Analytic Analysis of Convergent Shocks to Multi-Gigabar ... · from the location of peak emission...
4
J. J. RUBY, 1 J. R. RYGG, 1 G. W. COLLINS, 1 B. BACHMANN, 2 T. DOEPPNER, 2 Y. PING, 2 J. GAFFNEY, 2 A. LAZICKI, 2 A. L. KRITCHER, 2 D. C. SWIFT, 2 J. NILSEN, 2 O. L. LANDEN, 2 R. HATARIK, 2 N. MASTERS, 2 S. R. NAGEL, 2 P. A. STERNE, 2 T. PARDINI, 2 S. KHAN, 2 P. M. CELLIERS, 2 P. K. PATEL, 2 D. O. GERICKE, 3 and R. W. FALCONE 4 Analytic Analysis of Convergent Shocks to Multi-Gigabar Conditions Motivation and results E26512 • The Gigabar Platform at the National Ignition Facility created states of 1.2 keV, 100 g/cm 3 , and 10 s • Self-similar solutions to hydrodynamic systems offer intuition and simplicity that cannot be achieved with hydrodynamic codes • Understanding experiments in the context of self-similar solutions allows insight into the state variables and transport properties of the system • The Guderley self-similar hydrodynamic solution accurately recreates experimental results and offers insight into the energy partitioning between ions and electrons in spherical implosions • Electron–ion energy partitioning plays an important role in what is observed during these types of experiments and is not well understood G. Guderley, Luftfahrtforschung 19, 302 (1942); P. Reinicke and J. Meyer-ter-Vehn, Phys. Fluids A 3, 1807 (1991). t (ns) 200 300 400 500 600 700 800 900 Distance (nm) Normalized x-ray emission Fitted shock trajectory X-ray emission comparison t (ns) 0.0 –0.2 –0.4 0.2 0.4 0 1 –1 –2 –3 0.0 0.2 0.4 0.6 0.8 1.0 0 500 1000 1500 2000 2500 3000 3500 4000 8000 7000 6000 5000 4000 3000 2000 1000 0 x (pixels) Intensity (counts) Time relative to center (ns) 0 –2 –4 2 4 Fit Radiograph data Measured signal (x-ray streak camera) Guderley solution E26719 PB Using the Guderley solution to understand experimental results • Guderley has free parameters set by experiment – initial density – outer radius – shock trajectory • Shock trajectory is set to fit to the experimental trajectory in the radiograph • The time of shock collapse is determined from the location of peak emission in the radiograph • There is qual energy partitioning between ions and electrons • The Guderley model does a good job of predicting experimental observables • The question of how to partition ion and electron energies is still present • Development of a heat-conduction treatment is ongoing Value Guderley Experiment Neutron yield 1.74 × 10 10 7 × 10 9 GIon temperatureH 1.2 keV 0.94 keV X-ray yield 4.3 mJ/sr (>8 keV) 9.3 mJ/sr (filtered) . – –. . . –. t t 0 7323 0 213 7 750 0 00064 0 213 s c 0 0 a = a a m ns / r 270 p n p = = res = b l 1 University of Rochester, Laboratory for Laser Energetics 2 Lawrence Livermore National Laboratory; 3 University of Warwick; 4 University of California, Berkeley Guderley versus Reinicke temperature profile 0.000 10,000 5,000 15,000 25,000 20,000 0.050 0.025 0.100 0.075 T (eV) 0.150 0.175 0.125 0.200 r/r 0 Guderley Reinicke Thermal conduction distributes the temperature to a farther radial extent than the shock alone Hydrodynamic consideration results only in diverging temperature at the center E26513 PB Creating a model that makes experimental sense • Diverging temperature at the center means a large thermal gradient • Larger thermal gradients give rise to heat waves • Thermal conduction is dominated by electrons • Hydrodynamic transport is carried out by ions • How they equilibrate becomes very important • Within the region of observable emission, the Guderley and hydrodynamic codes have the same behavior • The Guderley and Reinicke solutions are used as a benchmark for hydrodynmic codes* –1.0 –0.5 0.0 0.0 0.5 1.0 0.5 Shock Flow Guderley shock trajectory r/r 0 (t – t c )/t 0 Shock Fuel–shell interface Hydrodynamic (1-D LILAC) simulation shock trajectory –1.0 –0.5 0.0 0.5 (t – t c )/t c Neutrons and x rays are emitted here J. R. Rygg, Ph.D. thesis, Massachusetts Institute of Technology, 2006. * https://github.com/lanl/ExactPack (2 October 2017).
