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Evidence for suprathermal ion distribution in burning plasmas


At the National Ignition Facility, inertial confinement fusion experiments aim to burn and ignite a hydrogen plasma to generate a net source of energy through the fusion of deuterium and tritium ions. The energy deposited by α-particles released from the deuterium–tritium fusion reaction plays the central role in heating the fuel to achieve a sustained thermonuclear burn. In the hydrodynamic picture, α-heating increases the temperature of the plasma, leading to increased reactivity because the mean ion kinetic energy increases. Therefore, the ion temperature is related to the mean ion kinetic energy. Here we use the moments of the neutron spectrum to study the relationship between the ion temperature (measured by the variance in the neutron kinetic energy spectrum) and the ion mean kinetic energy (measured by the shift in the mean neutron energy). We observe a departure from the relationship expected for plasmas where the ion relative kinetic energy distribution is Maxwell–Boltzmann, when the plasma begins to burn. Understanding the cause of this departure from hydrodynamic behaviour could be important for achieving robust and reproducible ignition.

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Fig. 1: Indirect-drive inertial confinement fusion.
Fig. 2: Neutron spectra recorded by a single line-of-sight QCD nToF detector.
Fig. 3: Interdependence of isotropic velocity (viso) and ion temperature (Tion).
Fig. 4: Relation between the measured neutron yield (YDT) and isotropic velocity (viso).
Fig. 5: Neutron spectra generated by different DT ion distribution functions.

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Data availability

Raw data were generated at the National Ignition Facility and are not available to the general public. Derived experimental data supporting the findings of this study shown in Figs. 3 and 4, but not in Table 1 are available from the corresponding authors upon reasonable request.

Code availability

The simulation codes used in this manuscript are not available to the general public.


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We would like to acknowledge many discussions with our colleagues O. Landen, P. Patel, L. Divol, P. Springer and C. Cerjan. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security for the US Department of Energy, National Nuclear Security Administration, under contract no. DE-AC52- 07NA27344. This Article (LLNL-JRNL-824268) was prepared as an account of work sponsored by an agency of the US government. Neither the US government nor Lawrence Livermore National Security, nor any of their employees make any warranty, expressed or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US government or Lawrence Livermore National Security and shall not be used for advertising or product endorsement purposes.

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Authors and Affiliations



E.P.H.: neutron diagnostics, wrote sections of paper. A.S.M.: neutron diagnostics, wrote sections of paper. A.J.C.: theory. B.D.A. theory. P.A.A.: hohlraum physics. K.L.B.: hybrid ‘shot RI’ (shot responsible individual). D.T.C.: hybrid shot RI. D.S.C.: high-resolution 3D simulations. T.D.: hybrid shot RI. M.J.E.: nToF diagnostics. J.E.F.: simulation methods. M.G.J.: neutron diagnostics. G.P.G.: neutron diagnostics development. R.H.: neutron diagnostics development and analysis code. J.J.: neutron diagnostics deployment and operations. S.M.K.: neutron diagnostics deployment and operations. J.K.: neutron diagnostics development. A.L.K.: hybrid-E design lead. K.D.M.: γ-ray diagnostics. J.L.M.: high-resolution 3D simulations. D.H.M.: theory methodology. R.C.N.: post-shot simulations. A.E.P.: hybrid and I-Raum shot RI. J.E.R.: N201101 and N210207 experimentalist and shot RI. H.F.R.: original I-Raum design lead. J.S.R.: I-Raum experimental lead and N201122 shot RI. D.J.S.: neutron diagnostics. S.M.S.: HYDRA details. B.K.S.: simulations lead. C.V.Y.: present I-Raum design lead. A.B.Z.: hybrid-E experimental lead.

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Correspondence to E. P. Hartouni, A. S. Moore or A. J. Crilly.

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Hartouni, E.P., Moore, A.S., Crilly, A.J. et al. Evidence for suprathermal ion distribution in burning plasmas. Nat. Phys. 19, 72–77 (2023).

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