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The Effects of Radiation Transport on Line Ratios Used as Temperature and Density Diagnostic

Steven H. Langer Christopher J. Keane

This paper was prepared for submittal to the 22nd Ancmalous Absorption Conference 1992

Lake Placid, NY July 12-17,1992

W- o i i July 1992

This is a preprint of a paper intended fo rpnh" cation in a journal orproeecdings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author.

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The Effects of Radiation Transport on Line Ratios used as Temperature and Density Diagnostics

Steven H. Langer Christopher J. Keane

Lawrence Livermore National Laboratory1

Abstract

The ability to diagnose the conditions in the fuel of an Inertial Con­finement Fusion (ICF) capsule is a fundamental requirement for progress in ICF. Current ICF experiments are concentrating on high convergence capsules, and capsules will be larger on the more power­ful lasers that are currently under development. Both of these devel­opments make it harder to diagnose fuel conditions because of the larger column density in the target. This has led to increased interest in the use of line ratios as temperature and density diagnostics. For a line ratio to be a good temperature diagnostic, the ratio must be rela­tively insensitive to density and vary strongly with temperature. Giv­en the atomic rates, it is relatively easy to find candidate line ratios in the coronal limit where all lines are optically thin.

In this paper, we consider the effects of optical depth on line ratios. We show that, even if both of the lines used in the ratio are optically thin, the line ratio can depend on optical depth effects if one of the lev­els involved in the line ratio is pumped by an optically thick line. We present results from several different radiation transport models and attempt to draw conclusions about whether it is possible to calculate the effects of optical depth accurately enough that line ratios can still be used as diagnostics. We also consider the effects of uncertainties in atomic rates on predicted line ratios.

Introduction The ratio of the strength of two atomic lines has been used as a den­

sity or temperature diagnostic for many years in astronomy and plas-

1. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

ma physics. Interest in the use of line ratios as diagnostics for 1CF targets has greatly increased in the last few years. This paper consid­ers some of the difficulties associated with turning line ratios into ro­bust diagnostics of ICF targets. The particular area we will consider is requirements for the accurate modeling of line ratios (i.e. establishing the connection between a measured line ratio and the corresponding temperature and/or density). The first step in modeling a line ratio is to obtain an accurate database of atomic energy levels and transition rates. In this paper we use a database obtained from the RATION code and a database originally intended for use with DCA.

The atomic databases used in this paper contain energy levels and statistical weights for various atomic configurations. In some configu­rations the levels are described only by the principal quantum num­ber n, other levels are described bv both n and 1, and some levels are described by n, 1, and j . Each database will select a set of configura­tions that are expected to be important for a given model and supply energies and rates for them. The configurations selected will cover the expected range of ionization states and will include ground states and selected excited states. A database contains energy levels, statistical weights, Einstein A-values, electron impact excitation rates, electron impact ionization rates, auto-ionization rates, and photoionization cross sections. These rates are used to derive rates for the inverse pro­cesses: radiative recombination, electron impact de-excitation, three-body recombination, di-electronic recombination, and free-bound emission.

RATION (Lee, Whitten, and Strout, 1984) is a code that contains a built-in atomic database. This database contains configuration aver­aged states (i.e. n and 1 quantum numbers) for helium-like species up through n=2 and for lithium-like species up through n=5. All other levels are described by quantum number n only. RATION contains ground state, singly excited, and auto-ionizing configurations. We will refer to this as the RATION database in the rest of this paper.

The other database includes full term splitting (i.e. n, 1, andj quan­tum numbers) for electrons in the n=l through n=4 levels of hydro­gen-, helium-, lithium-, and beryllium-like argon. Boron- through Nitrogen-like species are also included, but with fewer configurations. This database completely ignores any states with electrons in n=5 or above and contains ground state, singly excited, and auto-ionizing

configurations. We will refer to this as the "detailed" database throughout the rest of this paper

Once a database is available, the next step is to select a code to solve the population kinetics equations for the population for each configuration. In the absence of optical depth effects, the kinetics equations can be solved in each zone independently. For the problems we consider here, optical depth effects cannot be ignored, so all of the solvers we consider couple a solution of the radiative transfer equa­tion to the solution of the kinetics equation.

The RATION code solves the kinetics equations in one zone, but ig­nores radiation transport. DSP (Keane et al., 1991) is a spectral post­processor that incorporates the RATION database, detailed line shapes, continuum lowering, and a non-local escape probability mod­el to handle the effects of radiation transport. DSP can also be told to ignore all radiative excitations, which means that each zone is treated as an independent, optically thin problem. After the populations have been determined, DSP solves the radiation transport equations along a set of rays to compute the emerging spectrum. This ray transfer cal­culation always includes the optical depth, no matter what was used in the kinetics solution. Because DSP has the RATION database built in, it was not used with the detailed database.

