Theory of ignition and burn propagation in inertial fusion implosions

Christopherson, A. R.; Betti, R.; Miller, S.; Gopalaswamy, V.; Mannion, O. M.; Cao, D.

doi:10.1063/1.5143889

Title: Theory of ignition and burn propagation in inertial fusion implosions

Journal Article · Thu May 21 00:00:00 EDT 2020 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5143889· OSTI ID:1631033

^[1]; Betti, R. ^[1];

^[1];

^[2]; Cao, D. ^[2]

Univ. of Rochester, NY (United States). Lab. for Laser Energetics
Univ. of Rochester, NY (United States)

A detailed analytic model is presented here to investigate the physics of burn propagation in inertially confined plasmas. The onset of ignition and burn propagation occurs when alpha heating of the hot spot causes rapid ablation of shell mass into the hot spot. This allows large energy gains to be achieved since most of the fuel mass is located in the shell. Here, we first present a comprehensive review of previous analytic models that have been used to describe the physics of hot-spot evolution and ignition; we then show that a proper description of a propagating burn wave requires a comprehensive model of hot spot and shell evolution that includes proper mass conservation in the shell, fusion reactivity, and fuel depletion. The analytic theory is in good agreement with detailed radiation-hydrodynamic simulations that predict the onset of burn propagation as occurring when the yield enhancement caused by alpha heating is between 15- and 25-fold, $$f_α$$ ~ 1.4, where $$f_α$$ = alpha energy deposited/hot-spot energy at bang time, and the hot-spot burnup fraction is approximately 2%. We show that the definition of ignition is not sensitive to the alpha-particle stopping power nor asymmetries provided that the absorbed fraction of alpha particles $$θ_α$$ is correctly accounted for. Finally, we use the results of 2-D simulations to show that even when $$θ_α$$ is small and unknown (as is true in hot spots with mid modes that have significant leakage of alpha particles into the surrounding cold bubbles), one can still relate the experimentally measureable parameter $$\chi^{53}_α$$ to the yield amplification and the burning-plasma parameter $$Q^{\text{hs}}_α$$ = alpha energy deposited/total input work delivered to the hot spot

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Research Organization:: Univ. of Rochester, NY (United States). Lab. for Laser Energetics

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); New York State Energy Research and Development Authority

Grant/Contract Number:: NA0003856

OSTI ID:: 1631033

Alternate ID(s):: OSTI ID: 1630376

Report Number(s):: 2019-287; 2522; 1566; 2019-287, 2522, 1566; TRN: US2200731

Journal Information:: Physics of Plasmas, Vol. 27, Issue 5; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 18 works

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References (71)

