BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Statistically Informed Physics Understanding and Design Optimizati
on of Direct-Drive Inertial Confinement Fusion Experiments
DTSTART;VALUE=DATE-TIME:20210512T162500Z
DTEND;VALUE=DATE-TIME:20210512T164500Z
DTSTAMP;VALUE=DATE-TIME:20210417T023150Z
UID:indico-contribution-17391@conferences.iaea.org
DESCRIPTION:Speakers: Varchas Gopalaswamy (University of Rochester/Laborat
ory for Laser Energetics)\nFinding an optimized Inertial Confinement Fusio
n[1–3](ICF) experimental design is a challenge due to the large number o
f physical parameters that can be modified from experiment to experiment\,
and the inability of simulations to accurately\nand rapidly a priori pred
ict experimental results when these changes are made. Recently\, a novel m
ethod[4] has been developed to address this issue by statistically couplin
g simulation and experimental outcomes\, resulting in the first truly pred
ictive models for the observables of ICF experiments. These models have be
en used to design the highest performing experiments on the OMEGA laser sy
stem[5]\, which are predicted to result in about 500 kJ of fusion yield at
\nenergies typical of the National Ignition Facility (NIF)[6]. Analyzing t
he dependencies of the models have also resulted in an improved scientific
understanding of the degradation mechanisms affecting implosions on the O
MEGA laser system. and has led to facility upgrades that have increased p
erformance and reproducibility for ICF experiments.\n\nThe rather large pa
rameter space over which design optimization takes place necessitates the
existence of a rapid and accurate predictive tool to conduct any optimizat
ion scheme whose end goal is ignition[7\,8]\, a necessity for inertial fus
ion energy (IFE) to become a reality. Historically\, the primary tool in I
CF design has been the radiation-hydrodynamic (RH) simulation[9–13]. Tho
ugh recent advances in physics understanding has led to RH simulations ach
ieving better\nagreement with experimental observations[14–17]\, these s
imulations (regardless of spatial dimension) are not yet able to predict t
he results of a future experiment in which the initial conditions have bee
n changed a priori.\n\nThe inability of RH codes to accurately predict the
effect of changes in their designs is likely a major obstacle in achievin
g ignition in ICF\, since it precludes any effective implementation of ite
rative optimization methodologies that could be use to rapidly increase pe
rformance. This predictive deficit also\nseverely restricts the ability of
scientists to identify degradation mechanisms directly from experimental
data\, as the effect of a degradation mechanism cannot be easily decoupled
from varying initial conditions in the absence of an accurate predictive
model (statistical\, or otherwise).\n\nHowever\, consider that if the outp
uts of an RH code $\\mathbf{O}_{\\textrm{1D}}^{\\textrm{sim}}$ uniquely de
fine the inputs to the code \n $\\mathbf{I}_{\\textrm{1D}}$ (which are als
o the inputs to the experiment)\, then it follows that the outputs of the
experiment \n$\\mathbf{O}_{\\textrm{3D}}^{\\textrm{exp}}$ are $ \\begin{eq
uation} \n\\mathbf{O}_{\\textrm{3D}}^{\\textrm{exp}} = \\mathbf{F}_{\\text
rm{3D}}^{\\textrm{exp}}\\left[ \\mathbf{I}_{\\textrm{1D}}\,\\mathbf{S}_{\\
textrm{3D}}^{\\textrm{sys}}\,\\mathbf{S}_{\\textrm{3D}}^{\\textrm{ran}} \\
right]\,\n\\end{equation}$ \n\nwhere \n$\\mathbf{S}_{\\textrm{3D}}^{\\text
rm{sys}}$ and $\\mathbf{S}_{\\textrm{3D}}^{\\textrm{ran}}$ are systematic
and random 3D perturbations in the experiment. For a repeatable experiment
\, $\\mathbf{S}_{\\textrm{3D}}^{\\textrm{ran}} << \\mathbf{S}_{\\textrm{3D
}}^{\\textrm{sys}}$\, and we have \n$\\begin{equation}\n \\mathbf{O}_{\
\textrm{3D}}^{\\textrm{exp}} =\\mathbf{F}_{\\textrm{3D}}^{\\textrm{exp}}\\
left[ \\mathbf{I}_{\\textrm{1D}}\,\\mathbf{S}_{\\textrm{3D}}^{\\textrm{sys
}} \\right]=\\mathbf{F}_{\\textrm{3D}}^{\\textrm{map}}\\left[ \\mathbf{O}_
{\\textrm{1D}}^{\\textrm{sim}} \\right]\n\\end{equation}$ \n\nsince $\\mat
hbf{S}_{\\textrm{3D}}^{\\textrm{sys}}$ are constants. This implies that th
e results of an experiment can be related to the outputs of a 1D RH code b
y the function $\\mathbf{F}_{\\textrm{3D}}^{\\textrm{map}}$. Ref. 4 approx
imates $\\mathbf{F}_{\\textrm{3D}}^{\\textrm{map}}$ with power laws\, and
reconstructs it statistically by comparing a database of over 200 OMEGA di
rect-drive cryogenic implosions spanning a wide range of initial condition
s\, resulting in models for the neutron yield\, areal density and hotspot
radius (Fig.1). Ensemble averages of several semi-independent models const
ructed using this method can be taken to generate predictions. These predi
ctions are typically accurate to within 10%\, (Fig. 1) making them conside
rably more accurate than 1D simulation results. They are also pessimistic
compared to 1D simulations\, which fail to predict the rapid drop-off in y