DCA (Detailed Configuration Accounting, Lee, 1987) is a stand­alone code that solves the coupled kinetics and radiative transfer equations by a complete linearization method. DCA includes the ef­fects of continuum lowering. DCA is also available as a package built into LASNEX, and it is this version that is used in our calculations. DCA was run with both the RATION database and the detailed data­base. The LASNEX version makes the escaping spectrum available as part of the output from its SN radiation transfer package.

Xraser was originally developed to simulate x-ray lasers. Xraser solves the coupled kinetics and radiative transfer equations using a complete linearization method. Xraser ignores continuum lowering. After Xraser has determined the populations, the radiation spectrum is calculated along a set of rays by a separate code called Spectre. Xraser can be used with both the RATION and detailed atomic data­bases. At this time, Xraser/Spectre cannot correctly handle Stark broadening. In a future paper, we will compare Xraser to DSP and DCA LASNEX.

The Lvman beta and Hielium beta lines of argon are bright and are optically thin tor the conditions we consider. The ratio of the two is sensitive to temperature, so we will use the ratio of these two lines as our diagnostic for the rest of this paper. Many other line ratios are available, and many elements other than argon could be used. The choice of which line and element to use should be made on a case by case basis. The line ratio we have chosen is suitable for use in current ICF targets, and will serve to show the effects of interest in this paper.

Figure 1 shows the ratio of the strength of the Lyman beta line to the helium beta line as a function of temperature. Several curves cor­responding to different electron densities are shown. The dependence on temperature is much stronger than that on density. With the avail­able knowledge of the electron density, an observation of this line ra­tio permits an accurate determination of the temperature. The ratio shown in the figure is based on the assumption that the populations can be calculated without including the effects of absorbing radiation. The results presented below show that it is important to include radia­tive excitation processes.

Figure 2 shows the relationship between the width of the beta lines and the electron density. For these densities, the width is determined by Stark broadening. A line width of a few eV can be measured if the line is bright enough. This means that a density diagnostic can be ob­tained from the same lines that are used for the temperature diagnos­tic. The results shown in figures 1 and 2 are calculated using the RATION atomic data rates and the DSP kinetics code (Keane, Lee, and Grandy, 1991).

The Test Problem

We have chosen a test problem to study the effects of radiation transport and different atomic databases. The test problem consists of a sphere of deuterium gas with an ion density of 9x l0 2 3 cm"3 doped with 0.1 % of argon by number of atoms. The radius of the sphere is 30 um. The temperature at the center of the sphere is 2 keV dropping to 1 keV at the edge of the sphere. The temperature profile is parabolic with the profile flat at the origin. In a companion test problem, the temperature is 1.4 keV throughout the sphere (1.4 keV is the average temperature of the sphere in the main test problem). This sphere is large enough that the Lyman alpha and helium alpha lines are optical-

ly thick. We split the sphere into 15 equal size zones in our models (more zones could be used to achieve higher accuracy).

Figure 3 shows the spectrum calculated by DSP for the test prob­lem with a temperature gradient. Figure 4 shows the area around the beta lines and figure 5 shows the area around the alpha lines. The heli­um beta line is almost unaffected by the inclusion of optical depth ef­fects in the kinetics, while the Lyman beta line is significantly altered. This means that the ratio of helium beta to Lyman beta is significantly altered by including optical depth effects in the kinetics. The helium alpha and Lyman alpha lines are both optically thick, and both are sig­nificantly altered by including optical depth effects in the kinetics. Figures 6-8 repeat figures 3-5 except that the temperature of the sphere is held constant at 1.4 keV. The effects of optical depth are the same as for the case with a temperature gradient.

Figures 9-11 compare the spectra for the case with a temperature gradient to the case where the temperature is constant. Both curves in­clude the effects of optical depth in the kinetics calculation. The spec­tra are very similar. The largest difference is in the Lyman alpha line, which has a very large optical depth and thus only escapes from a thin layer near the sui face where the temperature is very different for the two models. This result suggests that the spectrum does not depend strongly on the temperature distribution within the sphere (note that the total thermal energy is the same for both spheres).

