat less detailed atomic physics. Both methods are in general agreement. 3.1. Ionization balance Figure 1 shows the ionization balance for chlorine as a function of electron temperature for an electron density of 10”. The figure shows the ionization balance for T, = 0, 200, and 300 eV. The fraction for an ion species i is given by
The figure shows that the ion distribution for T, = 200 eV is slightly more ionized than the T, = 0 results as expected. However, the T, = 300 eV radiation field produces dramatic change in the ionization state by stripping most nuclei of all bound electrons, even at very low electron 0.36
I”“I”“I”“I”“!““I”“I”“I”“I”“_
0.30
0.25
._0 !!
0.20
0.15
0.10
0.05
,,,,I,,~lI~~~~I~,~~I~~~~I,I,,I~~~~I~~~~I',,,I~~~~
0.00 0
50
100
150
200
250
300
radiation temperature
350
( eV
400
450
1
Fig. 5. The 3-1/2-l line ratio of He-like as a function of radiation temperature for various electron densities at an electron temperature of 1OOOeV.The curves are labeled by log,,N,.
500
Radiation field effects on spectroscopic properties of plasmas
97
10’
10"
._0
5
10-l
-----a__
16'
---___
--.__
----____
---_
--__
-__,_
I/ 19:
1O-3
0
( 500
I I I I I I I I I I I I I I I I I I I I I I I I * I I I I I 1000
1500
2000
2500
electron temperature
3000
( eV
3500
4000
1
Fig. 6. The chlorine #/He 2-1 line ratio as a function of electron. temperature at various electron densities. The solid curves correspond to T, = 0 at N. = 1019, Ido, I@‘, and 1022cme3. The curves are difficult to distinguish and are unlabeled. The dashed curves correspond to T, = 200 eV and are labeled by the log,,N,.
temperatures. The ion distribution has only a slight dependence on electron temperature indicating the dominance of photon collisions at T, = 300 eV and low electron density. Figure 2 is a plot of mean ion charge (Z) as a function of radiation temperature for various electron densities at T,= 1000 eV. The figure shows that low levels of radiation have little effect on the ionization state and gives an estimate of the radiation temperature required to alter the ionization state for a given density. It also illustrates how the effect of radiation decreases with increasing electron density. For example, at N, = 1022cmb3, the T,= 300 eV result differs only slightly from the T,= 0 result, in comparison to the large difference for N, = 10” noted above. Figure 3 is a plot of the mean ion charge as a function of radiation temperature for different models at N, - 10” cmd3 and T,= 1000eV. The solid line is the full model, the dashed line is the full model excluding radiative excitation, and the dotted line is the full model excluding photoionization. Hence the dashed line represents the role of photoionization while the dotted line represents the role of the radiative excitation in producing the plasma charge state. The full model and the photoionization model are in general agreement indicating that photoionization is more important than radiative excitation in establishing the ionization balance. It is also interesting to note that radiative excitation can actually retard rather than enhance plasma ionization. This occurs in Fig. 3 for relatively low radiation temperatures between about 100 and 200 eV. Here the radiative excitation of He-like metastables becomes important. The mechanism depletes metastable 1~2s levels via excitations to the 1~2~ levels which can undergo spontaneous decay to the ground state, resulting in decreased ionization. As the radiation temperature is increased, radiative excitation tends to enhance ionization, Note that all three models approach the fully stripped limit at large radiation temperature. Figure 4 is a comparison of the calculated photoionization and the electron collisional ionization cross sections for ionization from the ground state of He-like chlorine. The figure shows that photons are more effective “ionizers” if they have energies of less than about 3 in threshold units.
J.
