Publications

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We report on the progress made to date for a Laboratory Directed Research and Development (LDRD) project aimed at diagnosing magnetic flux compression on the Z pulsed-power accelerator (0-20 MA in 100 ns). Each experiment consisted of an initially solid Be or Al liner (cylindrical tube), which was imploded using the Z accelerator's drive current (0-20 MA in 100 ns). The imploding liner compresses a 10-T axial seed field, B z ( 0 ) , supplied by an independently driven Helmholtz coil pair. Assuming perfect flux conservation, the axial field amplification should be well described by B z ( t ) = B z ( 0 ) x [ R ( 0 ) / R ( t )] 2 , where R is the liner's inner surface radius. With perfect flux conservation, B z ( t ) and dB z / dt values exceeding 10 4 T and 10 12 T/s, respectively, are expected. These large values, the diminishing liner volume, and the harsh environment on Z, make it particularly challenging to measure these fields. We report on our latest efforts to do so using three primary techniques: (1) micro B-dot probes to measure the fringe fields associated with flux compression, (2) streaked visible Zeeman absorption spectroscopy, and (3) fiber-based Faraday rotation. We also mention two new techniques that make use of the neutron diagnostics suite on Z. These techniques were not developed under this LDRD, but they could influence how we prioritize our efforts to diagnose magnetic flux compression on Z in the future. The first technique is based on the yield ratio of secondary DT to primary DD reactions. The second technique makes use of the secondary DT neutron time-of-flight energy spectra. Both of these techniques have been used successfully to infer the degree of magnetization at stagnation in fully integrated Magnetized Liner Inertial Fusion (MagLIF) experiments on Z [P. F. Schmit et al. , Phys. Rev. Lett. 113 , 155004 (2014); P. F. Knapp et al. , Phys. Plasmas, 22 , 056312 (2015)]. Finally, we present some recent developments for designing and fabricating novel micro B-dot probes to measure B z ( t ) inside of an imploding liner. In one approach, the micro B-dot loops were fabricated on a printed circuit board (PCB). The PCB was then soldered to off-the-shelf 0.020- inch-diameter semi-rigid coaxial cables, which were terminated with standard SMA connectors. These probes were recently tested using the COBRA pulsed power generator (0-1 MA in 100 ns) at Cornell University. In another approach, we are planning to use new multi-material 3D printing capabilities to fabricate novel micro B-dot packages. In the near future, we plan to 3D print these probes and then test them on the COBRA generator. With successful operation demonstrated at 1-MA, we will then make plans to use these probes on a 20-MA Z experiment.

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We report on experiments where cylindrical beryllium liners filled with liquid deuterium were compressed to extreme pressure and density with current pulse shaping. In one set of experiments the pressure at stagnation is inferred to be & 100 Mbar using penetrating radiography. A peak liner convergence ratio (initial radius over final radius) of 7.6 was measured resulting in an average deuterium density of 10 g=cm³ and areal density of 0.45 g=cm². The stagnation shock propagating radially outward through the liner wall was directly measured with a strength of ≈ 120 Mbar. In a second set of experiments the liner was imploded to a peak convergence of 19 resulting in a density of 55 g=cm³ and areal density of 0.5 g=cm². The pressure at stagnation in this experiment is estimated to be 2 Gbar. This platform enables the study of high-pressure, high-density, implosion deceleration and stagnation dynamics at spatial scales that are readily diagnosable (R ~ 0.1 -- 0.4 mm). Thus, these experiments are directly relevant to both Inertial Con nement Fusion and the study of material properties under extreme conditions.

The long-term goal of the pulsed-­power based, magnetically driven target approach is to achieve high single­shot yields (0.5-­1 GJ per shot). This goal may take decades to achieve, but if successful we believe it would be a key capability for the Stockpile Stewardship program, as noted as far back as 1988 in the Laboratory Microfusion Capability Phase 1 (U) study. If this approach is successful, it may be possible to achieve these yields from targets absorbing up to 10 MJ in a laboratory pulsed power facility with a stored energy of roughly 130 MJ. Such a facility would be substantially cheaper, and not as complex, than the corresponding pulsed power facility required for producing comparable yields from x-ray driven capsule targets.

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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.

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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.