Physical Models for NIC EOS, Opacity, Transport, … · Physical Models for NIC EOS, Opacity,...

LLNL-PRES-557971

Physical Models for NIC EOS, Opacity, Transport, Nuclear, Kinetics

J. Wark and G. Collins

P. Sterne, C. Mauche, S. Hamel, B. Heeter, R. Rygg, E. Schwegler, D. Clark, S. Haan, L. Benedict, J. Gaffney, D. Fratanduono, P. Celliers, Y. Ping, O. Landen, J. Eggert, R. Marrs, C. Bellei, P. Amendt, S. Wilks, M.

Akin, J. Hammer, C. Iglesias, D. Hicks, H. Scott, J. Castor, A. Lazicki, B. Wilson, T. Luu, D. McNabb, G. Zimmerman

LLNL-PRES-557971

Several physical models are important for manipulating HED matter to ignition

2 LLNL-PRES 557971 dT/dx

Fuel assembly, transport,burn-physics

PLS

Laser Energy = 1.3 MJ

X-ray Energy = 1 MJ

Energy to capsule =120 kJ Set adiabat

Fuel K.E. = 12 KJ, Shell K.E. ~ 20 KJ

Hot spot = 10KJ

Burn propagation

LLNL-PRES-557971

3

Laser Energy = 1.3 MJ

X-ray Energy = 1 MJ

Energy to capsule =120 kJ Set adiabat

Fuel K.E. = 12 KJ, Shell K.E. ~ 20 KJ

Hot spot = 10KJ

Burn propagation

Opacity, laser-plasma interaction, heat & e-transport

Ablator opacity & EOS, drive Spectrum,radiation,e- production & transport

Ablator opacity, drive spectrum, heat & radiation transport, CH & DT EOS

Heat transport, MIX, CH & DT EOS, Kinetics

Transport, MIX, CH& DT EOS, Bremmstrahlung, reaction rates, Kinetics

dT/dx

Fuel assembly, transport,burn-physics

Several physical models are important for manipulating HED matter to ignition

LLNL-PRES 557971

LLNL-PRES-557971

Several NIC discoveries are motivating improvements in our physical models

•  Drive and ablation physics:

•  Implosion velocity, Vimp, is low (EOS, Opacity, drive, Kinetics)

•  Vimp difference between Si and Ge capsules (Opacity, drive)

•  Ablator is thicker than predicted (EOS, NLTE, e- transport)

•  Ablator release into D2 shows was initially off (EOS)

•  Matching shock timing data with simulations requires drive multipliers (EOS, Opacity, drive, LPI)

•  Stagnation Physics and Mix:

•  Yield for a given Vimp and rho-R is low (EOS, Kinetics, transport)

•  Hot spot pressure is low (EOS, Kinetics, transport)

•  More low energy neutrons (<9MeV) than expected (Nuclear, kinetics)

•  τNuclear Burnwidth > τx-ray burnwidth (transport)

•  Mix cliff occurs at higher ablator mass than expected (Transport, kinetics) LLNL-PRES 557971

LLNL-PRES-557971

Our panel will break up into groups focused on physical models, in contrast to implosion stages

Drive Tr(t), drive spectrum

Implosion dynamics

Bangtime, Vimp, shell thickness, shk timing

Stagnation Physics Yield, PHS, rho-R, Ti

Mix Atwood #

Opacity

EOS

Transport

Kinetics

Nuclear

Au, U

Implosion Performance and NIC Observables Physical models

LLNL-PRES 557971

LLNL-PRES-557971

• Ablator opacity (C, Si, Ge) is important for tuning ablation performance, mix and preheat.

• Both NLTE and LTE opacities have been improved recently (H. Scott, S. Hansen, HEDP 6, (2010). B.G. Wilson, et al PRE 76, 032103 (2007). ) but still DCA differs from more sophisticated models and EOS and Opacity are not self consistent.

•  Important to consider convergence effects in photon binning and material zoning while considering effects of Opacity (Hill and Rose).

