A comprehensive alpha-heating model for inertial confinement fusion

Christopherson, A. R.; Betti, R.; Bose, A.; Howard, J.; Woo, K. M.; Campbell, E. M.; Sanz, J.; Spears, B. K.

doi:10.1063/1.4991405

Title: A comprehensive alpha-heating model for inertial confinement fusion

Journal Article · Mon Jan 08 00:00:00 EST 2018 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4991405· OSTI ID:1427517

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

^[1];

^[1]; Woo, K. M. ^[1];

^[1]; Sanz, J. ^[2]; Spears, B. K. ^[3]

Univ. of Rochester, NY (United States). Fusion Science Center. Lab. for Laser Energetics
Technical Univ. of Madrid (Spain)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

In this paper, a comprehensive model is developed to study alpha-heating in inertially confined plasmas. It describes the time evolution of a central low-density hot spot confined by a compressible shell, heated by fusion alphas, and cooled by radiation and thermal losses. The model includes the deceleration, stagnation, and burn phases of inertial confinement fusion implosions, and is valid for sub-ignited targets with ≤10× amplification of the fusion yield from alpha-heating. The results of radiation-hydrodynamic simulations are used to derive realistic initial conditions and dimensionless parameters for the model. It is found that most of the alpha energy (~90%) produced before bang time is deposited within the hot spot mass, while a small fraction (~10%) drives mass ablation off the inner shell surface and its energy is recycled back into the hot spot. Of the bremsstrahlung radiation emission, ~40% is deposited in the hot spot, ~40% is recycled back in the hot spot by ablation off the shell, and ~20% leaves the hot spot. We show here that the hot spot, shocked shell, and outer shell trajectories from this analytical model are in good agreement with simulations. Finally, a detailed discussion of the effect of alpha-heating on the hydrodynamics is also presented.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Univ. of Rochester, NY (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: NA0001944; FC02-04ER54789

OSTI ID:: 1427517

Alternate ID(s):: OSTI ID: 1416080

Journal Information:: Physics of Plasmas, Vol. 25, Issue 1; ISSN 1070-664X

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

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 18 works

Citation information provided by
Web of Science

References (33)

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
Hydrodynamic scaling of the deceleration-phase Rayleigh–Taylor instability Bose, A.; Woo, K. M.; Nora, R. Physics of Plasmas, Vol. 22, Issue 7 https://doi.org/10.1063/1.4923438	journal	July 2015
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
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
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
Study of the ion kinetic effects in ICF run-away burn using a quasi-1D hybrid model Huang, C. -K.; Molvig, K.; Albright, B. J. Physics of Plasmas, Vol. 24, Issue 2 https://doi.org/10.1063/1.4976323	journal	February 2017
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
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
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
The Physics of Inertial Fusion Atzeni, Stefano; Meyer-ter-Vehn, Jürgen https://doi.org/10.1093/acprof:oso/9780198562641.001.0001	book	January 2004
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
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
Higher velocity, high-foot implosions on the National Ignition Facility lasera) Callahan, D. A.; Hurricane, O. A.; Hinkel, D. E. Physics of Plasmas, Vol. 22, Issue 5 https://doi.org/10.1063/1.4921144	journal	May 2015
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
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
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
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
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
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
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
Knudsen Layer Reduction of Fusion Reactivity Molvig, Kim; Hoffman, Nelson M.; Albright, B. J. Physical Review Letters, Vol. 109, Issue 9 https://doi.org/10.1103/PhysRevLett.109.095001	journal	August 2012
Improved performance of direct-drive inertial confinement fusion target designs with adiabat shaping using an intensity picket Goncharov, V. N.; Knauer, J. P.; McKenty, P. W. Physics of Plasmas, Vol. 10, Issue 5 https://doi.org/10.1063/1.1562166	journal	May 2003
Inertially confined fusion plasmas dominated by alpha-particle self-heating Hurricane, O. A.; Callahan, D. A.; Casey, D. T. Nature Physics, Vol. 12, Issue 8 https://doi.org/10.1038/nphys3720	journal	April 2016
High-Adiabat High-Foot Inertial Confinement Fusion Implosion Experiments on the National Ignition Facility Park, H. -S.; Hurricane, O. A.; Callahan, D. A. Physical Review Letters, Vol. 112, Issue 5 https://doi.org/10.1103/PhysRevLett.112.055001	journal	February 2014
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
The Gaunt Factor for Free-Free Transitions in Pure Hydrogen. Kulsrud, Russell M. The Astrophysical Journal, Vol. 119 https://doi.org/10.1086/145836	journal	January 1954
Electron Radiative Transitions in a Coulomb Field. Karzas, W. J.; Latter, R. The Astrophysical Journal Supplement Series, Vol. 6 https://doi.org/10.1086/190063	journal	May 1961
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
X-ray continuum as a measure of pressure and fuel–shell mix in compressed isobaric hydrogen implosion cores Epstein, R.; Goncharov, V. N.; Marshall, F. J. Physics of Plasmas, Vol. 22, Issue 2 https://doi.org/10.1063/1.4907667	journal	February 2015
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
Improved formulas for fusion cross-sections and thermal reactivities Bosch, H. -S; Hale, G. M. Nuclear Fusion, Vol. 33, Issue 12 https://doi.org/10.1088/0029-5515/33/12/513	journal	December 1993

Cited By (9)

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
Effects of residual kinetic energy on yield degradation and ion temperature asymmetries in inertial confinement fusion implosions Woo, K. M.; Betti, R.; Shvarts, D. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5026706	journal	May 2018
Analysis of trends in experimental observables: Reconstruction of the implosion dynamics and implications for fusion yield extrapolation for direct-drive cryogenic targets on OMEGA Bose, A.; Betti, R.; Mangino, D. Physics of Plasmas, Vol. 25, Issue 6 https://doi.org/10.1063/1.5026780	journal	June 2018
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
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
On alpha-particle transport in inertial fusion Zylstra, A. B.; Hurricane, O. A. Physics of Plasmas, Vol. 26, Issue 6 https://doi.org/10.1063/1.5101074	journal	June 2019
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
Review of hydrodynamic instability experiments in inertially confined fusion implosions on National Ignition Facility Smalyuk, V. A.; Weber, C. R.; Landen, O. L. Plasma Physics and Controlled Fusion, Vol. 62, Issue 1 https://doi.org/10.1088/1361-6587/ab49f4	journal	October 2019
Ion friction at small values of the Coulomb logarithm Sprenkle, Tucker; Dodson, Adam; McKnight, Quinton arXiv https://doi.org/10.48550/arxiv.1905.08715	text	January 2019