Polychromatic tomography of high-energy-density plasmas

HEDSA Symposium, November 1st, 2009, Atlanta, GA

R. C. ManciniPhysics Department, University of Nevada, Reno

Students and collaborators

• Former students: Igor Golovkin (Prism), Leslie Welser (LANL) • Current students: Taisuke Nagayama, Heather Johns• Post-doc: Ricardo Florido

• S. Louis, Computer Science Dep., UNR• R. Tommasini, N. Izumi, J. Koch, LLNL• J. Delettrez, F. Marshall, S. Regan, V. Smalyuk, LLE• J. Bailey, G. Rochau, SNL

Spatial structure of high-energy-density plasmas

• Theory and modeling of x-ray line emission from tracers in plasmas: ─ collisional-radiative atomic kinetics, ─ detailed Stark-broadened line shapes including ion dynamic effects,─ spectroscopic quality radiation transport.

• Instrumentation and spectroscopic data:─ GEKKO XII implosions: XMFC (toroidally bent crystal) x-ray imger1,2

─ OMEGA indirect-drive implosions: MMI (pinhole array) x-ray imager3

− Z implosions: TREX slit x-ray spectrometer− OMEGA direct-drive implosions: DDMMI (pinhole array) x-ray imager

• Data analysis methods need to solve an inversion problem:─ quasi-analytic methods,− multi-objective search & reconstruction driven by genetic algorithms,− analysis of spatially-resolved line spectra.

1I. Golovkin, R. Mancini, S. Louis, Y. Ochi, K. Fujita, H. Nishimura, H. Shirga, N. Miyanaga, H. Azechi, R. Butzbach et al, Phys. Rev. Letters 88, 045002 (2002)2Y. Ochi, I. Golovkin, R. Mancini, I. Uschmann, A. Sunahara, H. Nishimura, K. Fujita, S. Louis, M. Nakai, H. Shiraga, N. Miyanaga et al, Rev. Sci. Instrum. 74, 1683 (2003)3L. Welser-Sherrill, R. Mancini, J. Koch, N. Izumi, R. Tommasini, S. Haan, D. Haynes, I Golovkin, J. MacFarlane, J. Delettrez et al, Phys. Rev. E 76, 056403 (2007)

Implosion cores: significant progress has been made in three areas

Z-pinch dynamic-hohlraum experiments

• Capsule implosion driven by a z-pinch dynamic-hohlraum1

• Nested W (Ti) wires, 240/120 wires, 40/20 mm diameter, 12 mm tall pinch

• Radiation temperature 220 eV• Plastic capsule absorbs 20-40 kJ of X-ray energy• Plastic shell, diameter/wall thickness (mm/m): 2/50 z1155, 2/70 z1467• Gas fill: 20-25 atm of D2 doped with 0.085 atm of Ar• At the implosion collapse, Ar line emission is observed for over 1 ns• Several quasi-orthogonal LOS: parallel to z-axis (trex1), and on plane

perpendicular (trex2/trex5) to z-axis• Space- and time-resolved argon line spectra from implosion core• Argon K-shell line spectra from n = 2, 3, 4 and 5 in H- and He-like ions,

and associated He- and Li-like satellites• Spectral resolution E/E 1000, spatial resolution X 30-50 m

1J. Bailey, G. Chandler, A. Slutz, I. Golovkin, P. Lake, J. MacFarlane, R. Mancini, T. Burris-Mog, G. Cooper, R. Leeper et al, Phys. Rev. Letters 92, 085002 (2004)

Z shot z1155: trex1f3 gated slit-imaged data

trex1 (Å)Ly Ly LyHe He He

X (m)

• 2 mm/50 m, 20 atm D2 & 0.085 atm Ar. • Gated image data shows space-resolved spectra recorded by the trex1 instrument.• A second instrument, trex2, recorded similar data along an orthogonal LOS.• Each space-resolved lineout represents a spatial integration over a core slice, labeled by the coordinate X and with a thickness given by the spatial resolution.