Optimizing implosion performance requires accurate opacities and emissivities (Si, C, Ge, Au, U)

C, Ge and Si opacity at .1g/cc and 300 eV

Energy (eV) κ

(cm

2 /mol

e)

Bν

kT=300 eV ρ=0.1 g/cc

C Si

Ge

106

102

10-2

100 1000 10,000

300 eV black body

Preheat shielding

Preheat X-rays (>~1.8 keV)

LLNL-PRES 557971

LLNL-PRES-557971

ICF requires knowledge of the hohlraum, ablator and fuel EOS over a broad range of conditions

Cold curve

GDP ablator

Dashed Hugoniot

Pres

sure

(Mba

r)

Density (g/cc)

Complex chemistry

Trajectory for glow discharge polymer (GDP), CH1.3 ablator in ICF implosion

Ablation

Ionization e- thermal

100

10

1

0.1

0.01 10 20 2 1 5

We need to know DT to 1.5 Kg/cc

Other ablator candidates include diamond, Be, B4C, Al LLNL-PRES 557971

LLNL-PRES-557971

Transport processes implicit to forming a burning plasma are largely untested in relevant regeims

•  e-ion coupling in hot spot & dense fuel: •  Stopping power in hot spot & dense fuel: •  Thermal conductivities hot spot & dense fuel: •  Thermal conductivities in CH

Slightly more detailed example (Steve Rose)

• Viscosity models…..

• How to handle mixtures…..

• Bremmstrahlung

• Compton scattering

α

n

radiation Inelastic collisions

Inelastic collisions

Inelastic collsns em+nuclear

nuclear reactions

bremmsstrahlung/ scattering

thermal non-thermal

free electrons

Inelastic collisions

Inelastic collisions DT ions

For Te < 32keV

Thermal conductivity is important for predicting mix and hotspot dynamics

Purgatorio and QMD are in good agreement with D2 data on-Hugoniot but not off-Hugoniot

D2 Data compared to Purgatorio Hugoniot

Off-Hugoniot

Variations in thermal conductivity of a few times effect hydrodynamics at 10g/cc and 10eV

Experimental data: Nellis1992, Nellis1999, Celliers2000, Fortov2003, Ternovoi2009, This work Shell radius (µm)

Theory: Purgatorio from Sterne et al.

LLNL-PRES 557971

LLNL-PRES-557971

11

Thermonuclear (TN) burn in DT plasma involves many complex processesof comparable time scales that compete with dis-assembly

fi(e)

E (keV)

TT= 76 keV

TD= 93 keV

0.01

0.1

1

10 100T (keV)

!"-e /!fusion

!"-DT /!fusion

E" ~ 1 MeV

"'s couple first to electrons,then to ions as T increases

D & T distributions differ& Not quite Maxwellian

" stopping moderates TN burn

Tem

pera

ture

(keV

)

Time (ns)

D

T

electron

radiation

#T$

!" = 0!"

Use VPIC code to simulate infiniteD-T plasma @ % = 100 g/cc, T = 10 keV

Bowers et al., Phys Plasma 15, 55703 (08)

Kinetic ions, D, T, "'s

Fluid electrons

Radiation energy sink

Need to coupleresults to ICFdesign code

Brian Albright

Thermonuclear burn in DT involves many complex processes of comparible time scales that compete with confinement time

G. Dimonte et al

Dimonte

11


fi(e)

E (keV)

TT= 76 keV

TD= 93 keV

0.01

0.1

1

10 100T (keV)

!"-e /!fusion

!"-DT /!fusion

E" ~ 1 MeV




Tem

pera

ture

(keV

)

Time (ns)

D

T

electron

radiation

#T$

!" = 0!"




Fluid electrons



Brian Albright

11


fi(e)

E (keV)

TT= 76 keV

TD= 93 keV

0.01

0.1

1

10 100T (keV)

!"-e /!fusion

!"-DT /!fusion

E" ~ 1 MeV




Tem

pera

ture

(keV

)

Time (ns)

D

T

electron

radiation

#T$

!" = 0!"




