The radial convergence required to reach fusion conditions is considerably higher for cylindrical than for spherical implosions since the volume is proportional to r2 versus r3, respectively. Fuel magnetization and preheat significantly lowers the required radial convergence enabling cylindrical implosions to become an attractive path toward generating fusion conditions. Numerical simulations are presented indicating that significant fusion yields may be obtained by pulsed-power-driven implosions of cylindrical metal liners onto magnetized (>10 T) and preheated (100–500 eV) deuterium-tritium (DT) fuel. Yields exceeding 100 kJ could be possible on Z at 25 MA, while yields exceeding 50 MJ could be possible with a more advanced pulsed power machine delivering 60 MA. These implosions occur on a much shorter time scale than previously proposed implosions, about 100 ns as compared to about 10 μs for magnetic target fusion (MTF) [I. R. Lindemuth and R. C. Kirkpatrick, Nucl. Fusion 23, 263 (1983)]. Consequently the optimal initial fuel density (1–5 mg/cc) is considerably higher than for MTF (∼1 μg/cc). Thus the final fuel density is high enough to axially trap most of the α-particles for cylinders of approximately 1 cm in length with a purely axial magnetic field, i.e., no closed field configuration is required for ignition. According to the simulations, an initial axial magnetic field is partially frozen into the highly conducting preheated fuel and is compressed to more than 100 MG. This final field is strong enough to inhibit both electron thermal conduction and the escape of α-particles in the radial direction. Analytical and numerical calculations indicate that the DT can be heated to 200–500 eV with 5–10 kJ of green laser light, which could be provided by the Z-Beamlet laser. The magneto-Rayleigh-Taylor (MRT) instability poses the greatest threat to this approach to fusion. Two-dimensional Lasnex simulations indicate that the liner walls must have a substantial initial thickness (10–20% of the radius) so that they maintain integrity throughout the implosion. The Z and Z-Beamlet experiments are now being planned to test the various components of this concept, e.g., the laser heating of the fuel and the robustness of liner implosions to the MRT instability.

Point design targets have been specified for the initial ignition campaign on the National Ignition Facility [G. H. Miller, E. I. Moses, and C. R. Wuest, Opt. Eng. 443, 2841 (2004)]. The targets contain D-T fusion fuel in an ablator of either CH with Ge doping, or Be with Cu. These shells are imploded in a U or Au hohlraum with a peak radiation temperature set between 270 and 300 eV. Considerations determining the point design include laser-plasma interactions, hydrodynamic instabilities, laser operations, and target fabrication. Simulations were used to evaluate choices, and to define requirements and specifications. Simulation techniques and their experimental validation are summarized. Simulations were used to estimate the sensitivity of target performance to uncertainties and variations in experimental conditions. A formalism is described that evaluates margin for ignition, summarized in a parameter the Ignition Threshold Factor (ITF). Uncertainty and shot-to-shot variability in ITF are evaluated, and sensitivity of the margin to characteristics of the experiment. The formalism is used to estimate probability of ignition. The ignition experiment will be preceded with an experimental campaign that determines features of the design that cannot be defined with simulations alone. The requirements for this campaign are summarized. Requirements are summarized for the laser and target fabrication.

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The magnetized liner inertial fusion concept has been presented as a path toward obtaining substantial thermonuclear fusion yields using the Z accelerator [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)]. We present the first integrated magnetohydrodynamic simulations of the inertial fusion targets, which self-consistently include laser preheating of the fuel, the presence of electrodes, and end loss effects. These numerical simulations provided the design for the first thermonuclear fusion neutron-producing experiments on Z using capabilities that presently exist: peak currents of Imax = 18–20 MA, pre-seeded axial magnetic fields of Bz0=10 T, laser preheat energies of about Elas = 2 kJ delivered in 2 ns, DD fuel, and an aspect ratio 6 solid Be liner imploded to 70 km/s. Specific design details and observables for both near-term and future experiments are discussed, including sensitivity to laser timing and absorbed preheat energy. The initial experiments measured stagnation radii rstag<75 μm, temperatures around 3 keV, and isotropic neutron yields up to YnDD=2×1012, with inferred alpha-particle magnetization parameters around rstag/rLα=1.7 [M. R. Gomez et al., Phys. Rev. Lett. (submitted)].