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Transcript of Analytic Analysis of Convergent Shocks to Multi-Gigabar ... · from the location of peak emission...
J. J. RUBY,1 J. R. RYGG,1 G. W. COLLINS,1 B. BACHMANN,2 T. DOEPPNER,2 Y. PING,2 J. GAFFNEY,2 A. LAZICKI,2 A. L. KRITCHER,2 D. C. SWIFT,2 J. NILSEN,2 O. L. LANDEN,2
R. HATARIK,2 N. MASTERS,2 S. R. NAGEL,2 P. A. STERNE,2 T. PARDINI,2 S. KHAN,2 P. M. CELLIERS,2 P. K. PATEL,2 D. O. GERICKE,3 and R. W. FALCONE4
Analytic Analysis of Convergent Shocks to Multi-Gigabar Conditions
Motivation and results
E26512
• The Gigabar Platform at the National Ignition Facility created states of 1.2 keV, 100 g/cm3, and 10 s
• Self-similar solutions to hydrodynamic systems offer intuition and simplicity that cannot be achieved with hydrodynamic codes
• Understanding experiments in the context of self-similar solutions allows insight into the state variables and transport properties of the system
• The Guderley self-similar hydrodynamic solution accurately recreates experimental results and offers insight into the energy partitioning between ions and electrons in spherical implosions
• Electron–ion energy partitioning plays an important role in what is observed during these types of experiments and is not well understood
G. Guderley, Luftfahrtforschung 19, 302 (1942);P. Reinicke and J. Meyer-ter-Vehn, Phys. Fluids A 3, 1807 (1991).
t (ns)
200
300
400
500
600
700
800
900
Dis
tan
ce (n
m)
No
rmal
ized
x-r
ay e
mis
sio
n
Fitted shock trajectory
X-ray emission comparison
t (ns)
0.0–0.2–0.4 0.2 0.4
0 1–1–2–3
0.0
0.2
0.4
0.6
0.8
1.0
0
500
1000
1500
2000
2500
3000
3500
4000 8000
7000
6000
5000
4000
3000
2000
1000
0
x (p
ixel
s)
Inte
nsi
ty (
cou
nts)
Time relative to center (ns)
0 –2 –424
FitRadiograph data
Measured signal(x-ray streak camera)Guderley solution
E26719
PB
Using the Guderley solution to understand experimental results
• Guderley has free parameters set by experiment
– initial density
– outer radius
– shock trajectory
• Shock trajectory is set to fi t to the experimental trajectory in the radiograph
• The time of shock collapse is determined from the location of peak emission in the radiograph
• There is qual energy partitioning between ions and electrons
• The Guderley model does a good job of predicting experimental observables
• The question of how to partition ion and electron energies is still present
• Development of a heat-conduction treatment is ongoing
Value Guderley Experiment
Neutron yield 1.74 × 1010 7 × 109
GIon temperatureH 1.2 keV 0.94 keV
X-ray yield 4.3 mJ/sr (>8 keV)
9.3 mJ/sr(fi ltered)
.
–
– ..
.– .
t t
0 7323
0 2137 750
0 000640 213
s c
0
0
a =a
a
m ns/
r
270p n
p
=
=
res = b l
1University of Rochester, Laboratory for Laser Energetics2Lawrence Livermore National Laboratory; 3University of Warwick; 4University of California, Berkeley
Guderley versus Reinicke temperature profile
0.000
10,000
5,000
15,000
25,000
20,000
0.0500.025 0.1000.075
T (e
V)
0.150 0.1750.125 0.200
r/r0
Guderley Reinicke
Thermal conduction distributes the temperature to a farther radial extent than the shock alone
Hydrodynamic consideration results only in diverging temperature at the center
E26513
PB
Creating a model that makes experimental sense
• Diverging temperature at the center means a large thermal gradient
• Larger thermal gradients give rise to heat waves
• Thermal conduction is dominated by electrons
• Hydrodynamic transport is carried out by ions
• How they equilibrate becomes very important
• Within the region of observable emission, the Guderley and hydrodynamic codes have the same behavior
• The Guderley and Reinicke solutions are used as a benchmark for hydrodynmic codes*
–1.0 –0.5 0.00.0
0.5
1.0
0.5
Shock
Flow
Guderley shock trajectory
r/r 0
(t – tc)/t0
Shock Fuel–shell interface
Hydrodynamic (1-D LILAC) simulation shock trajectory
–1.0 –0.5 0.0 0.5
(t – tc)/tc
Neutrons and x raysare emitted here
J. R. Rygg, Ph.D. thesis, Massachusetts Institute of Technology, 2006.* https://github.com/lanl/ExactPack (2 October 2017).