Fluid electrons



Brian Albright

LLNL-PRES 557971

LLNL-PRES-557971

Electron ion equilibration is important for hotspot dynamics, shock equilibration, and laser coupling

5

Thermonuclear burn in ICF plasma involves many collisionaltransport processes whose rates can be improved

D

T !

n D

e

T

3.5 MeV

14.1 MeV"i-e

Radiation

0.01 0.1 1 10

T (keV)

1

10

102

103

104

Bremsstrahlung

Fusionion-electron#T ~ 0.1 T

$ = 100 g/cc

dEdt

Thermonuclear processes in ICF

Transport rates depend on long-rangeCoulomb collisions

Maxwellian electrons & ions

Thermal relaxation

Thermal conductivity

Electrical conductivity

Radiative

dTi

dt~ ! ie Te " Ti( )

! process ~ !o ln# process $n

Te3/2ln

bmax

bmin

%

&'(

)*

Temperature decay not exponentialbecause " % T-3/2

Uncertainty in Coulomb log

(relativistic correction)(degeneracy correction)

6

Legacy calculations of temperature relaxation between electrons& ions diverge due to Coulomb force ! r-2

!o

=8

3

2"m

M

e2ei

2

T3 / 2

n

i

e

b

Particle collisions can be described by integrating Rutherford cross-sectionin Boltzman equation, but this diverges due to distant encounters

a !3

4"n#

$ %

&

' (

1/ 3

!ie

= !o

b db

b2

+ Ze2/mv

2( )2

0

bmax

"

!ie

=!o

2ln 1+ 3

bmax

bmin

#

$ %

&

' (

2#

$

% %

&

'

( (

bmin

=Ze

2

kBTe

bmax

)*

Screening parameter bmax

!De

=kBT

4"ne2

!DH

=!De

1+ Z

a =4"n3

#

$ %

&

' (

)1/ 3

Spitzer:

Landau:

Chandrasekhar:

"Dei

Plasma fluctuations (#(k,$) ~ 0) due to discrete electrons & ions aredescribed by Lenard-Balescu, but this diverges due to close encounters

!ie

= !o

k3dk

k •" k,0( ) • k2

0

kmax

#

!ie

= !o

dk

k

k4

k2

+ kDe

2( )2

0

kmax

# = !oln

$De

bmin

%

& '

(

) *

kmax~1

bmin

+,

Need to capture close & distant encounters self-consistently

bmin ~ 1 / kmax

RL =Ze

2

kBT

!Q =!

mkBT

Landau:

deBroglie:

Particle collisions can be described by integrating Rutherford cross-section in Boltzman equation, but this diverges due to distant encounters Plasma fluctuations due to discrete electrons & ions are described by Lenard-Balescu, but this diverges due to close encounters

LLNL-PRES 557971

LLNL-PRES-557971

Electron ion equilibration is important for hotspot dynamics, shock equilibration, and laser coupling

Log(Λ) for hydrogen Lee and More (solid), GMS (dotted), BPS(dashed)

20 40 60 80 100density �g�cc�

5�10�13

1�10�12

2�10�12

5�10�12

1�10�11Tau electron�ion at 1 KeV

Electron ion equilibration time for Lee and More (red), GMS(blue), and BPS (green)

Equilibration times are ~ps while burn durations 10-100 ps

LLNL-PRES 557971

LLNL-PRES-557971

Stopping of charged particles is dominated by electron-ion interactions and contains ion-ion scattering

Alpha stopping

dEdx

=CiondEdx i

+CiondEdx e

+CiondEdx b

Contribution from Ions Free e- Bound e-

Details for stopping power

Te=1 KeV, ne= 5e25

dE/d

x (M

eV/m

icro

n)

.8

.4

0 0 2 4

Vp/Ve Vp/Ve

Te=10 KeV, ne= 1e24

dE/d

x (M

eV/m

icro

n)

0 2 4

.004

.002

0

NIC estimate: solid BPS: Circles Landau & Lifshitz: dashed Li & Petrasso: triangle

LLNL-PRES 557971

LLNL-PRES-557971 Summary of candidate multi-species and kinetic effects Shock Separation

Frictional Shock Heating of DT Heating Due to Tail of Distribution

Species Separation in Ablator

Pressure gradient-induced E-field causes lighter species to accelerate ahead of heavier species

Some fraction of ablation energy goes into separating C from H, resulting in loss of ablation efficiency

During hot spot formation, electrons in tail of energy distribution (~10 X Te) may heat fuel

Ion coupling heats T in front of T shock

D shock hits r=0 first T

[keV

]

Radius [µm] 0 100 200

1

2

3

4

--- Kinetic --- Fluid

T shock lags

Shocks in dense plasma cause relative drift speed between species: energy in directed V goes into heat

!M =Ni

2!H +!C + 7!e " kBT 2 ln9+ 7ln 9 / 7( )( )#$ %& !U =!M +"!

