Impact of First-Principles Calculated Properties of Warm ...

S. X. HuUniversity of RochesterLaboratory for Laser Energetics

56th Annual Meeting of theAmerican Physical SocietyDivision of Plasma Physics

New Orleans, LA27–31 October 2014

Impact of First-Principles Calculated Properties of Warm-Dense Deuterium–Tritium on

Inertial Confinement Fusion Target Designs

Gain = 40.0 (SESAME/AOT/lLM)Gain = 23.8 (FPEOS/FPOT/lQMD)

T i (

eV)

0 100Radius (nm)

Peak compression

Den

sity

(g

/cm

3 )

0 0

5

10

15

20

100

200

300

400

500

600SESAME/AOT/lLMFPEOS/FPOT/lQMD

Accurate properties of deuterium–tritium (DT) fuel from first-principles calculations are crucial to inertial confinement fusion (ICF) target designs

Summary

• First-principles (FP) methods, including path-integral Monte Carlo (PIMC) and quantum molecular dynamics (QMD), are used to self-consistently calculate the properties of DT fuel for ICF applications

• Significant differences are identified when comparing FP-based equation of state (FPEOS), opacity table (FPOT), and thermal conductivity (lQMD) with models adopted in hydrocodes

• Hydro simulations using FP-based properties of DT have shown a factor of ~2 difference in ICF neutron yield compared to model simulations

• The lower the adiabat (a = 1.5 to 3.0), the larger the differences are in predicting ICF target performance

TC11488

Collaborators

V. N. Goncharov, T. R. Boehly, R. Epstein, R. L. McCrory, and S. Skupsky

University of RochesterLaboratory for Laser Energetics

L. A. Collins and J. D. Kress

Theoretical Division Los Alamos National Laboratory

B. Militzer

Department of Earth and Planetary Science and Astronomy University of California, Berkeley

Outline

TC11489

• Introduction: warm dense matter (WDM)

• First-principles methods for studying WDM

– path-integral Monte Carlo (PIMC)

– quantum molecular dynamics (QMD)

• Properties of warm dense DT: FPEOS/FPOT/lQMD compared to model predictions

• Impact of first-principles properties of DT fuel on ICF implosions

• Conclusions

Accurate knowledge of DT properties [equation of state (EOS), opacity, l, stopping power] is required to simulate ICF implosions

TC5723c

Early time

Laser drive

Acceleration phase

Peak compression Deceleration phase

EOS/opacity/l determines t–T conditions

Stopping power determines a heating

Laser drive

Shell

DT gas

Shock timing(EOS)

l determines ablation in hot spot

EOS is needed to close the hydrodynamics equations.

Coupled and degenerate warm dense matter are routinely accessed by imploding DT shells in ICF

TC11490

10–4 10–2 100

Density (g/cm3)

DT phase space

i = 1i = 1

i < 1i < 1

C > 1C > 1

C = 1C = 1

Tem

per

atu

re (

K)

102 104 106102

104

106

108ICF ignitionICF ignition

1010

Warm dense matter

Warm dense matter

PlasmaPlasma

GasGas

SolidSolid

Impl

odin

g DT

cap

sule

s

Impl

odin

g DT

cap

sule

s

The Coulomb coupling parameter:

The electron- degeneracy parameter:

,r k Tq

r n3 4 /

s Bs

21 3rC = = ^ h

TTF

i =

WDM:

;1 1$ #iC

A variety of models have been adopted in ICF hydrocodes to estimate the properties of WDM

TC11491

• Equation of state– SESAME/Kerley03* based on the chemical model of matter, with

perturbations of many-body coupling and electron degeneracy

• Thermal conductivity (l)– the Lee–More model** was based on the first-order

approximation to the Boltzmann equation, while the Purgatorio† (LLNL) is an average-atom model

• Opacity– the astrophysics opacity table (AOT)‡ has no available data

in the WDM regime

First-principles calculations using PIMC and QMD provide self-consistent and accurate properties of WDM.

* G. I. Kerley, Phys. Earth Planet. Inter. 6, 78 (1972); G. I. Kerley, “Equations of State for Hydrogen and Deuterium,” Sandia National Laboratory, Albuquerque, NM, Report SAND2003-3613(2003). ** Y. T. Lee and R. M. More, Phys. Fluids 27, 1273 (1984). † P. Sterne, Lawrence Livermore National Laboratory, Livermore, CA, Report UCRL-PROC-227242 (2006). ‡ W. F. Huebner et al., Los Alamos National Laboratory, Los Alamos, NM, Report LA-6760-M (1977).

Outline

TC11489a







• Conclusions

PIMC,* based on the convolution of the density matrix, uses the Monte Carlo method to efficiently evaluate multidimensional integrations

TC11492

* D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995); B. Militzer, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2000.

