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Polychromatic tomography of high-energy-density plasmas. R. C. Mancini Physics Department, University of Nevada, Reno. HEDSA Symposium, November 1 st , 2009, Atlanta, GA. Students and collaborators. Former students: Igor Golovkin (Prism), Leslie Welser (LANL) - PowerPoint PPT Presentation
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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
2.0
2.5
3.0
exp_spec1
I (a
rb. u
nits
)
Photon energy (eV) 3600 3700 3800 3900 4000 4100 42000.0
0.5
1.0
1.5
2.0
2.5
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
0.3
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
500
600
700
800
900
1000
1100
1200
1300
1400
1500
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
600
700
800
900
1000
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1300
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