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M. A. BARRIOS, D. G. HICKS*, T. R. BOEHLY, D. E. FRATANDUONO, J. H. EGGERT*, P. M. CELLIERS*, G. W .COLLINS*, AND D. D. MEYERHOFERM. A. BARRIOS, D. G. HICKS*, T. R. BOEHLY, D. E. FRATANDUONO, J. H. EGGERT*, P. M. CELLIERS*, G. W .COLLINS*, AND D. D. MEYERHOFER
High-Precision Measurements of the Equation of State of Hydrocarbons at 1 to 10 Mbar Using Laser-Driven Waves
High-Precision Measurements of the Equation of State of Hydrocarbons at 1 to 10 Mbar Using Laser-Driven Waves
University of Rochester, Laboratory for Laser Energetics*Lawrence Livermore National Laboratory, Livermore, CA
Hydrocarbon EOS experiments were performed using laser-driven shock waves on OMEGA
E18346a
• Experiments used laser energies between 200 to 1130 J delivered in a nominally 2-ns square pulse.
• Average laser irradiances on target were 0.3 to 1.1 × 1014 W/cm2
VISAR* has time resolution of <30 ps and shock-velocity precision of ~1%.
OMEGA Experiments
*Velocity Interferometer System for any Reflector
VISAR
OMEGA
20-nmablator
50-nm CH/CH2
90-nm a-quartz
Image relay from target to interferometer
Velocityinterferometer
Vacuumchamber
Target
Probe laser (532 nm)delivered through
multimode fiber
Self-emissionfrom target
SOP
VISAR*beamsplitter
Delay element
Streakcamera
Streakcamera
14
10
12
8
6
4
2
03025201510
Randomerrors Random
errors
Systematicerrors
50
Pre
ssu
re (
Mb
)
Particle velocity, Up (nm/ns)
Initial state(from Us in standard)
U sU p Release
isentrope(known std.)P=t
0
Known standard Hugoniot
Usl UpP=t0P
Up
x
Usl
SampleStandard
P
x
Us
SampleStandard
P
x
SampleStandard
Usl
Up
EOS data are obtained from the impedance-matching technique
E17323c
Impedance Matching Us = F(Up)
Rankine–Hugoniot Equations–
–
U U U
P P U U1 0
s s
s
p
p
0
0
1t
t
t
=
= _ i
Sample
VISAR-1 shot 29425
Integratedvelocity
Contactinterface
Instantaneousvelocities
AlSample
a-quartz
Al
Al
Al
VISAR-1 shot 52118
0 2 4 6ns
ns
200
nm 0
–200
500
nm 0
–500a-quartz pusher
Laser
Laser
Us
Sample
Us
Dx
Al
0 2–2 4Us is inferredfrom transit times
Sample
Higher precision is obtained with a transparent standard compared to an opaque standard
E17324c
Random Errors
• Only information is transit time
• Can use only integrated shock
• No knowledge of shock stability
10
8
6
Pre
ssu
re (
Mb
ar)
4
2
01.5 2.0 2.5 3.0
Density (g/cm3)
3.5 4.0
Total error
Random error
SESAME 7590SESAME 7591SESAME 7592SESAME 7171SESAME 7180
Gas gundata
CH2
CH
Precision EOS data tightly constrain polystyrene (CH) and polypropylene EOS models
E18347a
The polystyrene results have higher precision than previous studies
E18350a
1R. Cauble et al., Phys. Plasmas 4, 1857 (1997).2N. Ozaki et al., Phys. Plasmas 12, 124503 (2005).3N. Ozaki et al., Phys. Plasmas 16, 062702 (2009).
50
10
Pre
ssu
re (
Mb
ar)
5
1
2.52.0 3.0 3.5
Density (g/cm3)
4.0 4.5
SESAME 7590SESAME 7591SESAME 7592QEOS (CH)This studyCauble (1997)1Ozaki (2005)2Ozaki (2009)3
Shocked CH and CH2 become reflective at 1 to 2 Mbar
E18351a
Expected behavior of dielectrics undergoinginsulator-conductor transition.
• Reflectivity measurements are needed for temperature calculations
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Ref
lect
ivit
y
1 2 3 4Pressure (Mbar)
CH CH2
5 6 7 1 2 3 4Pressure (Mbar)
5 6 7
The measured brightness temperatures are consistent with models; but differences among models are too small to be discerned
E18384a
Pressure (Mbar)Pressure (Mbar)
0
1
2
3
4
5
6
7
Tem
per
atu
re (
eV)
0 2 4 6
CH
CH2
8 10 0 2 4 6 8 10
SESAME 7171SESAME 7180
SESAME 7590SESAME 7591SESAME 7592Ozaki (2009)
This provides a complete EOS of CH and CH2.