ield when the adiabat decreases and convergence increases. Instead\, the p
redictive models correctly expect low yields and areal densities for highl
y convergent\, low adiabat implosions.\n![Fig.1\, Model yield predictions
(circles) vs simulations (squares).][1]\nAs the statistically inferred $\\
mathbf{F}_{\\textrm{3D}}^{\\textrm{map}}$ operates on 1D simulations\, a l
arge swathe of parameter space can be rapidly scanned for viable designs\,
enabling rapid and iterative design. Using these models\, a performance i
mprovement campaign was conducted on OMEGA\, as reported in Ref. 4. By fol
lowing the recommendations of the models\, the neutron yield on OMEGA was
tripled\, and the areal density was increased by 60%. Due to OMEGA’s ene
rgy constraints\, the ignition-relevant performance of these implosions wa
s assessed by the theory of hydrodynamic scaling[18]\, and were predicted
to produce fusion yields of about 500 kJ\, with a normalized Lawson parame
ter[19] of about 0.7 when scaled to 1.9 MJ of symmetric drive (Fig. 2). Pr
evious results on OMEGA[20] were expected produce approximately 100 kJ of
fusion energy when scaled to 1.9 MJ of symmetric drive[21]\, and recent in
direct-drive experiments at the NIF have demonstrated 56 kJ of fusion ener
gy[22].\n\n![Fig.2\, Extrapolated fusion energy vs Lawson parameter[19].][
2]\n\nInspecting the exact form of a predictive model has also led to phys
ics insight regarding the degradation mechanisms active on OMEGA. In parti
cular\, it was observed[23] that targets filled with tritium close to the
shot date tended to be underpredicted\, while targets filled well before t
he shot tended to be overpredicted (Fig. 3). Accounting for this improved
the prediction accuracy\, including for a number of ‘outlier’ implosio
ns\, prompting an investigation for the underlying physical mechanism. One
hypothesis was the build-up of Helium-3\nfrom the beta decay of tritium\,
which considerably increases the initial vapor pressure of the target. A
new database of simulations that accounted for the initial vapor pressure
of He3 was constructed\, and it was found that the quality of prediction r
emained high even in the absence of ad-hoc variables to\naccount for the a
ge of the fill. As this is a relatively small (10-20% for moderate adiabat
s) effect relative to changes in design\, the statistical model was essent
ial in providing a baseline expectation from which deviations could be ide
ntified. Recent controlled experiments have confirmed this dependence (Fig
. 2)\, and changes to the OMEGA facility to minimize the fill age are unde
rway to maximize future performance. \n\n![Fig.3\, Left: Short fills (blac
k triangles) are under-predicted\; long fills (orange triangles) are over-
predicted. Right: He3 buildup is incorporated into simulations\; all shots
(including those with large fill time deviations) are predicted accuratel
y.][3]\n\nThough the US ICF program has not yet achieved ignition\, steady
progress over the last few decades means that only comparatively modest i
mprovements are required to demonstrate ignition (Fig. 2)\, which is neces
sary for the realization of IFE. While we cannot know the exact magnitude
of the improvements the statistical model can provide\, it is clear that a
pplying the statistical model to generating new designs\, and to investiga
te and eliminate degradation sources has the potential to push the ICF pro
gram to the high yields necessary for IFE.\n\n\n\n\n\n\n1. J. Nuckolls\, e
t. al\, Nature 239 (1972)\n2. S. Atzeni et. al\,(Oxford Univ. Press\, Oxfo
rd\, 2004).\n3. S. Craxton\, Phys. Plasmas 22 (2015)\n4. V. Gopalaswamy\,
et al. Nature 565\, 581–586 (2019).\n5. R. Boehly\, Opt.Commun. 133 (199
7)\n6. E. M. Campbell and W. J. Hogan\, Plasma Phys. Contr. Fusion 41 (199
9)\n7. A. R. Christopherson\, Phys. Plasmas 25 (2018)\,\n8. R. Betti\, Phy
s. Rev. Lett. 114 (2015)\n9. J. Delettrez\, et. al\, Phys. Rev. A 36 (1987
)\,\n10. P. B. Radha\, Phys. Plasmas 12 (2005)\,\n11. G. Zimmerman\, et. a
l\, J. Opt. Soc. Am. 68 (1978).\n12. M. M. Marinak\, Phys. Plasmas 8 (2001
)\,\n13. S. Atzeni\, Comput. Phys. Commun. 169 (2005)\n14. I. V. Igumenshc
hev\, Phys. Plasmas 17 (2010)\,\n15. D. T. Michel\, High Power Laser Sci.
Eng. 3 (2015)\n16. V. N. Goncharov\, Phys. Plasmas 13 (2006)\n17. S. X. Hu
\, Phys. Rev. E 92 (2015)\n18. R. Nora\, Phys. Plasmas 21(2014)\,\n19. R.
Betti\, Phys. Plasmas 17 (2010)\n20. S. Regan\, Phys.Rev. Lett. 117 (2016)
\n21. A. Bose\, Phys. Rev. E 94 (2016)\n22. S. Pape\, Phys. Rev. Lett. 120
(2018)\n23. A. Lees\, et. al\, Bull. Am. Phys. Soc. 64 (2019).\n\n\n [1]
: https://drive.google.com/thumbnail?id=1sWyeW_zk_C86DbgVWTfLCBbbwZ5_grPH\
n [2]: https://drive.google.com/thumbnail?id=1DqDJCg5AzLZJOj7puKSl9m2O_Hu
6ngt8\n [3]: https://drive.google.com/thumbnail?id=1AQrsiNR78aKzC6sP5nE0f
89Ac9_6C60t\n\nhttps://conferences.iaea.org/event/214/contributions/17391/
LOCATION:Virtual Event
URL:https://conferences.iaea.org/event/214/contributions/17391/
END:VEVENT
END:VCALENDAR