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This paper explores the role of electro-thermal instabilities on the dynamics of magnetically accelerated implosion systems. Electro-thermal instabilities result from non-uniform heating due to temperature dependence in the conductivity of a material. Comparatively little is known about these types of instabilities compared to the well known Magneto-Rayleigh-Taylor (MRT) instability. We present simulations that show electrothermal instabilities form immediately after the surface material of a conductor melts and can act as a significant seed to subsequent MRT instability growth. We also present the results of several experiments performed on Sandia National Laboratories Z accelerator to investigate signatures of electrothermal instability growth on well characterized initially solid aluminum and copper rods driven with a 20 MA, 100 ns risetime current pulse. These experiments show excellent agreement with electrothermal instability simulations and exhibit larger instability growth than can be explained by MRT theory alone.

The first controlled experiments measuring the growth of the magneto-Rayleigh-Taylor instability in fast (∼100  ns) Z-pinch plasmas are reported. Sinusoidal perturbations on the surface of an initially solid Al tube (liner) with wavelengths of 25-400  μm were used to seed the instability. Radiographs with 15  μm resolution captured the evolution of the outer liner surface. Comparisons with numerical radiation magnetohydrodynamic simulations show remarkably good agreement down to 50  μm wavelengths.

Magnetizing the fuel in inertial confinement fusion relaxes ignition requirements by reducing thermal conductivity and changing the physics of burn product confinement. Diagnosing the level of fuel magnetization during burn is critical to understanding target performance in magneto-inertial fusion (MIF) implosions. In pure deuterium fusion plasma, 1.01 MeV tritons are emitted during DD fusion and can undergo secondary DT reactions before exiting the fuel. Increasing the fuel magnetization elongates the path lengths through the fuel of some of the tritons, enhancing their probability of reaction. Based on this feature, a method to diagnose fuel magnetization using the ratio of overall DT to DD neutron yields is developed. Analysis of anisotropies in the secondary neutron energy spectra further constrain the measurement. Secondary reactions are also shown to provide an upper bound for volumetric fuel-pusher mix in MIF. The analysis is applied to recent MIF experiments [M. R. Gomez et al., to appear in PRL] on the Z Pulsed Power Facility, indicating that significant magnetic confinement of charged burn products was achieved and suggesting a relatively low-mix environment. Both of these are essential features of future ignition-scale MIF designs. PACS numbers:Introduction.-Magneto-inertial fusion (MIF) offers some key advantages over traditional inertial confinement fusion (ICF). In MIF, fuel magnetization relaxes the extreme pressure requirements characteristic of traditional ICF and enhances thermal insulation of the hot fuel from the colder pusher [1-10]. We consider paradigmatically the radial compression of a long, thin cylinder of fuel magnetized with a uniform, axial field prior to compression [11][12][13][14][15][16][17]. At stagnation, the compressed magnetic flux redirects charged burn products axially, increasing the effective fuel areal density from ρR to ρZ, where ρ is the fuel mass density, R is the fuel radius, Z is the fuel length, and A ≡ Z/R ≫ 1 is the aspect ratio.Sandia National Laboratories has fielded the first integrated experiments investigating Magnetized Liner I nertial F usion (MagLIF) [14][15][16][17], which involves direct compression of magnetized, preheated deuterium fuel by a solid metal (beryllium) liner, imploded on the 26 MA, 100 ns Z Pulsed Power Facility [18]. The imploding cylindrical liner compresses a pre-seeded axial magnetic field, B 0 (≈ 10 T in the first experiments), to high amplitude at stagnation, B, where perfect flux conservation would imply B = B 0 (R 0 /R) 2 , and R 0 = 2.325 mm is the initial fuel radius. However, detailed simulations suggest that multiple effects (e.g., resistive losses, Nerst effect) can lead to leakage of magnetic flux out of the hot fuel [14,17]. Thus, diagnosing the efficacy of flux compression in experiments is critical for understanding target performance and the viability of the concept.