Experimental tests are in progress to evaluate the accuracy of the modeled iron opacity at solar interior conditions, in particular to better constrain the solar abundance problem [S. Basu and H. M. Antia, Phys. Rep. 457, 217 (2008)]. Here, we describe measurements addressing three of the key requirements for reliable opacity experiments: control of sample conditions, independent sample condition diagnostics, and verification of sample condition uniformity. The opacity samples consist of iron/magnesium layers tamped by plastic. By changing the plastic thicknesses, we have controlled the iron plasma conditions to reach (1) Te = 167 ± 3 eV and ne = (7.1 ± 1.5)× 1021 cm−3, (2) Te = 170 ± 2 eV and ne = (2.0 ± 0.2) × 1022 cm−3, and (3) Te = 196 ± 6 eV and ne = (3.8 ± 0.8) × 1022 cm−3, which were measured by magnesium tracer K-shell spectroscopy. The opacity sample non-uniformity was directly measured by a separate experiment where Al is mixed into the side of the sample facing the radiation source and Mg into the other side. The iron condition was confirmed to be uniform within their measurement uncertainties by Al and Mg K-shell spectroscopy. The conditions are suitable for testing opacity calculations needed for modeling the solar interior, other stars, and high energy density plasmas.

1.
J. E.
Bailey
,
G. A.
Rochau
,
R. C.
Mancini
,
C. A.
Iglesias
,
J. J.
MacFarlane
,
I. E.
Golovkin
,
C.
Blancard
,
P.
Cosse
, and
G.
Faussurier
, “
Experimental investigation of opacity models for stellar interior, inertial fusion, and high energy density plasmas
,”
Phys. Plasmas
16
,
058101
(
2009
).
2.
A. N.
Cox
, “
The masses of Cepheid
,”
Annu. Rev. Astron. Astrophys.
18
,
15
(
1980
).
3.
C. A.
Iglesias
,
F. J.
Rogers
, and
B. G.
Wilson
, “
Reexamination of the metal contribution to astrophysical opacity
,”
Astrophys. J.
322
,
L45
(
1987
).
4.
C. A.
Iglesias
,
F. J.
Rogers
, and
B. G.
Wilson
, “
Opacities for classical Cepheid models
,”
Astrophys. J.
360
,
221
(
1990
).
5.
F. J.
Rogers
and
C. A.
Iglesias
, “
Equation of state and opacity of stellar plasmas
,” in
GONG 1992. Seismic Investigation of the Sun and Stars
, edited
by Timothy M.
Brown
(
ASP Conference Series
,
1993
), Vol.
42
,
p
155
.
6.
M.
Asplund
,
N.
Grevesse
, and
A. J.
Sauval
, “
The solar chemical composition
,” in
Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis in honor of David L. Lambert, ASP Conference Series
, edited by
Thomas G.
Barnes
 III
and
Frank N.
Bash
, Vol. 336 (
2005
).
7.
S.
Basu
and
H. M.
Antia
, “
Helioseismology and solar abundances
,”
Phys. Rep.
457
,
217
(
2008
).
8.
M.
Asplund
,
N.
Grevesse
,
A. J.
Sauval
, and
P.
Scott
, “
The chemical composition of the Sun
,”
Annu. Rev. Astron. Astrophys.
47
,
481
(
2009
).
9.
S.
Basu
and
H. M.
Antia
, “
Revisiting the issue of solar abundances
,”
J. Phys.: Conf. Ser.
440
,
012017
(
2013
).
10.
T.
Perry
,
P.
Springer
,
D.
Fields
,
D.
Bach
,
F.
Serduke
,
C.
Iglesias
,
F.
Rogers
,
J.
Nash
,
M.
Chen
,
B.
Wilson
,
W.
Goldstein
,
B.
Rozsynai
,
R.
Ward
,
J.
Kilkenny
,
R.
Doyas
,
L.
Da Silva
,
C.
Back
,
R.
Cauble
,
S.
Davidson
,
J.
Foster
,
C.