Motivation and results
E26512
• The Gigabar Platform at the National Ignition Facility created states of 1.2 keV, 100 g/cm3, and 10 s
• Self-similar solutions to hydrodynamic systems offer intuition and simplicity that cannot be achieved with hydrodynamic codes
• Understanding experiments in the context of self-similar solutions allows insight into the state variables and transport properties of the system
• The Guderley self-similar hydrodynamic solution accurately recreates experimental results and offers insight into the energy partitioning between ions and electrons in spherical implosions
• Electron–ion energy partitioning plays an important role in what is observed during these types of experiments and is not well understood
G. Guderley, Luftfahrtforschung 19, 302 (1942);P. Reinicke and J. Meyer-ter-Vehn, Phys. Fluids A 3, 1807 (1991).
Guderley versus Reinicke temperature profile
0.000
10,000
5,000
15,000
25,000
20,000
0.0500.025 0.1000.075
T (e
V)
0.150 0.1750.125 0.200
r/r0
Guderley Reinicke
Thermal conduction distributes the temperature to a farther radial extent than the shock alone
Hydrodynamic consideration results only in diverging temperature at the center
E26513
PB
Creating a model that makes experimental sense
• Diverging temperature at the center means a large thermal gradient
• Larger thermal gradients give rise to heat waves
• Thermal conduction is dominated by electrons
• Hydrodynamic transport is carried out by ions
• How they equilibrate becomes very important
• Within the region of observable emission, the Guderley and hydrodynamic codes have the same behavior
• The Guderley and Reinicke solutions are used as a benchmark for hydrodynmic codes*
–1.0 –0.5 0.00.0
0.5
1.0
0.5
Shock
Flow
Guderley shock trajectory
r/r 0
(t – tc)/t0
Shock Fuel–shell interface
Hydrodynamic (1-D LILAC) simulation shock trajectory
–1.0 –0.5 0.0 0.5
(t – tc)/tc
Neutrons and x raysare emitted here
J. R. Rygg, Ph.D. thesis, Massachusetts Institute of Technology, 2006.* https://github.com/lanl/ExactPack (2 October 2017).
t (ns)
200
300
400
500
600
700
800
900
Dis
tan
ce (n
m)
No
rmal
ized
x-r
ay e
mis
sio
n
Fitted shock trajectory
X-ray emission comparison
t (ns)
0.0–0.2–0.4 0.2 0.4
0 1–1–2–3
0.0
0.2
0.4
0.6
0.8
1.0
0
500
1000
1500
2000
2500
3000
3500
4000 8000
7000
6000
5000
4000
3000
2000
1000
0
x (p
ixel
s)
Inte
nsi
ty (
cou
nts)
Time relative to center (ns)
0 –2 –424
FitRadiograph data
Measured signal(x-ray streak camera)Guderley solution
E26719
PB
Using the Guderley solution to understand experimental results
• Guderley has free parameters set by experiment
– initial density
– outer radius
– shock trajectory
• Shock trajectory is set to fit to the experimental trajectory in the radiograph
• The time of shock collapse is determined from the location of peak emission in the radiograph
• There is qual energy partitioning between ions and electrons
• The Guderley model does a good job of predicting experimental observables
• The question of how to partition ion and electron energies is still present
• Development of a heat-conduction treatment is ongoing
Value Guderley Experiment
Neutron yield 1.74 × 1010 7 × 109
GIon temperatureH 1.2 keV 0.94 keV
X-ray yield 4.3 mJ/sr (>8 keV)
9.3 mJ/sr (filtered)
.
–
– ..
.– .
t t
0 7323
0 2137 750
0 000640 213
s c
0
0
a =a
a
m ns/
r
270p n
p
=
=
res = b l