trex2X

X

Z shot z1155: trex1f3, spatially-resolved spectra

3000 3200 3400 3600 3800 4000 42000

1

2

3

4

Ly

Ly

He

He

Ly

Inte

nsi

ty (

arb

. un

its)

Photon energy (eV)

z1155trex1f3x = 0m

He

3000 3200 3400 3600 3800 4000 42000

1

2

3

4

Ly

Ly

He

He

Ly

Inte

nsi

ty (

arb

. un

its)

Photon energy (eV)

z1155trex1f3x =+50m

He

3000 3200 3400 3600 3800 4000 42000

1

2

Ly

LyHe

He

Ly

Inte

nsity

(ar

b. u

nits

)

Photon energy (eV)

z1155trex1f3x =+100mHe

3000 3200 3400 3600 3800 4000 42000.0

0.5

1.0

1.5

LyLyHe

He

LyIn

ten

sity

(a

rb. u

nits

)

Photon energy (eV)

z1155trex1f3x =+150m

He

The line intensity distribution gradually changes as a function of the core slice coordinate X

Multi-objective spectroscopic analysis

• Multi-objective data analysis driven by a Pareto Genetic Algorithm (PGA).

• Search for Te and Ne spatial profiles that yield the best simultaneous and self-consistent fits to a set of spatially-resolved spectra recorded in Z-driven implosions.

• The type of objective is the line intensity distribution, and the number of objectives is defined by the number of spectra in the dataset.

• It relies on the Te and Ne dependence of the line intensity distribution over a broad photon energy range.

Problem set up and implementation

• Geometry approximation: assume spherical geometry spatial structure is determined in terms of radial coordinate r.

• Given Te(r) and Ne(r) in the source use a detailed atomic and radiation physics model to compute emissivity (r) and opacity (r).

rX

.LOS

Core volume

Image plane

Core slice

Z shot z1155 trex1f3: set of self-consistent/simultaneous fits

3600 3700 3800 3900 4000 4100 42000.0

0.5

1.0

1.5

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3.0

exp_spec1

I (a

rb. u

nits

)

Photon energy (eV) 3600 3700 3800 3900 4000 4100 42000.0

0.5

1.0

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I (a

rb. u

nits

)

Photon energy (eV)

exp_spec2

3600 3700 3800 3900 4000 4100 42000.00

0.25

0.50

0.75

1.00

I (a

rb. u

nits

)

Photon energy (eV)

exp_spec3

3600 3700 3800 3900 4000 4100 42000.0

0.1

0.2

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0.4

I (a

rb. u

nits

)

Photon energy (eV)

exp_spec4

Simultaneous and self-consistent fits are systematically found for different LOS and time frame datasets

0 20 40 60 80 100 120 140400

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Te

(e

V)

r (m)

z1155trex1f2, 1trex1f3, 2trex2f4, 3trex1f4, 4

1

2

3

4

0 20 40 60 80 100 120 1405.0x1022

1.0x1023

1.5x1023

2.0x1023

2.5x1023

3.0x1023

z1155trex1f2, 1trex1f3, 2trex2f4, 3trex1f4, 4

Ne

(cm

)

r (m)

1

2

3

4

Z shot z1155: time-history of Te and Ne spatial profiles

• Each frame is time-integrated over t = 0.5 ns each spatial profile represents a time-average over 0.5 ns. • Earliest is trex1f2, latest is trex1f4; trex2f4 is in between trex1f3 and trex1f4.• Note: LOS of trex1 and trex2 are quasi-orthogonal.• During the period of observation, first, Te(r) and Ne(r) spatial profiles increase in value.• Then, Te(r) values decrease while Ne(r) remains relatively high in value.