Smith
,
A.
Bar-Shalom
, and
R.
Lee
, “
Absorption experiments on x-ray-heated mid-Z constrained samples
,”
Phys. Rev. E
54
,
5617
(
1996
).
11.
S. J.
Davidson
,
J. M.
Foster
,
C. C.
Smith
,
K. A.
Warburton
, and
S. J.
Rose
, “
Investigation of the opacity of hot, dense aluminum in the region of its K edge
,”
Appl. Phys. Lett.
52
,
847
(
1988
).
12.
T.
Perry
,
S.
Davidson
,
F.
Serduke
,
D.
Bach
,
C.
Smith
,
J.
Foster
,
R.
Doyas
,
R.
Ward
,
C.
Iglesias
,
F.
Rogers
,
J.
Abdallah
,
R.
Stewart
,
J.
Kilkenny
, and
R.
Lee
, “
Opacity measurements in a hot dense medium
,”
Phys. Rev. Lett.
67
,
3784
(
1991
).
13.
J.
Foster
,
D.
Hoarty
,
C.
Smith
,
P.
Rosen
,
S.
Davidson
,
S.
Rose
,
T.
Perry
, and
F.
Serduke
, “
L-shell absorption spectrum of an open-M-shell germanium plasma: Comparison of experimental data with a detailed configuration-accounting calculation
,”
Phys. Rev. Lett.
67
,
3255
(
1991
).
14.
C.
Chenais-Popovics
,
M.
Fajardo
,
F.
Gilleron
,
U.
Teubner
,
J. C.
Gauthier
,
C.
Bauche-Arnoult
,
A.
Bachelier
,
J.
Bauche
,
T.
Blenski
,
F.
Thais
,
F.
Perrot
,
A.
Benuzzi
,
S.
Turck-Chieze
,
J. P.
Chièze
,
F.
Dorchies
,
U.
Andiel
,
W.
Foelsner
, and
K.
Eidmann
, “
L-band x-ray absorption of radiatively heated nickel
,”
Phys. Rev. E
65
,
016413
(
2001
).
15.
J. E.
Bailey
,
P.
Arnault
,
T.
Blenski
,
G.
Dejonghe
,
O.
Peyrusse
,
J. J.
MacFarlane
,
R. C.
Mancini
,
M. E.
Cuneo
,
D. S.
Nielsen
, and
G. A.
Rochau
, “
Opacity measurements of tamped NaBr samples heated by z-pinch X-rays
,”
J. Quant. Spectrosc. Radiat. Transfer
81
,
31
(
2003
).
16.
P.
Renaudin
,
C.
Blancard
,
J.
Bruneau
,
G.
Faussurier
,
J. E.
Fuchs
, and
S.
Gary
, “
Absorption experiments on X-ray-heated magnesium and germanium constrained samples
,”
J. Quant. Spectrosc. Radiat. Transfer
99
,
511
(
2006
).
17.
L.
Da Silva
,
B.
MacGowan
,
D.
Kania
,
B.
Hammel
,
C.
Back
,
E.
Hsieh
,
R.
Doyas
,
C.
Iglesias
,
F.
Rogers
, and
R.
Lee
, “
Absorption measurements demonstrating the importance of Δn = 0 transitions in the opacity of iron
,”
Phys. Rev. Lett.
69
,
438
(
1992
).
18.
P.
Springer
,
D.
Fields
,
B.
Wilson
,
J.
Nash
,
W.
Goldstein
,
C.
Iglesias
,
F.
Rogers
,
J.
Swenson
,
M.
Chen
,
A.
Bar-Shalom
, and
R.
Stewart
, “
Spectroscopic absorption measurements of an iron plasma
,”
Phys. Rev. Lett.
69
,
3735
(
1992
).
19.
G.
Winhart
,
K.
Eidmann
,
C. A.
Iglesias
,
A.
Bar-Shalom
,
E.
Mínguez
,
A.