Polystyrene (CH) double-shock data are in agreement with single-shock results
E18352a
25
20
Qu
artz
sh
ock
vel
oci
ty (n
m/n
s)
15
10
12
10
8
6
CH
res
ho
ck p
ress
ure
(M
bar
)
4
2
10 15 20
CH shock velocity (nm/ns)
25 30
1 32 4 5CH single-shock pressure (Mbar)
6 7
SESAME 7590 (CH)SESAME 7591 (CH)SESAME 7592 (CH)
Inferred principal Hugoniot results for polystyrene from reshock data are consistent with single-shock measurements
E18909
10
8
6
Pre
ssu
re (
Mb
ar)
4
2
02.5 3.0
Density (g/cm3)
3.5 4.0
SESAME 7590SESAME 7591SESAME 7592
10
8
6
Pre
ssu
re (
Mb
ar)
4
2
02.0 2.5 3.0
Density (g/cm3)
3.5 4.0
SESAME 7591SESAME 7592SESAME 7590
2–2
–1
0
1
2
4Pressure (Mbar)
% d
iffer
ence
6
Accuracy of the inversion method is tested by using the effective gamma and shows to be in agreement with single-shock states, as predicted by models
E18927
Reflected shocks are used to create double shock states in CH
E18057b
Small differences in models are amplified using reshock to move off the Hugoniot.
VISAROMEGA
CH ablator
ReshockSingle shock
0
4
8
12
5 10 15 20 250
30 35
Particle velocity (nm/ns)
QuartzprincipalHugoniot
Initial statesfrom slightly
varying samplemodels
Reshock
Samplemodels
Pre
ssu
re (
Mb
ar)
0
–500
0
500
2 4 6ns
8 10
a-quartz a-quartzCH
a-quartz
a-quartz
CHUs
Up
P=t0
x
P Sample Standard
usl
x
P Sample Standard
nm
Up
x
usl
P Sample Standard
us
a-quartz’s experimental principal Hugoniot is used, and its release isentrope is approximated using the Mie-Grüneisen EOS
E17325c
1 D. G. Hicks et al., Phys. Plasmas 12, 082702 (2005).
Systematic Errors
35
30
25
20
15
10
5201510
Particle speed (nm/ns)
Sh
ock
sp
eed
(n
m/n
s)
50
Nuclear ~10 ns
Laser1 ~0.3 ns
1.4 4.5 9.45 15.94
a-quartz EOS (Al as reference)
Gas gun explosive~100s of ns
Mbar
Vi–1
PH , EH
Pi , Ei
Pi–1 , Ei–1
Vi
Calculatedisentrope
Specific volume
Pre
ssu
re
Hugoniot
• C describes pressure differences between equal volume states on
the Principal Hugoniot
• Combining the above with the first law of thermodynamics, dE = TdS – PdV, with dS = 0, leads to a recursion relation describing a loci of isentropes in the P–V plane
• Based on models, C is assumed to be constant in the high-pressure fluid regime, with value C = 0.64±0.11
VdEdP
vC = b l
Precision equation-of-state (EOS) measurements are obtained on various hydrocarbons at 1 to 10 Mbar
E18910
Summary/Conclusions
• Precise knowledge of ablator EOS is required for ICF target designs
• Laser-driven shock waves produce EOS data using the impedance-matching (IM) method
• CH data allows for model discrimination, favoring SESAME 7592 – mild softening is not accounted for between 2 to 4 Mbar – single- and double-shock results display similar behavior
– inferred single-shock results from double-shock data is in agreement with principal Hugoniot measurements
• Stoichiometry effects between CH and CH2 are well-predicted by models
• Both CH and CH2 reach similar compressions and temperatures as a function of pressure
Single-shock states are inferred from double-shock data via an inversion method
E18926
Hugoniot relations for single- and re-shock states
–U U Us p s1 1 1 10t t=_ i –ZU U U U2 s p s p2 2 1 2 1t t=_ _i i
– –ZP U U U UP2 s p pp1 2 1 2 11 t= _ _i iP U U0 s p1 1 1t=5 unknowns
Hugoniot equation:
Energy difference fromeffective gamma:
Eliminating DE21:
ZE P P21 11
121 2 1 2ttD = +^ ch m
/ /Z
ZE
P P1
2 121
12c
t tD =
u
/1ZZP
P P PP P
12
2
1 2
2 11t c
= ++ +u^ ^h h
15
2
3
4
20
UsCH (nm/ns)
Eff
ecti
ve c~
25 30
SESAME 7591SESAME 7592SESAME 7590
Abstract
The equation of state (EOS) of polystyrene and polypropylene was measured using laser-driven shock waves with pressures from 1 to 10 Mbar. Precision data resulting from the use of a-quartz as an impedance-matching (IM) standard tightly constrains the EOS of these hydrocarbons, even with the inclusion of systematic errors inherent to IM. The temperature at these high pressures was measured, which, combined with kinematic measurements, provide a complete shock EOS. Both hydrocarbons were observed to reach similar compressions and temperatures as a function of pressure. The materials were observed to transition from transparent insulators to reflecting conductors at pressures of 1 to 2 Mbar.
This work was supported by the U.S. D.O.E Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-08NA28302, the University of Rochester, and the New York State Energy Research and Development Authority. The support of DOE does not constitute an endorsement by DOE of the views expressed in this article.