98
ABDALLAH
JR. et al
However, the figure also shows that high-energy electrons are more effective than high-energy photons for producing ionization. Therefore, the dominating processes will be sensitive to the nature of the electron and photon distributions with respect to the relevant atomic ionization energies. 3.2. Line ratios Figure 5 shows the effect of radiation on the ls3p ‘P,-ls2’S,,/ls2P ‘PI-ls2’$ (3-1/2-l) line ratio of He-like chlorine (Cl XVI) for various densities at T, = 1000 eV. This ratio is mildly sensitive to electron temperature and provides useful information about the populations of different n levels for the same ion stage if optical depth effects are small. The ratios start out constant at values of T, near zero. At low electron density, as the radiation temperature is increased, the manifold of 2s-+3p transitions are pumped by photons and cause the ratio to increase by a factor of 3. The ratio begins to drop as 1s +2p transitions from the ground state become energetically possible. As the radiation temperature increases even further, the ratio begins to increase again due to direct excitation from ls+3p. As electron density increases, higher radiation temperatures must be attained to obtain these excitations because of increased photon-electron competition, and the curves are dispiaced toward the right. Also note that the variation of the curves decreases with increasing density. At N, = 1022cme3, the effect of 2s+3p photo-pumping becomes negligible. Figure 6 shows how an apparently good temperature diagnostic4 is affected by a radiation field. For this example, thejkZ/ls2p’P, - ls2’S,(jkZ/He 2-l) line ratio of Cl is considered. The notation jkl is used to specify the ls2p2*D-ls22p2P transition of the Li-like ion. The four solid curves represent the line ratios at 10“, 1O2O,102’, and 102’cme3 with T, = 0. Note that these curves are essentially independent of electron density, all of them practically lay on top of each other and hence provide an excellent temperature diagnostic. When a 200-eV radiation field (dashed curves) is applied the curves become nondegenerate. This is caused by photo-pumping of the n = 2 level by the radiation field. The effect is greatest for low electron densities and temperature. As electron density is increased, electron collisions become more dominant, and the effect of radiation 0.16
0.14 0.12 0.10 .;0
5
0.08 0.06 0.04 0.02 0.00 0
50
100
150
200
250
300
radiation temperature
350
( eV
400
450
)
Fig. 7. The chlorine &l/He 2-l line ratio as a function of radiation temperature for various densities at T, = 1000 eV. The curves are labeled by the log,&.
electron
500
Radiation field effects on spectroscopic properties of plasmas
99
ld 10’ 10"
0
ld
‘E;
2 lo'
10"
10-l
10"
0
500
1000
1500
2000
2500' 3000
electron temperature ( eV
3500
4000
1
Fig. 8. The chlorine He 2-l/H 2-I line ratio as a function of electron temperature for various values of radiation temperature at N, = 1019cm-3. The curves are labeled by radiation tempexature in eV.
decreases. Hence, it is difficult to infer a temperature from this line ratio when the plasma is in the presence of a radiation field. Figure 7 shows this line ratio as a function of radiation temperature at various densities. The electron temperature is fixed at T,= 1000eV. The figures predict the radiation temperatures where the Is+2p photopumping begins to have an effect on the line ratio. This occurs when the ratio begins to fall off rapidly. Note at low density, at JV,N lOi cm-‘, a bump occurs before the 13-2~ falloff. This enhancement is due to 2s+2P photoexcitation in the Li-like ion. Figure 8 shows the 1s2P’P1-1S*‘& 2p2P - ls2S
(8)
(He 2-l/H 2-l) line ratio for Cl as a function of electron temperature at N, = lOI cm-j. This ratio is a strong function of temperature because it depends mostly on the relative amounts of He-like ions to H-like ions through the ionization balance. The T,= 0 and T,= 100eV results are similar because the ionization balance is essentially unchanged by the radiation field. As T,is increased, the ionization balance is affected and these differences become apparent in the line ratio. The result for the line ratio involving the 3P upper level in the numerator and denominator of Eq. (8) is nearly identical to these results, since the ionization balance is the determining factor. It is sometimes advantageous to use the 3p line ratios as a diagnostic because of smaller optical depth effects. Note the line ratio has little practical diagnostic value at temperatures below 1000eV where it has very large values. Figure 9 shows the ls2P3P,-lS*‘S, lS2P ‘P,-lS*‘S, (IC/He 2-l) line ratio for He-like Cl as a function of electron density at T,= 1000eV. The
J.