Rickert
, and
S. J.
Rose
, “
XUV opacity measurements and comparison with models
,”
J. Quant. Spectrosc. Radiat. Transfer
54
,
437
(
1995
).
20.
P. T.
Springer
,
K. L.
Wong
,
C. A.
Iglesias
,
J. H.
Hammer
,
J. L.
Porter
,
A.
Toor
,
W. H.
Goldstein
,
B. G.
Wilson
,
F. J.
Rogers
,
C.
Deeney
,
D. S.
Dearborn
,
C.
Bruns
,
J.
Emig
, and
R. E.
Stewart
, “
Laboratory measurement of opacity for stellar envelopes
,”
J. Quant. Spectrosc. Radiat. Transfer
58
,
927
(
1997
).
21.
C.
Chenais Popovics
,
H.
Merdji
,
T.
Missalla
,
F.
Gilleron
,
J. C.
Gauthier
,
T.
Blenski
,
F.
Perrot
,
M.
Klapisch
,
C.
Bauche-Arnoult
,
J.
Bauche
,
A.
Bachelier
, and
K.
Eidmann
, “
Opacity studies of iron in the 15–30 eV temperature range
,”
Astrophys. J. Suppl. Ser.
127
,
275
(
2000
).
22.
C. A.
Iglesias
, “
Effects of backlight structure on absorption experiments
,”
J. Quant. Spectrosc. Radiat. Transfer
99
,
295
(
2006
).
23.
J.
Bailey
,
G.
Rochau
,
C.
Iglesias
,
J.
Abdallah
,
J.
MacFarlane
,
I.
Golovkin
,
P.
Wang
,
R.
Mancini
,
P.
Lake
,
T.
Moore
,
M.
Bump
,
O.
Garcia
, and
S.
Mazevet
, “
Iron-plasma transmission measurements at temperatures above 150 eV
,”
Phys. Rev. Lett.
99
,
265002
(
2007
).
24.
H.
Griem
, “
Semiempirical formulas for the electron-impact widths and shifts of isolated ion lines in plasmas
,”
Phys. Rev.
165
,
258
(
1968
).
25.
T. J.
Nash
,
G. A.
Rochau
, and
J. E.
Bailey
, “
Design of dynamic Hohlraum opacity samples to increase measured sample density on Z
,”
Rev. Sci. Instrum.
81
,
10E518
(
2010
).
26.
J. E.
Bailey
,
G. A.
Chandler
,
R. C.
Mancini
,
S. A.
Slutz
,
G. A.
Rochau
,
M.
Bump
,
T. J.
Buris-Mog
,
G.
Cooper
,
G.
Dunham
,
I.
Golovkin
,
J. D.
Kilkenny
,
P. W.
Lake
,
R. J.
Leeper
,
R.
Lemke
,
J. J.
MacFarlane
,
T. A.
Mehlhorn
,
T. C.
Moore
,
T. J.
Nash
,
A.
Nikroo
,
D. S.
Nielsen
,
K. L.
Peterson
,
C. L.
Ruiz
,
D. G.
Schroen
,
D.
Steinman
, and
W.
Varnum
, “
Dynamic hohlraum radiation hydrodynamics
,”
Phys. Plasmas
13
,
056301
(
2006
).
27.
G. A.
Rochau
,
J. E.
Bailey
,
R. E.
Falcon
,
G.
Loisel
,
T.
Nagayama
,
B. T.
Hutsel
,
R. C.
Mancini
,
I.
Hall
,
D. E.
Winget
,
M. H.
Montgomery
, and
D. A.
Liedahl
, “
ZAPP: The Z astrophysical plasma properties collaboration
,”
Phys. Plasmas
21
,
056308
(
2014
).
28.
B. L.
Henke
,
S. L.
Kwok
,
J. Y.
Uejio
,
H. T.
Yamada
, and
G. C.
Young
, “
Low-energy x-ray response of photographic films. I. Mathematical models
,”
J. Opt. Soc. Am. B
1
,
818
(
1984
).
29.
