Publications

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In magnetizing the fusion fuel in inertial confinement fusion (ICF) systems, we found that the required stagnation pressure and density can be relaxed dramatically. This happens because the magnetic field insulates the hot fuel from the cold pusher and traps the charged fusion burn products. This trapping allows the burn products to deposit their energy in the fuel, facilitating plasma self-heating. Here, we report on a comprehensive theory of this trapping in a cylindrical DD plasma magnetized with a purely axial magnetic field. Using this theory, we are able to show that the secondary fusion reactions can be used to infer the magnetic field-radius product, BR, during fusion burn. This parameter, not ρR, is the primary confinement parameter in magnetized ICF. Using this method, we analyze data from recent Magnetized Liner InertialFusion experiments conducted on the Z machine at Sandia National Laboratories. Furthermore, we show that in these experiments BR ≈ 0.34(+0.14/-0.06) MG · cm, a ~ 14× increase in BR from the initial value, and confirming that the DD-fusion tritons are magnetized at stagnation. Lastly, this is the first experimental verification of charged burn product magnetization facilitated by compression of an initial seed magnetic flux.

Magnetized Liner Inertial Fusion experiments performed at Sandia's Z facility have demonstrated significant thermonuclear fusion neutron yields (∼10¹² DD neutrons) from multi-keV deuterium plasmas inertially confined by slow (∼10 cm/μs), stable, cylindrical implosions. Effective magnetic confinement of charged fusion reactants and products is signaled by high secondary DT neutron yields above 10¹⁰. Analysis of extensive power, imaging, and spectroscopic x-ray measurements provides a detailed picture of ∼3 keV temperatures, 0.3 g/cm³ densities, gradients, and mix in the fuel and liner over the 1-2 ns stagnation duration.

In this study, the magnetized liner inertial fusion concept [S. A. Slutz et al., Phys. Plasmas17, 056303 (2010)] utilizes a magnetic field and laser heating to relax the pressure requirements of inertial confinement fusion. The first experiments to test the concept [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)] were conducted utilizing the 19 MA, 100 ns Z machine, the 2.5 kJ, 1 TW Z Beamlet laser, and the 10 T Applied B-field on Z system. Despite an estimated implosion velocity of only 70 km/s in these experiments, electron and ion temperatures at stagnation were as high as 3 keV, and thermonuclear deuterium-deuterium neutron yields up to 2 × 10¹² have been produced. X-ray emission from the fuel at stagnation had widths ranging from 50 to 110 μm over a roughly 80% of the axial extent of the target (6–8 mm) and lasted approximately 2 ns. X-ray yields from these experiments are consistent with a stagnation density of the hot fuel equal to 0.2–0.4 g/cm³. In these experiments, up to 5 ×10¹⁰ secondary deuterium-tritium neutrons were produced. Given that the areal density of the plasma was approximately 1–2 mg/cm², this indicates the stagnation plasma was significantly magnetized, which is consistent with the anisotropy observed in the deuterium-tritium neutron spectra. Control experiments where the laser and/or magnetic field were not utilized failed to produce stagnation temperatures greater than 1 keV and primary deuterium-deuterium yields greater than 10¹⁰. An additional control experiment where the fuel contained a sufficient dopant fraction to substantially increase radiative losses also failed to produce a relevant stagnation temperature. The results of these experiments are consistent with a thermonuclear neutron source.

The standard approaches to inertial confinement fusion (ICF) rely on implosion velocities greater than 300 km/s and spherical convergence to achieve the high fuel temperatures (T > 4 keV) and areal densities (ρr > 0.3 g/cm2) required for ignition1. Such high velocities are achieved by heating the outside surface of a spherical capsuleeither directly with a large number of laser beams (Direct Drive) or with x-rays generated within a hohlraum (Indirect Drive). A much more energetically efficient approach is to use the magnetic pressure generated by a pulsed power machine to directly drive an implosion. In this approach 5-10% of the stored energy can be converted to the implosion of a metal tube generally referred to as a “liner”. However, the implosion velocity is not very high 70-100 km/s and the convergence is cylindrical (rather than spherical) making it more difficult to achieve the high temperatures and areal densities needed for ignition.

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Temperature measurements are very important in shock and ramp type dynamic materials experiments. In particular, accurate temperature measurements can provide stringent additional constraints on determining the equation of state for materials at high pressure. The key to providing these constraints is to develop diagnostic techniques that can determine the temperature with sufficient accuracy. To enable such measurements, we are working to improve our diagnostic capability with three separate techniques, each of which has specific applicability in a particular temperature range. To improve our capability at low temperatures (< 1 eV) we are working on a technique that takes advantage of the change in reflectivity of Au as the temperature is increased. This is most applicable to ramp type experiments. In the intermediate range (~1 eV < T< 5-10 eV) we are improving our optical pyrometry diagnostic by adding the capability of doing an absolute calibration as part of the diagnostic procedure for the shock or shock ramp dynamic materials experiment. This will enable more accurate temperature measurements for shock and shock ramp type experiments. For higher temperatures that occur in very high-pressure shock experiments, above 10 eV, we are developing the capability of doing x-ray Thomson scattering measurements. Such measurements will enable us to characterize strongly shocked or warm dense matter materials. Work on these diagnostic approaches is summarized in this report.

This Letter presents results from the first fully integrated experiments testing the magnetized liner inertial fusion concept [S.A. Slutz et al., Phys. Plasmas 17, 056303 (2010)], in which a cylinder of deuterium gas with a preimposed axial magnetic field of 10 T is heated by Z beamlet, a 2.5 kJ, 1 TW laser, and magnetically imploded by a 19 MA current with 100 ns rise time on the Z facility. Despite a predicted peak implosion velocity of only 70 km/s, the fuel reaches a stagnation temperature of approximately 3 keV, with T_e ≈ T_i, and produces up to 2e12 thermonuclear DD neutrons. In this study, X-ray emission indicates a hot fuel region with full width at half maximum ranging from 60 to 120 μm over a 6 mm height and lasting approximately 2 ns. The number of secondary deuterium-tritium neutrons observed was greater than 10¹⁰, indicating significant fuel magnetization given that the estimated radial areal density of the plasma is only 2 mg/cm².

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