Figure 12 compares two DCA LASNEX runs, one with the RATION database and one with the detailed database. This run has much coarser frequency bins than the DSP runs, so less detail is present in the spectrum. In general, the two spectra are in good agreement, al­though the additional lines found in the detailed model are obvious. The continuum above 4200 eV indicates that the population of fully stripped argon disagrees by no more than a factor of two. Figure 13 shows that the helium beta and gamma lines are in good agreement, while the Lyman beta line is much brighter when using the detailed database. Figure 14 shows that the helium alpha lines are in good agreement, while the Lyman alpha line is much brighter when using the detailed database. In future work, we will attempt to decide whether the stronger hydrogen-like lines are due to the inclusion of splitting or whether the neglect of highly excited states in the detailed database changed the ionization balance.

Conclusions ( t\- c \ '< • -\-'. - >- \ -J J

We have shown that the effects of radiation transfer can significant­ly alter line ratios, even if both of the lines involved in the ratio are op­tically thin. In our test problem, the spectrum with a temperature gradient was nearly the same as the spectrum with a constant temper­ature. The spectra obtained with DCA LASNEX using the RATION database and the detailed database were quite similar for the helium­like lines, but significantly different for the hydrogen-like lines. These two databases have a different maximum principal quantum number (in addition to differing in the amount of detail within each level) and this could have a significant influence on the ionization state.

In future work, we will try to quantify these effects and to improve the models. One improvement in the models will to obtain better spa­tial resolution at the outer edge of the hot gas- Another change will be to properly include the effects of continuum lowering. We will also consider the effects of experimental uncertainty and detector sensitiv­ity on our ability to use line rados as temperature diagnostics.

References

Lee, Y.T., "A Model for Ionization Balance and L-Shell Spectroscopy of Non-LTE Plasmas," J. Quant. Spec. Rad. Tran., 38,131-145 (1987). (DCA database).

Lee, R.W., Whitten, B.L., and Strout, J.E. Ill, J. Quant. Spec. Rad. Tran., 32,91 (1984).

Keane, C.J., Lee, R.W., and Grandy, J.P., "DSP: A Detailed Spectroscopic Postpro­cessor for H-, He-, and Li-like Ions," Radiative Properties of Hot Dense Matter, Pro­ceedings of the 4th International Workshop, World Scientific Publishing Co. (1991), Edited by W. Goldstein, C. Hooper, J. Gauthier, J. Seely, and R.W. Lee.

Temperature(keV)

Figure 1. This figure shows the ratio of the strength of the Lyman beta line to the Helium beta line for the test sphere of argon described in the text. The dependence on electron temperature is shown for four electron densities. The dependence on temperature is much stronger than the de­pendence on density, so this line is usable as a temperature diagnostic. In many experiments it is possible to determine the density to a factor of three from the Stark width of these lines. As a result, the temperature can be determined to within 20% or better from a measured line ratio.

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20 40 60 30

FWHM (eV)

Figure 2. This figure shows the electron density corresponding to the line width for the Lyman beta (dashed and +) and Helium beta (solid and *) lines of argon. Fcr this range of densities, the line width is determined by Stark broadening and is independent of temperature.

F l u x

E-7

I. ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I

I • I . I • I • 1 3200 3400 3600 3800 4000 4200 4400

Energy(eV)

Figure 3. This figure shows the spectrum for the test problem as calculated by DSP. The temperature drops from 2 keV at the center of the sphere to 1 keV at the surface with a parabolic profile. The RATION atomic data base was used and the effects of radiative transfer are included in the solid curve and ignored in the dashed curve. Ignoring radiative excitations in the population kinetics leads to lower excited state populations. As a result, there is less emission in the "optically thin" case.

Flux

1.0

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0.6

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Figure 4. This figure shows the spectrum around helium-beta and lyman-beta lines for the test problem as calculated by DSP. The inclusion of optical depth effects in the population kinetics clearly significantly changed the line ratio, even though neither of these two lines is optically thick. The temperature drops from 2 keV at the center of the sphere to 1 keV at the surface with a para­bolic profile. The RATION atomic data base was used and the effects of radia­tive transfer are included in the solid curve and ignored in the dashed curve. Ignoring radiative excitations in the population kinetics leads to lower excited state populations. As a result, there is less emission in the "optically thin" case.

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Lyman Alpha

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Energy(eV)

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Figure 5. This figure shows the spectrum around helium-alpha and lyman-al-pha lines for the test problem as calculated by DSP. The temperature drops from 2 keV at the center of the sphere to 1 keV at the surface with a parabolic profile. The RATION atomic data base was used and the effects of radiative transfer are included in the solid curve and ignored in the dashed curve. Ignor­ing radiative excitations in the population kinetics leads to lower excited state populations. As a result, there is less emission in the "optically thin" case.