Progress towards ignition on the National Ignition Facility Edwards, M. J.; Patel, P. K.; Lindl, J. D. Physics of Plasmas, Vol. 20, Issue 7 https://doi.org/10.1063/1.4816115	journal	July 2013
Laser-driven fusion Brueckner, Keith A.; Jorna, Siebe Reviews of Modern Physics, Vol. 46, Issue 2 https://doi.org/10.1103/RevModPhys.46.325	journal	April 1974
Escape of α Particles from a Laser-Pulse-Initiated Thermonuclear Reaction Krokhin, Oleg N.; Rozanov, Vladislav B. Soviet Journal of Quantum Electronics, Vol. 2, Issue 4 https://doi.org/10.1070/QE1973v002n04ABEH004476	journal	April 1973
Measuring the absolute deuterium–tritium neutron yield using the magnetic recoil spectrometer at OMEGA and the NIF Casey, D. T.; Frenje, J. A.; Gatu Johnson, M. Review of Scientific Instruments, Vol. 83, Issue 10 https://doi.org/10.1063/1.4738657	journal	October 2012
Review of the National Ignition Campaign 2009-2012 Lindl, John; Landen, Otto; Edwards, John Physics of Plasmas, Vol. 21, Issue 2 https://doi.org/10.1063/1.4865400	journal	February 2014
The physics of DT ignition in small fusion targets Kirkpatrick, R. C.; Wheeler, J. A. Nuclear Fusion, Vol. 21, Issue 3 https://doi.org/10.1088/0029-5515/21/3/008	journal	March 1981
Fuel gain exceeding unity in an inertially confined fusion implosion Hurricane, O. A.; Callahan, D. A.; Casey, D. T. Nature, Vol. 506, Issue 7488 https://doi.org/10.1038/nature13008	journal	February 2014
Theory of alpha heating in inertial fusion: Alpha-heating metrics and the onset of the burning-plasma regime Christopherson, A. R.; Betti, R.; Howard, J. Physics of Plasmas, Vol. 25, Issue 7 https://doi.org/10.1063/1.5030337	journal	July 2018
Progress toward a self-consistent set of 1D ignition capsule metrics in ICF Lindl, J. D.; Haan, S. W.; Landen, O. L. Physics of Plasmas, Vol. 25, Issue 12 https://doi.org/10.1063/1.5049595	journal	December 2018
Capsule modeling of high foot implosion experiments on the National Ignition Facility Clark, D. S.; Kritcher, A. L.; Milovich, J. L. Plasma Physics and Controlled Fusion, Vol. 59, Issue 5 https://doi.org/10.1088/1361-6587/aa6216	journal	March 2017
Neutron spectrometry—An essential tool for diagnosing implosions at the National Ignition Facility (invited) Johnson, M. Gatu; Frenje, J. A.; Casey, D. T. Review of Scientific Instruments, Vol. 83, Issue 10 https://doi.org/10.1063/1.4728095	journal	October 2012
Ignition condition and gain prediction for perturbed inertial confinement fusion targets Kishony, Roy; Shvarts, Dov Physics of Plasmas, Vol. 8, Issue 11 https://doi.org/10.1063/1.1412009	journal	November 2001
Deceleration phase of inertial confinement fusion implosions Betti, R.; Anderson, K.; Goncharov, V. N. Physics of Plasmas, Vol. 9, Issue 5 https://doi.org/10.1063/1.1459458	journal	May 2002
Hot-spot dynamics and deceleration-phase Rayleigh–Taylor instability of imploding inertial confinement fusion capsules Betti, R.; Umansky, M.; Lobatchev, V. Physics of Plasmas, Vol. 8, Issue 12 https://doi.org/10.1063/1.1412006	journal	December 2001
Integrated diagnostic analysis of inertial confinement fusion capsule performance Cerjan, Charles; Springer, Paul T.; Sepke, Scott M. Physics of Plasmas, Vol. 20, Issue 5 https://doi.org/10.1063/1.4802196	journal	May 2013
Generalized Measurable Ignition Criterion for Inertial Confinement Fusion Chang, Py.; Betti, R.; Spears, B. K. Physical Review Letters, Vol. 104, Issue 13 https://doi.org/10.1103/PhysRevLett.104.135002	journal	April 2010
Initial performance results of the OMEGA laser system Boehly, T. R.; Brown, D. L.; Craxton, R. S. Optics Communications, Vol. 133, Issue 1-6 https://doi.org/10.1016/S0030-4018(96)00325-2	journal	January 1997
Inertial confinement fusion ignition criteria, critical profiles, and burn wave propagation using self-similar solutions Kishony, Roy; Waxman, Eli; Shvarts, Dov Physics of Plasmas, Vol. 4, Issue 5 https://doi.org/10.1063/1.872314	journal	May 1997
