1. !
The Hydrodynamic Sensitivity of the NIF Low-Foot Pulse to Laser Power Variations
The National Ignition Facility works to achieve high gain inertial confinement fusion through the laser driven implosion of a Deuterium-Tritium ice capsule. This is an inherently unstable process, with
the Rayleigh-Taylor instability (RTI) being a primary contributor as it hinders the implosion at two points in time: capsule acceleration and deceleration. A sensitivity analysis was conducted on how
small changes in the laser power of the “Low-Foot” laser drive design affect the growth rate of RTI at the ablation front, when the capsule is accelerating inward during compression. A distribution of
low and high growth values were present in 1D Sn simulations but not in simulations with diffusion radiation transport. The 1D analytic stability trends were supported by 2D simulations. Statistical
trends in the Sn simulations show that a weaker final shock in the laser pulse can potentially increase RTI growth during rebound shock transit.
Introduction
Inertial confinement fusion (ICF) of an imploding capsule suffers from
hydrodynamic instabilities such as the Rayleigh-Taylor instability (RTI). !
!
RTI will occur when: !
1) a lighter fluid is supporting a heavier fluid!
2) a lighter fluid is accelerated into a denser fluid. !
!
Perturbations at the interface between these two fluids will!
grow in time due to the acceleration and other factors.!
!
The National Ignition Facility (NIF) uses a laser driven, indirect!
drive approach to ICF. Instability growth in the capsule is
dependent on the pulse shape of the laser being used. !
!
A sensitivity analysis was done on the RTI growth due to power fluctuations in
the Low-Foot Laser pulse used during the National Ignition Campaign.
• 1000 unique pulse variations were simulated in HYDRA in 1D. The same
variations were run for both Sn and diffusion radiation transport
!
•Laser pulse modifications were drawn
from a Gaussian distribution with mean
zero and a standard deviation based on
low-foot NIC laser delivery requirements1
!
• RTI growth was calculated for a given
Legendre mode with the equation:!
! ! ! ! ! ! ! η = ηo e ∫ 𝛾 dt!
With 𝛾 (RTI growth rate) being calculated
with analytic equations from Betti, et al2 !
!
• Analyzed data for trends in time
integrated growth values ( ∫𝛾 dt ) with
respect to laser power modifications!
Methods
Conclusions & Future Work
Lucas M. Rolison1,2, Luc Peterson2!
1University of Florida, 2Lawrence Livermore National Laboratory, WCI, AX Division
Results
⍴2 > ⍴1!
!
!
⍴1 ⍴2
a
Flux
±4% !
Flux!
±4% !
Flux!
±4% !
Flux!
±4% !
Flux!
±3.5%!
• Given the low-foot NIC laser delivery requirements, a probability exists for weaker finals shocks that may increase RTI
growth during rebound shock transit!
• 1D analytic trends are supported by 2D simulations but there is a disconnect between Sn1D and Dif1D methods!
• Implementation of an improved method for calculating RTI instability growth based on the following differential
equation:!
d2η/dt2 - 𝛾2η = 0!
• Account for spherical convergence in 1D simulations!
• Gather more samples in order to improve the statistics of the high growth histograms and improve confidence!
This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
LLNL-POST-658300
Two Distributions!
for Stability!
!
Low Growth
(More Stable)!
!
High Growth
(Less Stable)
• Stability different for Sn and diffusion radiation transport!
• High growth simulations tend to have weaker shock 4!
• High growth occurs during rebound shock transit
• Significant probability for high growth to occur in Sn1D,
especially at lower modes!
• Most stable 1D shows least growth in 2D
1. Haan, et al. “Point design targets, specifications, and requirements for the 2010 ignition campaign on the National Ignition Facility”, Phys. Plasmas 18, 051001 (2001);
doi: 10.1063/1.3592169!
2. Betti, et al. “Growth rates of the ablative Rayleigh-Taylor instability in inertial confinement fusion”, Physics of Plasmas (1994-present) 5, 1446 (1998); doi: 10.1063/1.878202
0 50 100 150
−500
0
500
Growth Factors, 200 um
Legendre Mode
Fuel−AblatorGrowthFactor
0 50 100 150
−1000
0
1000
Legendre Mode
AblationFrontGrowthFactor
Growth Factors, 200 um
2D Growth Simulations Using Diffusion
Least Stable in 1D!
Most Stable in 1D
Laser pulses with!
High Growth!
Low Growth