Flux

3200 3400 3600 3800 4000 4200 4400

Energy(eV)

Figure 6. This figure shows the spectrum for the test problem as calculated by DSP. The temperature is 1.4 keV throughout the sphere. The RATION atomic data base was used and the effects of radiative transfer are included in the solid curve and ignored in the dashed curve. Ignoring radiative excitations in the population kinetics leads to lower excited state populations. As a result, there is less emission in the "optically thin" case.

Flux

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3600 3700 3800 3900 4000

Energy(eV)

Eigwte 7. This figure shows the spettaim around the helium-beta and lyman-beta lines for the test problem as calculated by DSP. The inclusion of optical depth effects in the population kinetics clearly significantly changed the line ratio, even though neither of these two lines is optically thick. The 'emperatura is 1.4 keV throughout the sphere. The RATION atomic data base wus used and the effects of radiative transfer are included in the solid curve and ignored in the dashed curve. Ignoring radiative excitations in the population kinetics leads to lower excited stale populations. As a result, there is less emission in the "optically thin" case.

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figure 8. This figure shows the spectrum around helium-alpha aud iyman-a\-pha lines for the test problem as calculated by DSP. The temperature is 1.4 keV throughout the sphere. The RATION atomic data base was used and the effects of radiative transfer are included in the solid curve and ignored in the dashed curve. Ignoring radiative excitations in the population kinetics leads to lower excited state populations. As a result, there is less emission in the "optically thin" case.

Flux

3200 3400 3600 3800 4000 4200 4400 Energy(eV)

Figure 9. This figure shows the spectrum for the test problem as calculated by DSP. The temperature drops from 2 keV at the center of the sphere to 1 keV at the surface with a parabolic profile for the solid curve. The temperature is held constant at 1.4 keV for the dashed curve. The RATION atomic data base was used and the effects of radiative transfer are included. There is little change in the spectrum, suggesting that the spectrum is more sensitive to the average temperature, which is the same for both models, than to the temperature pro­file.

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3600 3700 3800 3900 4000 Energy(eV)

Figure 10. This figure shows the spectrum around the helium-beta and lyman-beta lines for the test problem as calculated by DSP. The temperature drops from 2 keV at the center of the sphere to 1 keV at the surface with a parabolic profile for the solid curve. The temperature is held constant at 1.4 keV for the dashed curve. The RATION atomic data base was used and the effects of radia­tive transfer are included. There is little change in the spectrum, suggesting that the spectrum is more sensitive to the average temperature, which is the same for both models, than to the temperature profile.

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" , , . , , [ w J Vj 3000 3100 3200 3300 3400 Energy(eV)

Figure 11. This figure shows the spectrum around the helium-alpha and lyman-alpha lines for the test problem as calculated by DSP. The temperature drops from 2 keV at the center of the sphere to 1 keV at the surface with a parabolic profile for the solid curve. The temperature is held constant at 1.4 keV for the dashed curve. The RATION atomic data base was used and the effects of radia­tive transfer are included. There is little change in the spectrum, suggesting that the spectrum is more sensitive to the average temperature, which is the same for both models, than to the temperature profile.

3000 3200 3400 3600 3800 4000 4200 4400 Energy(eV)

Figure 12. This figure shows the spectrum for the test problem as calculated by LASNEX. The temperature drops from 2 keV at the center of the sphere to 1 keV at the surface with a parabolic profile. The solid curve used the detailed database and the dashed curve used the RATION database. In general, the spectra are in good agreement, with some differences due to the additional lines in the detailed model.

Flux

2.0

E-14

1.5

1.0

0.5

I ' '— r '

Helium Beta

Helium Gamma

Lyman Beta

Vb„ _L 3600 3700 3800

Energy(eV)

3900 1000

Figure 13. This figure shows the spectrum around the helium-beta and lyman-beta lines for the test problem as calculated by LASNEX. The temperature drops from 2 keV at the center of the sphere to 1 keV at the surface with a para­bolic profile. The solid curve used the detailed database and the dashed curve used the RATION database. The helium beta lines are in good agreement, with significant differences for the Lyman beta line.

Flux

300C 3100 3200

Energy(eV)

i300 3400

Figure 14. This figure shows the spectrum around the heiium-aipha and lyman-alpha lines for the test problem as calculated by LASNEX. The temperature drops from 2 keV at the center of the sphere to 1 keV at the surface with a para­bolic profile. The solid curve used the detailed database and the dashed curve used the RATION database. The helium-alpha line is in good agreement, but the strength of the Lyman-alpha line is significantly different.