Knownt0(R, Rl; M × T)

Unknownt(R, Rl; T)

“Temperature path”

• The density matrix t(R, Rl; T), introduced by J. von Neumann in 1927, describes the statistical distribution of a quantum system in thermal equilibrium

• The convolution property of t(R, Rl; T) can be written as

, ;R R T R e R R R e/ –H kTn

nn

E kT– nt { {= =l l l^ ^ ^h h h/

, ;R R T R e RH KT–t = =l l^ h , ; , ;dR R R R R TT 221 1 1t t l^ ^h h#

The QMD method is based on the Kohn–Sham density functional theory (DFT)*

TC11493

• EOS is a direct output from QMD simulations

• Transport properties can be calculated using the Kubo–Greenwood formalism**

• Thermal conductivity and optical absorption coefficients can be derived from these Onsager coefficients Lij(~)

* W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). ** R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957); D. A. Greenwood, Proc. Phys. Soc. Lond. 71, 585 (1958).

–L

Vme

F D3

2

eij

i j

mnmn

mn2

42

– –

~~

r=^ ^h h /

– – –E E

H E E2

–m n

i j

m n

2# 'd ~

+ +c ^m h

Coupled and degenerate WDM conditions* are studied by PIMC and QMD methods

TC11442

10–3 10–2 10–1 100

Density (g/cm3)

C < 1, i > 1(classical plasmas)

PIMC (solid)PIMC (solid) C = 1

i = 10Te

mp

erat

ure

(K

)

101 102 103 104104

105

106

107

108

ICF D

T-shell

conditio

n

i = 1.0

i = 0.1

C > 1, i < 1 (strongly coupled anddegenerate plasmas)

QMD (open)QMD (open)

*S. X. Hu et al., Phys. Rev. Lett. 104, 235003 (2010).

Outline

TC11489b







• Conclusions

Differences in the principal Hugoniot of deuterium are identified between the FPEOS and EOS models

TC11444

3.2 3.6 4.0

Compression

4.4 4.8 5.210–1

101

103P

ress

ure

(M

bar

)

100

102

345 eV

43 eV

11 eV

2.7 eV

SESAMEKerley03FPEOS

Calculations of deuterium Hugoniot using QMD have been previously studied.*

* L. A. Collins et al., Phys. Rev. B 63, 184110 (2001); M. P. Desjarlais, Phys. Rev. B 68, 064204 (2003); B. Holst et al., Phys. Rev. B 77, 184201 (2008); S. X. Hu et al., Phys. Rev. B 84, 224109 (2011); L. Caillabet, S. Mazevet, and P. Loubeyre, Phys. Rev. B 83, 094101 (2011); C. Wang and P. Zhang, Phys. Plasmas 20, 092703 (2013).

The FPEOS-predicted Hugoniot of deuterium is better compared with experiments

TC11494

SESAMEKerley03Hicks et al.Boehly et al.Knudson et al.Boriskov et al.FPEOS

3.2 3.6 4.0

Compression

4.4 4.8 5.210–1

100

101

Pre

ssu

re (

Mb

ar)

Differences have been identified for warm dense deuterium between FPEOS* and EOS models

TC11445*S. X. Hu et al., Phys. Rev. B 84, 224109 (2011).

10–3 10–1

Density (g/cm3)

P/P

idea

l

101

0.8

0.7

0.6

0.9

1.0

FPEOSSESAMEKerley03Debye

10–3 10–1

Density (g/cm3)

E/E

idea

l

101

0.6

0.4

0.8

1.0

T = 10.77 eV

The QMD thermal conductivity* of warm dense deuterium is 3 to 10× higher than the Lee–More model**

TC11448

10–1 100 101

Temperature (eV)

t = 7.39 g/cm3

t = 24.95 g/cm3

Th

erm

al c

on

du

ctiv

ity

(W/m

/K)

102102

103

104

105

106

107

103 100 101

Temperature (eV)

102 103

Lee–MoreQMD fittingQMD

* S. X. Hu et al., Phys. Rev. E 89, 043105 (2014). ** Y. T. Lee and R. M. More, Phys. Fluids 27, 1273 (1984).

The QMD opacities* show a large difference in the WDM regime when compared to the cold-opacity–patched AOT

TC11449 *S. X. Hu et al., Phys. Rev. E 90, 033111 (2014).

100102

104

105

106

103

101 102

Temperature (eV)

t = 7.39 g/cm3

Cold opacity

Tota

l Ro

ssel

and

op

acit

y (c

m2 /

g)

AOTQMD

Enhanced opacity is caused by

• 35× compression

• Temperature increase

The QMD-predicted reflectivity along the Hugoniot of deuterium agreed with Nova and OMEGA experiments*

TC11447

* P. M. Celliers et al., Phys. Rev. Lett. 84, 5564 (2000); T. R. Boehly et al., Phys. Plasmas 16, 056302 (2009).

