Dependence of inertial confinement fusion ignition energy threshold on electron thermal conduction

  • Mauro TemporalEmail author
  • Benoit Canaud
  • Vincent Brandon
  • Rafael Ramis
Regular Article


In inertial confinement fusion, ignition conditions of the thermonuclear deuterium–tritium fusion reactions depend on the electron thermal heat conduction that affects the hot-spot mass accretion and energy balance. One-dimensional hydrodynamic calculations have been performed to simulate the implosion of a capsule directly irradiated by laser beams. For these calculations, the laser-capsule configuration has been scaled using homothetic transformations to scan the transition to ignition while keeping the implosion velocity constant. The electronic heat conduction has been modified by two alternative ways: (i) the classical Spitzer heat flux has been harmonically limited to the free streaming limit using a flux limit factor φ, and (ii) the classical Spitzer coefficient is reduced by a multiplicative factor α < 1. A change of the thermal conductivity affects the performances of the implosion and it can be beneficial or harmful. Parametric studies have been performed for both alternatives, looking for the kinetic energy threshold that generates a unitary energy gain as a function of parameters φ or α, respectively. These studies show how the energy threshold is modified by acting on the heat flux and that there is a minimum ignition energy that can be tuned by appropriately reducing the heat conduction. A simple qualitative model is developed to understand the relation between energy threshold and heat conduction.

Graphical abstract


Plasma Physics 


  1. 1.
    J.D. Lindl, Inertial  Confinement  Fusion: The Quest  for Ignition  and  High Gain  Using  Indirect  Drive (Springer, New York, 1998) Google Scholar
  2. 2.
    S. Atzeni, J. Meyer-ter-Vehn, The   Physics   of   Inertial Fusion (Oxford Science Press, Oxford, 2004) Google Scholar
  3. 3.
    J. Meyer-ter-Vehn, Nucl. Fusion 22, 561 (1982) CrossRefGoogle Scholar
  4. 4.
    R. Betti, K. Anderson, V.N. Goncharov, R.L. McCrory, D.D. Meyerhofer, S. Skupsky, R.P.J. Town, Phys. Plasmas 9, 2277 (2002) ADSCrossRefGoogle Scholar
  5. 5.
    R. Ramis, J. Meyer-ter-Vehn, Comput. Phys. Commun. 203, 226 (2016) ADSCrossRefGoogle Scholar
  6. 6.
    B. Canaud, F. Garaude, Nucl. Fusion 45, L43 (2005) ADSCrossRefGoogle Scholar
  7. 7.
    G.B. Zimmermann, Lawrence Livermore National Lab. UCRL-74811 (1973) Google Scholar
  8. 8.
    G.B. Zimmermann, W.L. Kruer, Comments Plasma Phys. Control. Fusion 2, 51 (1975) Google Scholar
  9. 9.
    S. Atzeni, A. Caruso, Il Nuovo Cimento 64, 383 (1981) CrossRefGoogle Scholar
  10. 10.
    S. Atzeni, Plasma Phys. Control. Fusion 29, 1535 (1987) ADSCrossRefGoogle Scholar
  11. 11.
    V. Brandon, B. Canaud, M. Temporal, R. Ramis, Nucl. Fusion 54, 083016 (2014) ADSCrossRefGoogle Scholar
  12. 12.
    M. Temporal, V. Brandon, B. Canaud, J.P. Didelez, R. Fedosejevs, R. Ramis, Nucl. Fusion 52, 103011 (2012) ADSCrossRefGoogle Scholar
  13. 13.
    L.J. Spitzer, Jr., Physics of Fully Ionized Plasmas (Wiley Interscience, New York, 1962) Google Scholar
  14. 14.
    D. Shvarts, J. Delettrez, R.L. McCrory, C.P. Verdon, Phys. Rev. Lett. 47, 247 (1981) ADSCrossRefGoogle Scholar
  15. 15.
    A.R. Bell, Phys. Fluids 28, 2007 (1985) ADSCrossRefGoogle Scholar
  16. 16.
    M.C. Herrmann, M. Tabak, J.D. Lindl, Nucl. Fusion 41, 99 (2001) ADSCrossRefGoogle Scholar
  17. 17.
    G.S. Fraley, E.J. Linnebur, R.J. Mason, R.L. Morse, Phys. Fluids 17, 474 (1974) ADSCrossRefGoogle Scholar
  18. 18.
    S. Atzeni, A. Caruso, Nuovo Cimento 80B, 71 (1984) ADSCrossRefGoogle Scholar
  19. 19.
    M.M. Basko, Nucl. Fusion 30, 2443 (1990) MathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Mauro Temporal
    • 1
    Email author
  • Benoit Canaud
    • 2
  • Vincent Brandon
    • 2
  • Rafael Ramis
    • 3
  1. 1.Centre de Mathématiques et de Leurs Applications, ENS Cachan and CNRSCachan CedexFrance
  2. 2.CEA, DIFArpajon CedexFrance
  3. 3.ETSI Aeronáutica y del Espacio, Universidad Politécnica de MadridMadridSpain

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