Improving the hot-spot pressure and demonstrating ignition hydrodynamic equivalence in cryogenic deuterium–tritium implosions on OMEGA Goncharov, V. N.; Sangster, T. C.; Betti, R. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4876618	journal	May 2014
Alpha Heating and Burning Plasmas in Inertial Confinement Fusion Betti, R.; Christopherson, A. R.; Spears, B. K. Physical Review Letters, Vol. 114, Issue 25 https://doi.org/10.1103/PhysRevLett.114.255003	journal	June 2015
Point design targets, specifications, and requirements for the 2010 ignition campaign on the National Ignition Facility Haan, S. W.; Lindl, J. D.; Callahan, D. A. Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3592169	journal	May 2011
Erratum: “Review of the National Ignition Campaign 2009-2012” [Phys. Plasmas 21, 020501 (2014)] Lindl, J. D.; Landen, O. L.; Edwards, J. Physics of Plasmas, Vol. 21, Issue 12 https://doi.org/10.1063/1.4903459	journal	December 2014
A multiscale analysis of the hotspot dynamics during the deceleration phase of inertial confinement capsules Garnier, Josselin; Cherfils, Catherine Physics of Plasmas, Vol. 12, Issue 1 https://doi.org/10.1063/1.1825389	journal	January 2005
Alpha heating enhancement in MagLIF targets: A simple analytic model Paradela, J.; García-Rubio, F.; Sanz, J. Physics of Plasmas, Vol. 26, Issue 1 https://doi.org/10.1063/1.5079519	journal	January 2019
Effect of laser illumination nonuniformity on the analysis of time-resolved x-ray measurements in uv spherical transport experiments Delettrez, J.; Epstein, R.; Richardson, M. C. Physical Review A, Vol. 36, Issue 8 https://doi.org/10.1103/PhysRevA.36.3926	journal	October 1987
Laser-driven isentropic hollow-shell implosions: the problem of ignition Kidder, R. E. Nuclear Fusion, Vol. 19, Issue 2 https://doi.org/10.1088/0029-5515/19/2/006	journal	February 1979
Deflagration-to-detonation transition in inertial-confinement-fusion baseline targets Gauthier, P.; Chaland, F.; Masse, L. Physical Review E, Vol. 70, Issue 5 https://doi.org/10.1103/PhysRevE.70.055401	journal	November 2004
Laser-Driven Implosion of Spherical DT Targets to Thermonuclear Burn Conditions Clarke, J. S.; Fisher, H. N.; Mason, R. J. Physical Review Letters, Vol. 30, Issue 3 https://doi.org/10.1103/PhysRevLett.30.89	journal	January 1973
Burn performance of inertial confinement fusion targets Harris, D. B.; Miley, G. H. Nuclear Fusion, Vol. 28, Issue 1 https://doi.org/10.1088/0029-5515/28/1/003	journal	January 1988
Demonstration of Fuel Hot-Spot Pressure in Excess of 50 Gbar for Direct-Drive, Layered Deuterium-Tritium Implosions on OMEGA Regan, S. P.; Goncharov, V. N.; Igumenshchev, I. V. Physical Review Letters, Vol. 117, Issue 2 https://doi.org/10.1103/PhysRevLett.117.025001	journal	July 2016
On thermonuclear ignition criterion at the National Ignition Facility Cheng, Baolian; Kwan, Thomas J. T.; Wang, Yi-Ming Physics of Plasmas, Vol. 21, Issue 10 https://doi.org/10.1063/1.4898734	journal	October 2014
Publisher’s Note: Demonstration of Fuel Hot-Spot Pressure in Excess of 50 Gbar for Direct-Drive, Layered Deuterium-Tritium Implosions on OMEGA [Phys. Rev. Lett. 117 , 025001 (2016)] Regan, S. P.; Goncharov, V. N.; Igumenshchev, I. V. Physical Review Letters, Vol. 117, Issue 5 https://doi.org/10.1103/PhysRevLett.117.059903	journal	July 2016
Thermonuclear Detonation Wave Structure Fuller, Ann L. Physics of Fluids, Vol. 11, Issue 3 https://doi.org/10.1063/1.1691950	journal	January 1968
Some Criteria for a Power Producing Thermonuclear Reactor Lawson, J. D. Proceedings of the Physical Society. Section B, Vol. 70, Issue 1 https://doi.org/10.1088/0370-1301/70/1/303	journal	January 1957
The National Ignition Facility - applications for inertial fusion energy and high-energy-density science Campbell, E. Michael; Hogan, William J. Plasma Physics and Controlled Fusion, Vol. 41, Issue 12B https://doi.org/10.1088/0741-3335/41/12B/303	journal	December 1999