CH C H 1-c1 c1

Fuel region

T ion

[eV

]

40

60

80

100

120 130 140

Hot Spot

Radius [µm]

E-field Pressure

D D

D D

D D

D D

D D D D D

T D

D D

D D D

Shock front structure

Ther

mal

sho

ck p

recu

rsor

T T T

T

T T

T T T

T T

T

T T T

T T

T

e- e-

e-

e-

e- e-

e-

e-

e-

e-

e-

e- e-

e-

e- !!d !

2!i!" 2DkE #

e!E

kBT

@ 2.5 ps

LLNL-PRES 557971

LLNL-PRES-557971

Thermonuclear Burn as well as nuclear diagnostic data interpretation depend on nuclear reaction rates

D-T reaction rate is extremely dependent on Tion. α-particles can heat up electrons and ions differently.

LLNL-PRES-557971

The first nuclear cross section measurement using an ICF facility has been made at Omega

Measurements of the Differential Cross Sections for the Elastic n-3H and n-2H Scatteringat 14.1 MeV by Using an Inertial Confinement Fusion Facility

J. A. Frenje, C. K. Li, F. H. Seguin, D. T. Casey, and R.D. PetrassoPlasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

D. P. McNabb, P. Navratil, and S. QuaglioniLawrence Livermore National Laboratory, Livermore, California 94550, USA

T. C. Sangster, V. Yu Glebov, and D.D. Meyerhofer*

Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA(Received 18 June 2011; published 15 September 2011)

For the first time the differential cross section for the elastic neutron-triton (n-3H) and neutron-deuteron(n-2H) scattering at 14.1 MeV has been measured by using an inertial confinement fusion facility. In these

experiments, which were carried out by simultaneously measuring elastically scattered 3H and 2H ions

from a deuterium-tritium gas-filled inertial confinement fusion capsule implosion, the differential cross

section for the elastic n-3H scattering was obtained with significantly higher accuracy than achieved in

previous accelerator experiments. The results compare well with calculations that combine the resonating-

group method with an ab initio no-core shell model, which demonstrate that recent advances in ab initio

theory can provide an accurate description of light-ion reactions.

DOI: 10.1103/PhysRevLett.107.122502 PACS numbers: 25.40.Dn, 52.57.!z

The development of an accurate description of light-ionreactions is currently of great interest as it would providevaluable insight into low-energy nuclear reactions impor-tant to nuclear astrophysics. Radiative capture reactions, forexample, occur in red giants at temperatures low enoughthat the reaction rates are too small to be directly measuredin a laboratory. Extrapolation from measurements at higherenergies is also suspect without a fundamental theory forcomputing these reactions. Fusion energy research alsorequires accurate cross sections for light-ion reactions toconstrain models of inertial confinement fusion (ICF) ex-periments involving deuterium-tritium fuel. For instance,uncertainties in the differential cross section for the elasticn-3H scattering need to be"5% to reliably infer a fuel arealdensity (!R) from the yield ratio between scatteredneutrons and primary 14.1-MeV neutrons, called thedown-scatter ratio [1], produced in an ICF implosion. Thedetermination of the!R from the down-scatter ratio value isessential for understanding how the fuel is assembled in animplosion and for ultimately guiding the community to-wards the demonstration of thermonuclear ignition and netenergy gain [2] at the National Ignition Facility [3].

Since the 1950s, the differential cross section for theelastic n-3H scattering at 14.1 MeV has been subject toboth experimental and theoretical studies. Kootsey [4]measured the cross section at center-of-mass (CM) anglesranging from 55# to 165#, resulting in data with statisticaluncertainties of "20% and a systematic uncertainty of11%. Shirato et al. [5] and Debertin et al. [6] measuredthe cross section in the CM angular range of 100#–175#

