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