0.010 20 30

m = 532 nm

m = 808 nm

40Shock speed (km/s)

50 60 70

Ref

lect

ivit

y0.2

0.4

0.6

0.8

0.0

Ref

lect

ivit

y

0.2

0.4

0.6

0.8

Nova experimentQMD

OMEGA experimentQMD

; – dL P2–1 11 2 2 21v ~ ~ v ~ r ~ ~

~v ~~= =

l

ll^ ^ ^ ^eh h h h o#

– ;1 4 41 2 2 1f ~ ~

rv ~ f ~ ~r v ~= =^ ^ ^ ^h h h h

;–

n k2 22 1~

f ~ f ~~

f ~ f ~=

+=^ ^ ^ ^ ^ ^h h h h h h

–R

n n k

n n k

02 2

02 2

~~ ~

~ ~=

+

+

+^ ^ ^

^ ^h h hh h

66

@@

c n4 1K

m1

##a ~ t

a ~~

rv ~t= =^ ^

^^h hhh

Outline

TC11489c







• Conclusions

For a direct-drive OMEGA target (a á 2), a higher adiabat in DT was predicted in FP simulations of ICF implosions

TC11452

20

Den

sity

(g

/cm

3 )

T e (

eV)

0

4

8

12

20

40

60

80

60 100 140

Min

imu

m a

dia

bat

0

2

1

3

4

2 3

0

Den

sity

(g

/cm

3 )

T i (

keV

)

0

100

300

200

400

0

4

8

12

10 20 30 40 Neu

tro

n y

ield

(×

1014

)

0

2

4

6

3.0

Radius (nm) Time (ns)

Radius (nm) Time (ns)

Beginning of deceleration

Peak compression

3.4

SESAME/AOT/lLMFPEOS/FPOT/lQMD

A factor of ~2 difference in direct-drive target performance has been predicted between FPEOS/FPOT/lQMD and typical simulations for a National Ignition Facility (NIF) target

TC11454

* G. Fiksel et al., Phys. Plasmas 19, 062704 (2012); S. X. Hu et al., Phys. Rev. Lett. 108, 195003 (2012).

Gain = 40 (SESAME/AOT/lLM)Gain = 23 (FPEOS/FPOT/ lQMD)

0 2 4 6 8 10 12 14

4

8

10

6

2

0

Time (ns)Las

er in

ten

sity

(×

1014

W/c

m2 )

CHSi [7.4%]: 10 nm

CH26 nm

190 n

m

DT gas

DT ice

1500

nm

T i (

eV)

0 100

Peak compression

Radius (nm)

Den

sity

(g

/cm

3 )

0 0

5

10

15

20

100

200

300

400

500

600


Si-doped CH is used to reduce laser imprint*

High gain (G ~ 40) can be recovered for the same NIF target by retuning the laser pulse shape using FPEOS/FPOT/lQMD

TC11457

0 4Time (ns)

Las

er in

ten

sity

(×

1014

W/c

m2 )

2

0

4

6

8

8 12


Gain = 40 (SESAME/AOT/lLM)Gain = 40 (FPEOS/FPOT/ lQMD)

Future work will test these effects beyond 1-D as well as extend such FP studies to ablator materials

TC9631

• Two-dimensional simulations with FPEOS/FPOT/lQMD will show how these FP-based properties of DT may affect target performance (beyond 1-D)

• First-principles calculations for ablator materials have begun with studying the CH Hugoniot*

*S. X. Hu, T. R. Boehly, and L. A. Collins, Phys. Rev. E 89, 063104 (2014).

Consistent properties (FPEOS/FPOT/lQMD) of ablator materials in WDM conditions can be established with such first-principles calculations.

TC11488

Summary/Conclusions

Accurate properties of deuterium–tritium (DT) fuel from first-principles calculations are crucial to inertial confinement fusion (ICF) target designs

• First-principles (FP) methods, including path-integral Monte Carlo (PIMC) and quantum molecular dynamics (QMD), are used to self-consistently calculate the properties of DT fuel for ICF applications

• Significant differences are identified when comparing FP-based equation of state (FPEOS), opacity table (FPOT), and thermal conductivity (lQMD) with models adopted in hydrocodes

• Hydro simulations using FP-based properties of DT have shown a factor of ~2 difference in ICF neutron yield compared to model simulations

• The lower the adiabat (a = 1.5 to 3.0), the larger the differences are in predicting ICF target performance

The lower the adiabat becomes (a ≈ 2.2 " 1.5), the larger the variations (>2) in target performance are observed*

TC11458

* S. X. Hu et al., “Impact of First-Principles Property Calculations of Warm-Dense Deuterium- Tritium on Inertial Confinement Fusion Target Designs,” to be submitted to Physics of Plasmas.

0 2 4 6 8 10 12 14

6

7

5

4

3

2

1

0

Time (ns)

Las

er in

ten

sity

(×

1014

W/c

m2 )

20 40 60 80 100 120 1400

200

400

600

24

20

16

12

8

4

0

800

Radius (nm)

Den

sity

(g

/cm

3 )

T i (

keV

)

HDC: 11 nm

180 n

m

DT gas

DT ice

1300

nm


Gain = 28 (SESAME/AOT/lLM)Gain = 11 (FPEOS/FPOT/lQMD)

Impact of First-Principles Calculated Properties of Warm ...

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