Analysis of four time frames recorded at the implosion collapse permits the reconstruction of time-history

• The amount of Ar has to be very small:– Not to change the hydrodynamics

– To keep the optical depth of the He and Ly (n=3-1 transitions) small

• Laser:– 60 beams, several pulse shapes

– Smoothing: 2D-SSD/DPP-SG4/DPR

• Three identical DDMMI instruments:– DDMMI ≡ Direct-Drive Multi-Monochromatic

x-ray Imager

– Fielded along 3 quasi-orthogonal lines of sight

(TIM3/TIM4/TIM5)

– Record a collection of, gated, spectrally-resolved x-ray images of the implosion core

TIM4

TIM3

TIM5 ̂ TIM3 = 70.5 deg TIM3 ̂ TIM4 = 79.2 deg

TIM5 ̂ TIM4 = 79.2 deg

TIM5

OMEGA direct-drive implosions

DDMMI ≡ Direct-Drive Multi-Monochromatic x-ray Imager

1B. Yaakobi, F.J. Marshall and D.K. Bradley, App. Optics 37, 8074 (1998)2J.A. Koch, T.W. Barbee, Jr., N. Izumi, R. Tommasini, R.C. Mancini, L.A. Welser,,F.J. Marshall, Rev. Sci. Instrum. 76, 073708 (2005)

Spectrally-resolved core imaging with DDMMI

• A pinhole-array coupled to a multi-layer Bragg mirror produces many quasi-monochromatic core images, each one characteristic of a slightly

different photon energy range1,2

DDMMI data

F1

F2

F3

F4

• Collection of gated, spectrally-resolved images

• Time increases from F1 to F4

• Photon energy axis increases from left to right

• Streaked data is used for time-correlation

h(eV)

t

Ly He

Ly

3200 5000

Ly

He

DDMMI data

• From the array of spectrally-resolved images, one can extract:o Broad-band imageso Narrow-band imageso Space-integrated spectrumo Space-resolved spectra

3200 eV 5000 eV

Ly He Ly Narrow-band (He

Broad-band

Space-integrated

Space-resolved

h(eV)

• Collection of gated, spectrally-resolved images

• Photon energy axis increases from left to right

• Resolution:– Spatial: ∆x = 10 m

– Spectral: E/∆E = 150

TIM4

TIM3

TIM5

OMEGA shot 49956, frame 3 (t3)

He

HeHe

Ly

Ly

Ly

Ly

Ly

Ly140m

Broadband

Broadband

Broadband

Gated core images: broad-band and narrow-band based on argon spectral features

TIM4

TIM3

TIM5

OMEGA shot 49956, frame 4 (t4=t3+110ps)

He

HeHe

Ly

Ly

Ly

Ly

Ly

Ly

Gated core images: broad-band and narrow-band based on argon spectral features

140m

Broadband

Broadband

Broadband

Set of space-resolved spectra from one-LOS

OMEGA shot 49956 TIM4, Frame3

TIM3 TIM4 TIM5

142.62 63.44 100.81

342 342 270

OMEGA shot 49956, frame 3x-y-z axes correspond to those defined in the chamber

TIM3

TIM4

TIM5

140m

Volume determination based on three-LOS views

1. Consider a sphere of upper bound radius

2. Define boundaries (masks) based on broad-band images along each line of sight

3. Project these masks in space along each line of sight

4. Truncate the sphere with the intersections of projections

5. Get volume shape and size

• Limitation: upper bound• The more LOS, the more

accurate results

Interpretation of SRS

Interpretation of SRS

• Each space-resolved spectrum has temperature and density information integrated along chord parallel to LOS and perpendicular to the image plane

Interpretation of SRS

• Each space-resolved spectrum has temperature and density information integrated along chord parallel to LOS and perpendicular to the image plane

Interpretation of SRS

• Each space-resolved spectrum has temperature and density information integrated along chord parallel to LOS and perpendicular to the image plane• Each spatial region is located at the intersection of three chords• Spatial regions are constrained by their contributions to spatially-resolved spectra recorded along three LOS

Interpretation of SRS

• Each space-resolved spectrum has temperature and density information integrated along chord parallel to LOS and perpendicular to the image plane• Each spatial region is located at the intersection of three chords• Spatial regions are constrained by their contributions to spatially-resolved spectra recorded along three LOS

Interpretation of SRS

')'( )'( front

rear

xv dxexII

dx

dI

3600 3700 3800 3900 4000 4100

Ly

Photon energy (eV)

He

3600 3700 3800 3900 4000 4100

Photon energy (eV)

• Physics model: Te and Ne spatial distribution SRS• ABAKO1: collisional-radiative atomic kinetics model

