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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


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

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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

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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


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.