A 3D dynamic model to assess the impacts of low-mode asymmetry, aneurysms and mix-induced radiative loss on capsule performance across inertial confinement fusion platforms Springer, P. T.; Hurricane, O. A.; Hammer, J. H. Nuclear Fusion, Vol. 59, Issue 3 https://doi.org/10.1088/1741-4326/aaed65	journal	December 2018
Inertial confinement fusion: Ignition of isobarically compressed D-T targets Atzeni, S.; Caruso, A. Il Nuovo Cimento B, Vol. 80, Issue 1 https://doi.org/10.1007/BF02899374	journal	March 1984
Tripled yield in direct-drive laser fusion through statistical modelling Gopalaswamy, V.; Betti, R.; Knauer, J. P. Nature, Vol. 565, Issue 7741 https://doi.org/10.1038/s41586-019-0877-0	journal	January 2019
Thermonuclear ignition in inertial confinement fusion and comparison with magnetic confinement Betti, R.; Chang, P. Y.; Spears, B. K. Physics of Plasmas, Vol. 17, Issue 5 https://doi.org/10.1063/1.3380857	journal	May 2010
Energy gain of laser-compressed pellets: a simple model calculation Kidder, R. E. Nuclear Fusion, Vol. 16, Issue 3 https://doi.org/10.1088/0029-5515/16/3/003	journal	July 1976
Monte Carlo charged-particle tracking and energy deposition on a Lagrangian mesh Yuan, J.; Moses, G. A.; McKenty, P. W. Physical Review E, Vol. 72, Issue 4 https://doi.org/10.1103/PhysRevE.72.046706	journal	October 2005
Performance metrics for inertial confinement fusion implosions: Aspects of the technical framework for measuring progress in the National Ignition Campaign Spears, Brian K.; Glenzer, S.; Edwards, M. J. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.3696743	journal	May 2012
Approaching a burning plasma on the NIF Hurricane, O. A.; Springer, P. T.; Patel, P. K. Physics of Plasmas, Vol. 26, Issue 5 https://doi.org/10.1063/1.5087256	journal	May 2019
A comprehensive alpha-heating model for inertial confinement fusion Christopherson, A. R.; Betti, R.; Bose, A. Physics of Plasmas, Vol. 25, Issue 1 https://doi.org/10.1063/1.4991405	journal	January 2018
Laser R&D at the Lawrence Livermore National Laboratory for fusion and isotope separation applications Emmett, J.; Krupke, W.; Davis, J. IEEE Journal of Quantum Electronics, Vol. 20, Issue 6 https://doi.org/10.1109/JQE.1984.1072443	journal	June 1984
Fusion Energy Output Greater than the Kinetic Energy of an Imploding Shell at the National Ignition Facility Le Pape, S.; Berzak Hopkins, L. F.; Divol, L. Physical Review Letters, Vol. 120, Issue 24 https://doi.org/10.1103/PhysRevLett.120.245003	journal	June 2018
Inertial-confinement fusion with lasers Betti, R.; Hurricane, O. A. Nature Physics, Vol. 12, Issue 5 https://doi.org/10.1038/nphys3736	journal	May 2016
The role of nuclear reactions and α-particle transport in the dynamics of inertial confinement fusion capsules Garnier, Josselin; Cherfils-Clérouin, Catherine Physics of Plasmas, Vol. 15, Issue 10 https://doi.org/10.1063/1.2988333	journal	October 2008
The Physics of Inertial Fusion Atzeni, Stefano; Meyer-ter-Vehn, Jürgen https://doi.org/10.1093/acprof:oso/9780198562641.001.0001	book	January 2004
The physics of long- and intermediate-wavelength asymmetries of the hot spot: Compression hydrodynamics and energetics Bose, A.; Betti, R.; Shvarts, D. Physics of Plasmas, Vol. 24, Issue 10 https://doi.org/10.1063/1.4995250	journal	October 2017
Thermonuclear burn characteristics of compressed deuterium-tritium microspheres Fraley, G. S. Physics of Fluids, Vol. 17, Issue 2 https://doi.org/10.1063/1.1694739	journal	January 1974
Thermonuclear Reaction Waves at High Densities Chu, M. S. Physics of Fluids, Vol. 15, Issue 3 https://doi.org/10.1063/1.1693924	journal	January 1972
Core conditions for alpha heating attained in direct-drive inertial confinement fusion Bose, A.; Woo, K. M.; Betti, R. Physical Review E, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevE.94.011201	journal	July 2016
Beyond alpha-heating: driving inertially confined fusion implosions toward a burning-plasma state on the National Ignition Facility Hurricane, O. A.; Callahan, D. A.; Springer, P. T. Plasma Physics and Controlled Fusion, Vol. 61, Issue 1 https://doi.org/10.1088/1361-6587/aaed71	journal	November 2018