100
AE~DALLAH
JR. et al
transition in the numerator is often referred to as the intercombination (IC) line. The ratio is normally considered to be density sensitive for T,= 0. Since the oscillator strength from the ls2P 3P,to the ground level is small (the transition is spin forbidden), population builds up in the 3Pmultiplet through electron collisions at low density. As the electron density is increased, further electron collisions depopulate the 'P,causing the line ratio to fall. The T,= 0 curve in Fig. 9 shows this behavior and the T,= 100eV case shows little difference. However, for T,= 200 eV, the line ratio at low density is significantly decreased because of strong photoexcitations from the ground state to the 'P,level. As electron density is increased from 10” cme3, the line ratio gets larger because the 3P state population increases due to electron collisions. At about N, = 10” cm-’ collisional depopulation occurs and the line ratio decreases causing a maximum in the curve. At T,= 300 eV, the line ratio is almost completely independent of electron density. Note that all curves approach the same limit as N, gets large because electron collision processes become dominant. The ratios of certain satellite lines of Li-like and He-like ions have been used to determine electron density.4 Usually, the upper level of one line is mainly populated by collisional excitation, and the other is fed by dielectronic capture, making the ratio sensitive to electron density. However, these ratios were found to have a small variation (less than a factor of 2) in the density range studied here, even in the presence of radiation. These ratios become better diagnostics at electron densities somewhat higher than those considered here. Similar calculations were also performed for iron. In general, the effect of radiation is greater for Cl than Fe due to the larger energy separations in Fe. For example, the 300 eV radiation field which can fully strip Cl, leaves iron mostly in the He-like ion stage. Lines from the H-like iron ion are impractical to use except at the highest electron temperatures. However, the abed/He 2-l line ratio in iron was found to exhibit reasonably good properties as an electron temperature diagnostic for moderate black body radiation fields with T,< 300 eV. The notation abed is the standard designation for the ls22p(2P)-ls2P2(2P) manifold of transitions in Li-like ions. Figure 10 shows this line ratio for T,= 200 eV and T,= 300 eV at various densities. This ratio appears to be a good diagnostic above T,= 500eV for T,= 200 eV. Unfortunately, there is a slight spread 0.6
I
I
I I
IIll]
I
I
llllll~
I
I
,
Illil-
0.4
0.3 .-0 + 2 0.2
0.1
0.0
10"
IO’”
electron
density
( cd’
)
Fig. 9. The chlorine He IC/H 2-l line ratio as a function of electron density for various of radiation temperatures at T, = lOI9cm-‘. The curves are labeled by radiation temperature in eV.
101
Radiation field effects on spectroscopic properties of plasmas
"oJ."""'."."""""'."'.*'."'
-
600
1000
1600
2000
2500
electron temperature
3000
3600
4000
( eV 1
Fig. 10. The abed/He 2-1 line ratio for iron as a function of electron temperature for various electron densities between 1OL9and ld* cmw3. (-) corresponds to T,=200 eV, and (----) corresponds to T, = 300 eV. The dashed curves are labeled by the log,&, while the solid curves are too close to be distinguishable.
in the ratio at high temperature due to density effects. At T, = 300 eV, it is a reasonable diagnostic for T, 2 1000 eV and N, 2 1020cmM3.This ratio is effective because both the abed and He 2-1 upper levels are pumped by radiation, and the ionization state varies slowly with electron temperature. 4.
CONCLUSIONS
An externally applied black body radiation field with temperatures of a few hundred electron volts can have a significant effect on the spectroscopic properties of low to mid-Z plasmas in the electron temperature and density range considered here. Radiation fields can have adverse effects on line ratios which are generally considered to be diagnostics of electron temperature and density in the absence of radiation. A possible diagnostic for electron temperature in a known radiation field is suggested. The authors would like to thank R. W. Lee for useful discussions and for making the RATION program available. This work was performed under the auspices of the U.S. Department of Energy. REFERENCES 1. 2. 3. 4.
5. 6. 7. 8. 9.
10. 11. 12. 13.
A. H. Gabriel and C. Jordan, Case Stud. Atom. Collision Phys. II, 211 (1972). R. Mewe and J. Schrijver, Astron. Astrophys. 65, 99 (1978). M. H. Key and R. J. Hutcheon, A& Atom. Molec. Phys. 16, 201 (1980). C. DeMichelis and M. Mattioli, Nucl. Fusion 21, 677 (1981). T. F. Stratton, Plasma Diagnostic Techniques, R. H. Huddlestone and L. L. Leonard, eds., p. 359, Academic Press. New York. NY (1965). R. W. Lee, B. i. Whitten, &d R: E. Stout, JQSRT 32, 91 (1984). J. Abdallah Jr., R. E. H. Clark and J. M. Peek, Phys. Rev. A 45, 3980 (1992). R. D. Cowan, Theory of Atomic Spectra, Univ. of California Press, Berkeley, CA (1981). J. Abdallah Jr., R. E. H. Clark, and R. D. Cowan, Los Alamos Manual No. LA-11436-M-1, 1988 (unpublished). R. E. H. Clark, J. Abdallah Jr., G. Csanak, J. B. Mann, and R. D. Cowan, Los Alamos Manual, LA-1 1436-M-11, 1988 (unpublished). R. E. H. Clark, J. Abdallah Jr., and J. B. Mann, Astrophys J. 381, 597 (1991). R. W. Lee, “User Manual for Ration,” Lawrence Livermore National Laboratory report, 1990. J. F. Seely, Atom. Data Nucl. Data Tables 26, 137 (1981).