with an uncertainty varying from "10% to "70%, and

their results are in good agreement with each other but upto a factor of 2 smaller than the Kootsey data. Optical-model calculations conducted by DeVries et al. [7] and bySherif and Podmore [8] reproduced the Shirato andDebertin data in this CM angular range. Additionally,Hale et al. [9] conducted an R-matrix analysis of allexperimental data sets, and the result from that analysisforms the basis of the current ENDF/B-VII evaluation [10]of the differential cross section for the elastic n-3H scat-tering that can be found in nuclear databases. Althoughefforts have been made to quantify this fundamental crosssection, significant discrepancies exist between the differ-ent measurements and between measurements and models.However, a theoretical understanding of the n$ 3H scat-tering based on first principles calculations is within reach[11]. For example, ab initio variational calculations using ahyper-spherical harmonics basis expansion performed witha modern nuclear Hamiltonian consisting of an accuratenucleon-nucleon potential and a three-nucleon interactionprovide a good description of the differential cross sectionfor elastic n$ 3H scattering at low energies [12]. However,this type of calculation is currently limited to energiesbelow the breakup threshold.This Letter describes the first measurement of the dif-

ferential cross section for the elastic n-3H scattering at14.1 MeV by using an ICF facility. It also describes atheoretical calculation [13] of this cross section, whichcombines the ab initio no-core shell model [14] with theresonating-group method [15] into a unified method(NCSM/RGM) [16]. By using this theoretical approach,an accurate assessment of the n-3H cross section can be

PRL 107, 122502 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending

16 SEPTEMBER 2011

0031-9007=11=107(12)=122502(5) 122502-1 ! 2011 American Physical Society

Simultaneous measurements of d’ and t’ spectra scattered by d-t neutrons.

Comparison with ab initio calculations

1.  P. Navrátil et al., LLNL-TR-423504 (2010). 2.  Ga.A. Hale et al., Phys. Rev. C 42, 438 (1990).

n-D,T Elastic Scattering Plasma is neutron source and target

LLNL-PRES 557971

LLNL-PRES-557971

Next several talks will outline each of the physics models in the codes. What are we missing?

Drive Tr(t), drive spectrum

Implosion dynamics

Bangtime, Vimp, shell thickness, shk timing

Stagnation Physics Yield, PHS, rho-R, Ti

Mix Atwood #

Opacity

EOS

Transport

Kinetics

Nuclear

Au, U

Implosion Performance and NIC Observables Physical models

LLNL-PRES 557971

Details of our electron ion equilibration and stopping power follow in the next 6 vgs

LLNL-PRES-557971

Details for electron ion equilibration model used in NIC calculations

Details for electron ion equilibration

LLNL-PRES 557971

LLNL-PRES-557971

Log Λei is largely from Lee and More


LLNL-PRES 557971

LLNL-PRES-557971

Log( ) for hydrogen: Lee & More (solid), GMS6 (dotted), BPS (dashed)

!ei


9

6

3

0 1022 1023 1024 1025

T=10 KeV

T=1 KeV

T=0.1 KeV

!ei

ne(1/cm3)

LLNL-PRES 557971

LLNL-PRES-557971


Alpha stopping

dEdx

=CiondEdx i

+CiondEdx e

+CiondEdx b


Ion contribution is small accept at very high Te or electron density


LLNL-PRES 557971

LLNL-PRES-557971

Free electron stopping includes degeneracy and full range of ion-e- velocities

Bound electron stopping uses average excitation energy from More UCRL-84991, Sec VII

Alpha stopping

dEdx

=CiondEdx i

+CiondEdx e

+CiondEdx b




LLNL-PRES 557971

LLNL-PRES-557971

For burn conditions dE/dx used in ignition calculations agree with Brown, Preston and Singleton

Te=1 KeV, ne= 5e25

dE/d

x (M

eV/m

icro

n)

.8

.4

0 0 2 4

Vp/Ve Vp/Ve

Te=10 KeV, ne= 1e24

dE/d

x (M

eV/m

icro

n)

0 2 4

.004

.002

0

NIC estimate: solid BPS: Circles Landau & Lifshitz: dashed Li & Petrasso: triangle

LLNL-PRES 557971

End of Intro talk

Physical Models for NIC EOS, Opacity, Transport, … · Physical Models for NIC EOS, Opacity,...

Documents

Transcript of Physical Models for NIC EOS, Opacity, Transport, … · Physical Models for NIC EOS, Opacity,...