B. L.
Henke
,
F. G.
Fujiwara
,
M. A.
Tester
,
C. H.
Dittmore
, and
M. A.
Palmer
, “
Low-energy x-ray response of photographic films. II. Experimental characterization
,”
J. Opt. Soc. Am. B
1
,
828
(
1984
).
30.
H. R.
Griem
, “
Plasma spectroscopy in inertial confinement fusion and soft x-ray laser research
,”
Phys. Fluids B
4
,
2346
(
1992
).
31.
B. A.
Hammel
,
C. J.
Keane
,
M. D.
Cable
,
D. R.
Kania
,
J. D.
Kilkenny
,
R. W.
Lee
, and
R.
Pasha
, “
X-ray spectroscopic measurements of high densities and temperatures from indirectly driven inertial confinement fusion capsules
,”
Phys. Rev. Lett.
70
,
1263
(
1993
).
32.
J. E.
Bailey
,
G. A.
Chandler
,
S. A.
Slutz
,
I.
Golovkin
,
P. W.
Lake
,
J. J.
MacFarlane
,
R. C.
Mancini
,
T. J.
Burris-Mog
,
G.
Cooper
,
R. J.
Leeper
,
T. A.
Mehlhorn
,
T. C.
Moore
,
T. J.
Nash
,
D. S.
Nielsen
,
C. L.
Ruiz
,
D. G.
Schroen
, and
W. A.
Varnum
, “
Hot dense capsule-implosion cores produced by Z-pinch dynamic Hohlraum radiation
,”
Phys. Rev. Lett.
92
,
085002
(
2004
).
33.
J. E.
Bailey
,
G. A.
Rochau
,
R. C.
Mancini
,
C. A.
Iglesias
,
J. J.
MacFarlane
,
I. E.
Golovkin
,
J. C.
Pain
,
F.
Gilleron
,
C.
Blancard
,
P.
Cosse
,
G.
Faussurier
,
G. A.
Chandler
,
T. J.
Nash
,
D. S.
Nielsen
, and
P. W.
Lake
, “
Diagnosis of x-ray heated Mg/Fe opacity research plasmas
,”
Rev. Sci. Instrum.
79
,
113104
(
2008
).
34.
A.
Kramida
,
Y.
Ralchenko
,
J.
Reader
, and
NIST ASD Team
, “
NIST Atomic Spectra Database (version 5.1)
,” Technical Report,
2013
.
35.
M.
Baranger
, “
General impact theory of pressure broadening
,”
Phys. Rev.
112
,
855
(
1958
).
36.
E. W.
Smith
, “
A relaxation theory of spectral line broadening in plasmas
,” Ph.D. thesis (
University of Florida
,
1966
).
37.
H.
Griem
,
Spectral Line Broadening by Plasmas, Pure and Applied Physics Series
(
Academic Press
,
New York/London
,
1974
).
38.
R.
Tighe
and
C.
Hooper
, “
Stark broadening in hot, dense, laser-produced plasmas: A two-component, two-temperature formulation
,”
Phys. Rev. A
17
,
410
(
1978
).
39.
R. C.
Mancini
,
D. P.
Kilcrease
,
L. A.
Woltz
, and
C. F.
Hooper
, Jr.
, “
Calculational aspects of the Stark line broadening of multielectron ions in plasmas
,”
Comput. Phys. Commun.
63
,
314
(
1991
).
40.
S.
Alexiou
, “
Overview of plasma line broadening
,”
High Energy Density Phys.
5
,
225
(
2009
).
41.
C. A.
Iglesias
and
V.
Sonnad
, “
Robust algorithm for computing quasi-static stark broadening of spectral lines
,”
High Energy Density Phys.
6
,
399
(
2010
).
42.
E.
Stambulchik
and
Y.
Maron
, “
Plasma line broadening and computer simulations: A mini-review
,”
High Energy Density Phys.
6
,
9
(
2010
).
43.