– FAC for fundamental atomic data– Radiation transport effect on atomic kinetics using escape factors– Line shapes: detailed Stark, Doppler, and natural broadening effects– Continuum lowering based on Stewart-Pyatt approximation– Output: photon-, Te-, Ne-dependent emissivity () and opacity ()

• Calculation of emergent intensity SRS– No symmetry assumptions, general 3D x-y-z space discretization grid– Numerically integrate radiation equation along chords

Modeling: atomic kinetics and radiation transport

1R. Florido, R. Rodriguez, J. Gil, J. Rubiano, P. Martel, E, Minguez, R. Mancini, Phys. Rev E (2009, in press)

Synthetic-data test caseAnalysis method has to be tested:

Do the sets of space-resolved spectra (SRS) recorded along three-LOS constrain the Te and Ne spatial distributions?

Synthetic-data test case:• Step1: create random Te and Ne

distributions in a 3D x-y-z grid

Target Te and Ne distributions

Synthetic-data test caseAnalysis method has to be tested:

Do the sets of space-resolved spectra (SRS) recorded along three-LOS constrain the Te and Ne spatial distributions?

Synthetic-data test case:• Step1: create random Te and Ne

distributions in a 3D x-y-z grid

Target Te and Ne distributions

• Step 2: synthetic data calculation

target Te and Ne synthetic SRS

Synthetic-data test caseAnalysis method has to be tested:

Do the sets of space-resolved spectra (SRS) recorded along three-LOS constrain the Te and Ne spatial distributions?

Synthetic-data test case:• Step1: create random Te and Ne

distributions in a 3D x-y-z grid

Target Te and Ne distributions

• Step 2: synthetic data calculation

target Te and Ne synthetic SRS

Synthetic-data test caseAnalysis method has to be tested:

Do the sets of space-resolved spectra (SRS) recorded along three-LOS constrain the Te and Ne spatial distributions?

Synthetic-data test cases:• Step1: create random Te and Ne

distributions in a 3D x-y-z grid

Target Te and Ne distributions

• Step 2: synthetic data calculation

target Te and Ne synthetic SRS

• Step 3: use search and reconstruction

synthetic SRS find Te and Ne dist.

Synthetic-data test caseAnalysis method has to be tested:

Do the sets of space-resolved spectra (SRS) recorded along three-LOS constrain the Te and Ne spatial distributions?

Synthetic-data test Case:• Step1: create random Te and Ne

distributions in a 3D x-y-z grid

Target Te and Ne distributions

• Step 2: synthetic data calculation

target Te and Ne synthetic SRS

• Step 3: use search and reconstruction

synthetic SRS find Te and Ne dist.Uniqueness was checked

Synthetic-data test caseAnalysis method has to be tested:

Do the sets of space-resolved spectra (SRS) recorded along three-LOS constrain the Te and Ne spatial distributions?

Synthetic-data test case:• Step1: create random Te and Ne

distributions in a 3D x-y-z grid

Target Te and Ne distributions

• Step 2: synthetic data calculation

target Te and Ne synthetic SRS

• Step 3: use search and reconstruction

synthetic SRS find Te and Ne dist.Uniqueness was checked

• Compare target Te and Ne dist. with extracted Te and Ne dist. Solution was checked

Extracted Target

Results: OMEGA shot 49956 frame 3Te

(eV)

Ne

(cm

-3)

x = -21 m x = 0 m x = 21 m

• A total of 41 SRS were used to extract Te and Ne spatial structure• Te tends to be larger in central region Ne in the periphery • 3D asymmetries in the spatial structures are observed

Results: OMEGA shot 49956 frame 4Te

(eV)

Ne

(cm

-3)

x = -21 m x = 0 m x = 21 m

• A total of 23 SRS were used to extract Te and Ne spatial structure• Frame 4 is close to stagnation and the volume is smaller• Ne has increased while Te has decreased

Additional considerations• Analysis of streaked spectra recorded with SSCA yields space-

averaged temperature and density for frame 3 and 4 that are consistent with the range of values in the spatial distributions extracted from the DDMMI data

• Experimental He and Ly narrow-band images reconstructed from DDMMI data compare well with the narrow-band images computed with the spatial distributions extracted from the analysis of SRS

Experiment Analysis Experiment AnalysisHe Ly

Frame3TIM5

Conclusions

• Te and Ne spatial distributions have been extracted from the analysis of space-resolved spectra (SRS) obtained from spectrally-resolved images recorded with: (1) TREX and (2) three-identical DDMMI instruments fielded along quasi-orthogonal directions.