Laser Compression of Matter to Super-High Densities: Thermonuclear (CTR) Applications Nuckolls, John; Wood, Lowell; Thiessen, Albert Nature, Vol. 239, Issue 5368, p. 139-142 https://doi.org/10.1038/239139a0	journal	September 1972
A measurable Lawson criterion and hydro-equivalent curves for inertial confinement fusion Zhou, C. D.; Betti, R. Physics of Plasmas, Vol. 15, Issue 10 https://doi.org/10.1063/1.2998604	journal	October 2008
Improved formulas for fusion cross-sections and thermal reactivities Bosch, H. -S; Hale, G. M. Nuclear Fusion, Vol. 32, Issue 4 https://doi.org/10.1088/0029-5515/32/4/I07	journal	April 1992
Similarity solution of thermonuclear burn wave with electron and α-conductivities Gus'kov, S. Yu.; Krokhin, O. N.; Rozanov, V. B. Nuclear Fusion, Vol. 16, Issue 6 https://doi.org/10.1088/0029-5515/16/6/007	journal	December 1976
On energy gain of fusion targets: the model of Kidder and Bodner improved Meyer-Ter-Vehn, J. Nuclear Fusion, Vol. 22, Issue 4 https://doi.org/10.1088/0029-5515/22/4/010	journal	April 1982
Demonstration of High Performance in Layered Deuterium-Tritium Capsule Implosions in Uranium Hohlraums at the National Ignition Facility Döppner, T.; Callahan, D. A.; Hurricane, O. A. Physical Review Letters, Vol. 115, Issue 5 https://doi.org/10.1103/PhysRevLett.115.055001	journal	July 2015
Direct-drive inertial confinement fusion: A review Craxton, R. S.; Anderson, K. S.; Boehly, T. R. Physics of Plasmas, Vol. 22, Issue 11 https://doi.org/10.1063/1.4934714	journal	November 2015
Multidimensional analysis of direct-drive, plastic-shell implosions on OMEGA Radha, P. B.; Collins, T. J. B.; Delettrez, J. A. Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1882333	journal	May 2005
A generalized scaling law for the ignition energy of inertial confinement fusion capsules Herrmann, M. C.; Tabak, M.; Lindl, J. D. Nuclear Fusion, Vol. 41, Issue 1 https://doi.org/10.1088/0029-5515/41/1/308	journal	January 2001
Thermonuclear ignition and the onset of propagating burn in inertial fusion implosions Christopherson, A. R.; Betti, R.; Lindl, J. D. Physical Review E, Vol. 99, Issue 2 https://doi.org/10.1103/PhysRevE.99.021201	journal	February 2019
Effects of asymmetry and hot-spot shape on ignition capsules Cheng, B.; Kwan, T. J. T.; Yi, S. A. Physical Review E, Vol. 98, Issue 2 https://doi.org/10.1103/PhysRevE.98.023203	journal	August 2018
High-Performance Indirect-Drive Cryogenic Implosions at High Adiabat on the National Ignition Facility Baker, K. L.; Thomas, C. A.; Casey, D. T. Physical Review Letters, Vol. 121, Issue 13 https://doi.org/10.1103/PhysRevLett.121.135001	journal	September 2018
Theory of hydro-equivalent ignition for inertial fusion and its applications to OMEGA and the National Ignition Facility Nora, R.; Betti, R.; Anderson, K. S. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4875331	journal	May 2014
Laser-Driven Implosion of Spherical DT Targets to Thermonuclear Burn Conditions. Clarke, J. S.; Fisher, H. N.; Mason, R. J. Physical Review Letters, Vol. 30, Issue 6 https://doi.org/10.1103/PhysRevLett.30.249.4	journal	February 1973
Three-dimensional modeling of the neutron spectrum to infer plasma conditions in cryogenic inertial confinement fusion implosions Weilacher, F.; Radha, P. B.; Forrest, C. Physics of Plasmas, Vol. 25, Issue 4 https://doi.org/10.1063/1.5016856	journal	April 2018
Publisher’s Note: “A measurable Lawson criterion and hydro-equivalent curves for inertial confinement fusion” [Phys. Plasmas 15, 102707 (2008)] Zhou, C. D.; Betti, R. Physics of Plasmas, Vol. 16, Issue 7 https://doi.org/10.1063/1.3152994	journal	July 2009
Self-consistent analysis of the hot spot dynamics for inertial confinement fusion capsules Sanz, J.; Garnier, J.; Cherfils, C. Physics of Plasmas, Vol. 12, Issue 11 https://doi.org/10.1063/1.2130315	journal	November 2005

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