J. J.
MacFarlane
,
I. E.
Golovkin
,
P. R.
Woodruff
,
D. R.
Welch
,
B. V.
Oliver
,
T. A.
Mehlhorn
, and
R. B.
Campbell
, “
Simulation of the Ionization Dynamics of Aluminum Irradiated by Intense Short-Pulse Lasers
,”
Proc. Inertial Fusion and Sciences Applications 2003
, edited by
B. A.
Hammelp
(
Amer. Nucl. Soc.
,
2004
), Vol.
457
.
44.
J. J.
MacFarlane
,
I. E.
Golovkin
,
P.
Wang
,
P. R.
Woodruff
, and
N. A.
Pereyra
, “
SPECT3D—A multi-dimensional collisional-radiative code for generating diagnostic signatures based on hydrodynamics and PIC simulation output
,”
High Energy Density Phys.
3
,
181
(
2007
).
45.
T.
Nagayama
,
R. C.
Mancini
,
R.
Florido
,
D.
Mayes
,
R.
Tommasini
,
J. A.
Koch
,
J. A.
Delettrez
,
S. P.
Regan
, and
V. A.
Smalyuk
, “
Investigation of a polychromatic tomography method for the extraction of the three-dimensional spatial structure of implosion core plasmas
,”
Phys. Plasmas
19
,
082705
(
2012
).
46.
D. E.
Goldberg
,
Genetic Algorithms in Search, Optimization and Machine Learning
, 1st ed. (
Addison-Wesley Longman Publishing Co., Inc.
,
Boston, MA, USA
,
1989
).
47.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes in C: The Art of Scientific Computing
, 2nd ed. (
Cambridge University Press
,
New York, NY, USA
,
1992
).
48.
S.
Hansen
,
J.
Bauche
,
C.
Bauchearnoult
, and
M.
Gu
, “
Hybrid atomic models for spectroscopic plasma diagnostics
,”
High Energy Density Phys.
3
,
109
(
2007
).
49.
R.
Florido
,
R.
Rodríguez
,
J. M.
Gil
,
J. G.
Rubiano
,
P.
Martel
,
E.
Mínguez
, and
R. C.
Mancini
, “
Modeling of population kinetics of plasmas that are not in local thermodynamic equilibrium, using a versatile collisional-radiative model based on analytical rates
,”
Phys. Rev. E
80
,
56402
(
2009
).
50.
C.
Iglesias
,
H.
DeWitt
,
J.
Lebowitz
,
D.
MacGowan
, and
W.
Hubbard
, “
Low-frequency electric microfield distributions in plasmas
,”
Phys. Rev. A
31
,
1698
(
1985
).
51.
G.
Loisel
,
J. E.
Bailey
,
G. A.
Rochau
,
G. S.
Dunham
,
L. B.
Nielsen-Weber
, and
C. R.
Ball
, “
A methodology for calibrating wavelength dependent spectral resolution for crystal spectrometers
,”
Rev. Sci. Instrum.
83
,
10E133
(
2012
).
52.
C.
Chenais-Popovics
,
C.
Fievet
,
J. P.
Geindre
,
I.
Matsushima
, and
J. C.
Gauthier
, “
Saturation effects in Kα absorption spectroscopy of laser-produced plasmas
,”
Phys. Rev. A
42
,
4788
(
1990
).
53.
G.
Zimmerman
,
D.
Kershaw
,
D.
Bailey
, and
J.
Harte
, “
LASNEX code for inertial confinement fusion (A)
,”
J. Opt. Soc. Am.
68
,
549
(
1978
).
54.
D.
Mihalas
,
Stellar Atmospheres, A Series of Books in Astronomy and Astrophysics
(W. H. Freeman
,
1978
).
55.
T.
Nagayama
,
J. E.
Bailey
,
G. A.
Rochau
,
S. B.
Hansen
,
R. C.
Mancini
,
J. J.
MacFarlane
, and
I.
Golovkin
, “
Investigation of iron opacity experiment plasma gradients with synthetic data analyses
,”
Rev. Sci. Instrum.
83
,
10E128
(
2012
).
You do not currently have access to this content.