• Analysis method: – two step search and reconstruction: PGA followed up by fine-tuning,– method was tested with synthetic data test case,– this method can be interpreted as polychromatic tomography: number

of LOS is limited but there are multiple wavelengths associated with each LOS.

• Related presentations: Monday 2PM, CP8 50 (T. Nagayama) and CP8 51 (R. Florido).

• Work in progress: extraction of mixing spatial profiles.

Work supported by DOE/NLUF Grant DE-FG52-09NA29042, LLNL and SNL

-150 -100 -50 0 50 100 150500

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Te

(e

V)

X,r disk/slice, radial coordinate (m)

z1155trex1f3core slice, Xsph. sym. fits, rsph. sym. inv., r

-150 -100 -50 0 50 100 1505.0x1022

1.0x1023

1.5x1023

2.0x1023

2.5x1023

3.0x1023

z1155trex1f3core slice, Xsph. sym. fits, r

Ne

(cm

-3)

X,r disk/slice,radial coordinate (m)

Z shot z1155 trex1f3: comparison of several methods

• Note: X = core slice coordinate, r = radial coordinate.• Core slice analysis yields spatial averages over core slices of different sizes and locations in the core (i.e. “non-local”). • Inversion method assumes spherical symmetry and optically thin and lines.• Multi-objective fits assumes only spherical symmetry.

Trends are consistent, and details can be interpreted in terms of methods’ approximations and assumptions

DDMMI narrow-band image reconstruction1 pixel column

1 pix

7 pix

33 pix• For a given narrow band range, pixels are collected and

reassembled into the local positions of the image with their nearest centers as their reference points

• Space-integrated spectrum can be computed by summing up intensities vertically

Ly

Ly

He

Ly Image

∆E~70eV

Ly Ti abs

Tim

e c

orr

ela

tion

SS

CA

-MM

IS

hot

# 4

9956

F1 F2 F3 F4• X-ray streaked spectrometer (SSCA) and gated imager (MMI) record time-resolved data.

• A time-correlation function method is used to establish thecorrespondence between the time-axis of SSCA and the F1, F2, F3 and F4 frames of MMI.

• Good consistency is found usingthe time-histories of Ly, He andLy spectral features.

• The same method is used to time-correlate SSCA with the LILAC 1D hydro simulation. The label Rm denotes the time of maximum compression (i.e. minimum coreradius).

TIM3

Lyα

Lyβ

Heβ

Rm

Ly

SSCA – MMI Time Correlation

Search and reconstruction method

1) Pareto Genetic Algorithm (PGA)1

Genetic Algorithms (GA) are fast and robust, search and optimization algorithms inspired by evolutionary biology

Pareto Genetic Algorithm (PGA) is the multi-objective version of GA Search is initialized by random number generator (unbiased) Uniqueness can be checked by changing random seed

2) Fine-tuning step: Levenberg-Marquardt non-linear least squares minimization method

1 I. Golovkin et al, Phys. Rev. Letters 88, 045002 (2002); L. Welser et al, J. Quant. Spec. Radiative. Transfer 99, 649 (2006); T. Nagayama et al. Rev. Sci. Instrum. 77, 10F525 (2006); T. Nagayama et al, Rev. Sci. Instrum. 79, 10E921 (2008)

The method is general and can be applied to other problems of multi-objective data analysis

Search and reconstruction method + physics model: SRS Te and Ne• Find Te and Ne spatial distributions that yield simultaneous and self-

consistent fits to the given sets of SRS recorded along three-LOS• Two steps: Pareto genetic algorithm followed up by fine-tuning step