(1)Iron opacity measurements on

Z at 150 eV temperaturesThanks to:

James E. Bailey, Sandia National Laboratories (jebaile@sandia.gov)

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy’s National Nuclear Security Administration

under contract DE-AC04-94AL85000.

with Fe + Mgwithout Fe

Warm Dense Matter Winter SchoolLawrence Berkeley National Laboratory

January 10-16, 2008

Wavelength-dependent opacity governs radiation transport that is critical in HED plasmas

• Bound-bound and bound free transitions in mid to high Z

elements dominate opacity

• As Z grows, the number of transitions becomes enormous

(~ 1-100 million line transitions in typical detailed calculations)

• Approximations are required and experimental tests are vital

• Example 1: Solar interior

• Example 2: Cu-doped Be ablator ICF capsule

Radiation controls heat transport in solar interior

T(eV) ne (cm-3) r/R0

1360 6x1025

293 4x1023

182 9x1022

54 1x1022

radiation convection

• boundary position depends on transport• measured with helioseismology

Solar model : J.N. Bahcall et al, Rev. Mod. Phys. 54, 767 (1982)

Transport depends on opacity, composition, ne, Te

0.55

0.90

0.7133

0

• measured boundary RCZ = 0.713 + 0.001

• Predicted RCZ= 0.726

• Thirteen difference

Bahcall et al, ApJ 614, 464 (2004).Basu & Antia ApJ 606, L85 (2004).

• Boundary location depends on radiation transport• A 1% opacity change leads to observable RCZ changes.• This accuracy is a challenge – experiments are needed to know if the solar problem arises in the opacities or elsewhere.

convection radiation

R/R0

Te (e

V)

ne

(cm

-3)

0.40.20.0 0.80.6 11022

1023

1024

1025

800

1200

400

0

Te

ne

Modern solar models disagree with observations. Why?

Transitions in Fe with L shell vacancies influence the radiation/convection boundary opacity

opac

ity (

cm2 /

g)

inte

nsity

(10

10 W

atts

/cm

2 /eV

)

h (eV)1000 1400600200

M-shell

b-f (excited states)

L-shell

104

106

0

1

2

103

104

2

4

0

solar interior182 eV, 9x1022 cm-3

Z conditions155 eV, 1x1022 cm-3

b-f (ground states)

105

105

103

Cu dopant is intended to control radiation flow into Be ICF capsule ablator

• Pre-heat suppression requires opacity knowledge in the 1-3 keV

photon energy range

• Tailoring the ablation front profile requires opacity knowledge in

vicinity of Planckian radiation drive maximum

• Cu transitions that influence the opacity are very similar to the Fe

transitions that control solar opacity near the radiation/convection

boundary

Goal of opacity experiments: test the physics foundations of the opacity models

Agreement at a single Te/ne value is difficult, but not sufficient

It is impractical to perform experiments over the entire Te/ne range

Therefore we seek to investigate individual processes:

1. charge state distribution

2. Term structure needed? Fine structure?

3. Principal quantum number range

4. Bundling transitions into unresolved arrays

5. Multiply excited states

6. Low probability transitions (oscillator strength cut off)

7. Bound free cross sections

8. Excited state populations

9. Line broadening

Anatomy of an opacity experiment

tamper (low Z)

sample

heating x-rays

backlighter

spectrometerspectrometer

Comparison of unattenuated and attenuated spectra determines transmissionT = exp –{x}

Model calculations of transmission are typically compared with experiments, rather than opacity. This simplifies error analysis.

Dynamic hohlraum radiation source is created by accelerating a tungsten plasma onto a low Z foam

tungsten plasma

4 mm

CH2 foamradiating shock

capsule

gatedX-ray

camera1 nsec

snapshots

radiating shock

The radiation source heats and backlights the sample

time (nsec)-20 -10 0 10

T (

eV)

0

100

200

300 h > 1 keVbacklightphotons

radiationtemperature

sample

radiationsource

X-rays

The dynamic hohlraum backlighter measures transmission over a very broad range

(Angstroms)

tran

smis

sion

4 6 8 10 12 14

Fe L-shell

Z1363-1364Fe+Mgsample

0.0

0.2

0.4

0.6

0.8

1.0

bound-free

Mg K-shell

Samples consist of Fe/Mg mixtures fully tamped with 10 m CH

backlighter

CH tamper Fe/Mg sample

spectrometer

heating x-rays

spectrometer

CH • Fe & Mg coated in alternating ~

100-300 Angstrom layers

• CH tamper is ~ 10x thicker than in typical laser driven experiments

• Compare shots with and without Fe/Mg to obtain transmission

• Mg serves as “thermometer” and density diagnostic

(Angstroms)

tran

smis

sion

Fe + Mg at Te ~ 156 eV, ne ~ 6.9x1021 cm-3

Fe XVI-XX

Mg XI

8.0 10.0 12.0 14.0

0.4

0.0

0.8

• Mg is the “thermometer”, Fe is the test element

• Mg features analyzed with PrismSPECT, Opal, RCM, PPP, Opas

Fe & Mg sample

radiationsource

X-rays

J.E. Bailey et al., PRL 99, 265002 (2007)

Z opacity experiments reach T ~ 156 eV, two times higher than in prior Fe research

Modern detailed opacity models are in remarkable overall agreement with the Fe data

h (eV)800 900 11001000 1200

Red = MUTAJ. Abdallah, LANL

Red = OPALC. Iglesias, LLNL

Red = PRISMSPECTJ. MacFarlane, PRISM

tran

smis

sio

n

Red = OPASOPAS team, CEA

0

0.4

0.8

0.0

0.4

0.8

0.0

0.4

0.8

0

0.4

0.8

The transmission is reproducible from shot to shot

7 9 11 12(Angstroms)

Inte

nsity

Z1650Z1649

• Both experiments used 10 m CH | 0.3 m Mg + 0.1 m Fe | 10 m CH sample

• No scaling was applied for this comparison

• Reproducibility is not always this extraordinary, but variations are less than approximately +10%

8 10

(Angstroms)

8.0 9.0 13.011.010.07.0 12.0 14.0 15.0

Multiple reproducible experiments enables averaging to improve transmission S/N

Fe L-shell

Z1466,1467,1646,1648,1649,1650,1651,1652,1653Fe+Mg

Mg K-shell

tran

smis

sion

0.4

0.0

0.2

0.6

0.8

1.0

Conclusions of present work

• The excellent agreement between PRISMSPECT and the measurements demonstrates a promising degree of understanding for both modeling and experiments

• Comparisons with the Los Alamos ATOMIC/MUTA and OPAL are just as good, if not better.

• Modern DTA opacity models are accurate, if sufficient attention is paid to setting up and running the code.

• With an accurate model in hand, the accuracy penalty imposed by various approximations used in applications can be investigated

• The Z dynamic hohlraum opacity platform is capable of accurate measurements in an important and novel regime

Future: evaluate impact of present data on solar models and design higher density experiments

• Question: Can this work tell us whether prior solar opacities were accurate to better than 20%?

• Construct Rosseland and Planck mean opacities

• Compare:

Data to modern detailed models

Data to prior models used in solar application

Modern models to prior models (extend h range)

• With reasonable understanding for this class of L-shell transitions, now we are ready for new experiments:

Increase density

Alter sample composition (e.g., Fe & O in CH2 plasma)