Effects of alpha stopping power modelling on the ignition threshold in a directly-driven inertial confinement fusion capsule

  • Mauro TemporalEmail author
  • Benoit Canaud
  • Witold Cayzac
  • Rafael Ramis
  • Robert L. SingletonJr.
Regular Article


The alpha-particle energy deposition mechanism modifies the ignition conditions of the thermonuclear Deuterium-Tritium fusion reactions, and constitutes a key issue in achieving high gain in Inertial Confinement Fusion implosions. One-dimensional hydrodynamic calculations have been performed with the code Multi-IFE [R. Ramis, J. Meyer-ter-Vehn, Comput. Phys. Commun. 203, 226 (2016)] to simulate the implosion of a capsule directly irradiated by a laser beam. The diffusion approximation for the alpha energy deposition has been used to optimize three laser profiles corresponding to different implosion velocities. A Monte-Carlo package has been included in Multi-IFE to calculate the alpha energy transport, and in this case the energy deposition uses both the LP [C.K. Li, R.D. Petrasso, Phys. Rev. Lett. 70, 3059 (1993)] and the BPS [L.S. Brown, D.L. Preston, R.L. Singleton Jr., Phys. Rep. 410, 237 (2005)] stopping power models. Homothetic transformations that maintain a constant implosion velocity have been used to map out the transition region between marginally-igniting and high-gain configurations. The results provided by the two models have been compared and it is found that – close to the ignition threshold – in order to produce the same fusion energy, the calculations performed with the BPS model require about 10% more invested energy with respect to the LP model.

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.
    R. Ramis, J. Meyer-ter-Vehn, Comput. Phys. Commun. 203, 226 (2016)ADSCrossRefGoogle Scholar
  4. 4.
    C.K. Li, R.D. Petrasso, Phys. Rev. Lett. 70, 3059 (1993)ADSCrossRefGoogle Scholar
  5. 5.
    L.S. Brown, D.L. Preston, R.L. Singleton Jr., Phys. Rep. 410, 237 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    R.L. Singleton Jr., Phys. Plasmas 15, 056302 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    B. Canaud, F. Garaude, Nucl. Fusion 45, L43 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    R. More, K.H. Warren, D.A. Young, G. Zimmermann, Phys. Fluids 31, 3059 (1988)ADSCrossRefGoogle Scholar
  9. 9.
    A. Kemp, J. Meyer-ter-Vehn, Nucl. Instrum. Meth. A 415, 674 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    G.B. Zimmermann, Lawrence Livermore National Lab. UCRL-74811 (1973)Google Scholar
  11. 11.
    G.B. Zimmermann, W.L. Kruer, Comments Plasma Phys. Contr. Fusion 2, 51 (1975)Google Scholar
  12. 12.
    S. Atzeni, A. Caruso, Il Nuovo Cimento 64, 383 (1981)CrossRefGoogle Scholar
  13. 13.
    S. Atzeni, Plasma. Phys. Contr. Fusion. 29, 1535 (1987)ADSCrossRefGoogle Scholar
  14. 14.
    V. Brandon, B. Canaud, M. Temporal, R. Ramis, Nuclear Fusion 54, 083016 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    M. Temporal, V. Brandon, B. Canaud, J.P. Didelez, R. Fedosejevs, R. Ramis, Nucl. Fusion 52, 103011 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    H.S. Bosch, G.M. Hale, Nucl. Fusion 32, 611 (1992)ADSCrossRefGoogle Scholar
  17. 17.
    G.S. Fraley, E.J. Linnebur, R.J. Mason, R.L. Morse, Physics Fluids 17, 474 (1974)ADSCrossRefGoogle Scholar
  18. 18.
    E.G. Corman, W.E. Loewe, G.E. Cooper, A.M. Winslow, Nucl. Fusion 15, 377 (1975)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Mauro Temporal
    • 1
    Email author
  • Benoit Canaud
    • 2
  • Witold Cayzac
    • 2
  • Rafael Ramis
    • 3
  • Robert L. SingletonJr.
    • 4
  1. 1.CMLA, Centre de Mathématiques et de Leurs Applications, ENS Cachan and CNRSCachan CedexFrance
  2. 2.CEAArpajon CedexFrance
  3. 3.ETSI Aeronáutica y del Espacio, Universidad Politécnica de MadridMadridSpain
  4. 4.Los Alamos National LaboratoryLos AlamosUSA

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