One-Dimensional Simulation of the Effectsof Unstable Mix on Neutron and Charged Particle Yield

from Laser-Driven Implosions

R. EpsteinUniversity of RochesterLaboratory for Laser Energetics

31st Annual AnomalousAbsorption Conference

Sedona, AZ3–8 June 2001

MITPrimary neutron yield

1010109

Experimental yield

1012

1010

Sim

ula

ted

yie

ld 1011

1091011 1012

Collaborators

J. A. DelettrezV. Yu. Glebov

V. N. GoncharovP. W. McKenty

P. B. RadhaV. A. Smalyuk

C. StoecklS. Skupsky

Laboratory for Laser EnergeticsUniversity of Rochester

J. FrenjeC. K. Li

R. D. PetrassoF. H. Séguin

Massachusetts Institute of Technology

MIT

Mix effects on particle yields can be described effectivelyby mix modeling in the 1-D hydrocode LILAC

TC5664

MIT

• The mix model includes the transport of target constituents,thermal energy, and turbulent energy due to both the accelerationand deceleration instabilities.

• Including mix in 1-D simulations of experiments providesimproved predictions of primary and secondary particle yieldsover a broad range of target performance.

Summary

Outline

TC5665

MIT

• Modeling of mix in 1-D

• Comparison of simulated and experimental yields

• Secondary neutron and proton production

• Conclusions

“Bubble and spike” mixing thickness is obtained froma multimode Rayleigh–Taylor perturbation model*

TC5195a *S. W. Haan, Phys. Rev. A 39, 5812 (1989).

Takabe/Betti form for γ2(t)

Haan saturationprocedure for

Initial perturbation spectrumAl(t = t0) specified at ablationsurface and fed through tofuel–pusher interface overtime.

Al t( ) �2R t( )*

l2

•

•

•

•

d2

dt2Al lγ 2 t( ) A=

including Bell-Plesset effects

Time (arbitrary units)

Rad

ius

(arb

itra

ry u

nit

s)

CH

D2

CH

CH

Mixing boundaries Ablation surface andfuel–pusher interface

Mix is modeled as a diffusivetransport process.

•

The mix model is based on carefullyformulated phenomenology

TC5666

• Perturbations due to single-beam imprint were obtained from ORCHIDcalculations based on measured single-beam nonuniformity.

• Beam-imbalance effects are based on power-imbalance measurementsfrom each shot and the geometrical superposition of the accelerationdistributions of 60 beams.

• The formulation of the perturbation growth using fully time-dependentperturbation equations allows secular nonuniform irradiation effectsand “feedthrough” from the outer to the inner instabilities to be treatedas driving terms, rather than as instantaneous effects.

• Plausible flux limitation of the diffusive mix transport is obtained byallowing that the mixed constituent profiles can remain self-similarunder expansion.

Mix modeling improves the agreement of simulatedprimary neutron yield with implosion data

TC5667

MIT

Clean

Mix

Clean, 3 atm

Mix, 3 atm

Primary neutron yield

1010109

Experimental yield

1012

1010

Sim

ula

ted

yie

ld 1011

109

• Data from eight shots (August 2000)

• Pure-CH shells, 20–27 µm, 900-µm diameter, D2 fill, 3–25 atm

1011 1012

Primary yield ratios indicate that implosion degradationis comparable to the predictions of mix modeling

TC5668

MITRatio of measured to simulated primaryneutron yield

20 2727 2720

Shell thickness (µm)

10.0

1.0

0.1

Dat

a/si

mu

late

d

3 atm 15 atm 25 atm

Clean

Mix

Mix, 1/2 powerimbalance

Simulated and measured neutron-averaged temperaturesshow some improved agreement with mix modeling

TC5669

MIT

Clean

Mix

Clean, 3 atm

Mix, 3 atm

Ion temperature

3.0 4.02.0Experimental (keV)

5.0

3.0

1.0

Sim

ula

ted

(K

eV) 4.0

2.0

Comparison of simulated with measured secondaryparticle yield ratios suggests sensitivity to dynamics

TC5670

MITSecondary production efficiencies

10

Experimental (× 10–3)

3

1

Sim

ula

ted

(× 10–3)

2

02 3

neutrons2/neutrons1 protons2/neutrons1

Clean

MixClean, 3 atm

Mix, 3 atm

10

Experimental (× 10–3)2

The spatial distribution of secondary particleproduction depends on the extent of mix

TC5671

MITTotal particle yields

0.01

Mass radius (µg) or [original CH thickness (µm)]

5

3

m ×

dn

/dm

(×1

07) 4

2

1.00.1

3 atm fill 15 atm fill3

2

1

1

0

• Mix thickness (mxth) is from the 1:3 to 3:1 mix points at the timeof peak n1 production rate.

• With the mass-spatial distribution as plotted here, the area underthe curve is preserved.

010.0 0.01 1.00.1 10.0

mxth

[1][0]

mxth

[1][0]

n1 × 10–3

n2p2

The relative timing of peak neutron production andpeak compression does not affect the coincidence ofprimary and secondary production times

TC5672

MIT20-µm shells

1.6

Time (ns)

1019

1017

dn

/dt

(s–1

)

1018

1016

2.01.8

3 atm fill 15 atm fill

1.61.4

Time (ns)

2.0

ρ Dr

(mg

/cm

2 )

15

10

5

5

0

ρDr p2n2 n1 × 10–3

1015 01.8

Mix effects on particle yields can be described effectivelyby mix modeling in the 1-D hydrocode LILAC

TC5673

MIT

• The mix model includes the transport of target constituents,thermal energy, and turbulent energy due to both the accelerationand deceleration instabilities.

• Including mix in 1-D simulations of experiments providesimproved predictions of primary and secondary particle yieldsover a broad range of target performance.

• The validity of approximating multidimensional hydrodynamicswith a spherically symmetric model remains an issue.

Summary/Conclusion