Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

Highly nonlinear solitary waves in periodic dimer granular chains

We investigate the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer and heavier beads (stainless steel) are alternated with softer and lighter ones (polytetrafluoroethylene beads). We find good agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously studied examples as special cases and also provides key insights into the influence of the dimer lattice on the properties (width and propagation speed) of the highly nonlinear wave solutions

Highly nonlinear solitary waves in heterogeneous periodic granular media

We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mass) cell structures in one-dimensional granular lattices. To vary the composition of the fundamental periodic units in the granular chains, we utilize beads of different materials (stainless steel, brass, glass, nylon, polytetrafluoroethylene, and rubber). This selection allows us to tailor the response of the system based on the masses, Poisson ratios, and elastic moduli of the components. For example, we examine dimer configurations with two types of heavy particles, two types of light particles, and alternating light and heavy particles. Employing a model with Hertzian interactions between adjacent beads, we find good agreement between experiments and numerical simulations. We also find good agreement between these results and a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments (dimer chains) and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of heterogeneous lattices on the properties (width and propagation speed) of the nonlinear wave solutions of this system

Hugoniot measurements utilizing in situ synchrotron X-ray radiation

Pressure–density relationships derived from the experimentally obtained shock and particle velocities are critical to define a material’s equation of state (EOS). Typically, impact experiments coupled with velocimetry are used to map a material’s Hugoniot. Limitations such as sample geometry and varying indices of refraction may prevent proper characterization using traditional techniques such as photon doppler velocimetry (PDV) or velocity interferometer system for any reflector (VISAR). Here, traditional Hugoniot measurements using PDV are compared to dynamic x-ray imaging encompassing two different sample geometries on the gas gun platform. Through each of these methods an experimentally derived Hugoniot is determined for a previously uncharacterized polymeric material, Somos Watershed XC11122, that is used 3D printed stereolithography parts. A Us–up relationship was determined to be Us = 2.93 us + 1.73 mm/μs through traditional PDV. Slope and sound speed values determined from x-ray imaging methods varied 11% from PDV measurements. Each method yielded a Hugoniot with densities similar to poly(methyl methacrylate) (PMMA). The similarity shows the viability of such analyses for dynamic properties and Hugoniot data. The performance and analysis of both PDV and dynamic x-ray measurements are laid out in this work. Comparing PDV and x-ray imaging highlights distinct advantages and disadvantages among each method. PDV provides less uncertainty for velocity measurements, however x-ray imaging is more spatially resolved allowing for shock steadiness observations of value when studying heterogeneous materials. Additionally, x-ray imaging provides greater insight into the shape and heterogeneity of the shock front as well as uniaxial strain state (1D zone) assumptions

Hugoniot measurements utilizing in situ synchrotron X-ray radiation

Pressure–density relationships derived from the experimentally obtained shock and particle velocities are critical to define a material’s equation of state (EOS). Typically, impact experiments coupled with velocimetry are used to map a material’s Hugoniot. Limitations such as sample geometry and varying indices of refraction may prevent proper characterization using traditional techniques such as photon doppler velocimetry (PDV) or velocity interferometer system for any reflector (VISAR). Here, traditional Hugoniot measurements using PDV are compared to dynamic x-ray imaging encompassing two different sample geometries on the gas gun platform. Through each of these methods an experimentally derived Hugoniot is determined for a previously uncharacterized polymeric material, Somos Watershed XC11122, that is used 3D printed stereolithography parts. A Us–up relationship was determined to be Us = 2.93 us + 1.73 mm/μs through traditional PDV. Slope and sound speed values determined from x-ray imaging methods varied 11% from PDV measurements. Each method yielded a Hugoniot with densities similar to poly(methyl methacrylate) (PMMA). The similarity shows the viability of such analyses for dynamic properties and Hugoniot data. The performance and analysis of both PDV and dynamic x-ray measurements are laid out in this work. Comparing PDV and x-ray imaging highlights distinct advantages and disadvantages among each method. PDV provides less uncertainty for velocity measurements, however x-ray imaging is more spatially resolved allowing for shock steadiness observations of value when studying heterogeneous materials. Additionally, x-ray imaging provides greater insight into the shape and heterogeneity of the shock front as well as uniaxial strain state (1D zone) assumptions

Hugoniot measurements utilizing in situ synchrotron X-ray radiation

Pressure–density relationships derived from the experimentally obtained shock and particle velocities are critical to define a material’s equation of state (EOS). Typically, impact experiments coupled with velocimetry are used to map a material’s Hugoniot. Limitations such as sample geometry and varying indices of refraction may prevent proper characterization using traditional techniques such as photon doppler velocimetry (PDV) or velocity interferometer system for any reflector (VISAR). Here, traditional Hugoniot measurements using PDV are compared to dynamic x-ray imaging encompassing two different sample geometries on the gas gun platform. Through each of these methods an experimentally derived Hugoniot is determined for a previously uncharacterized polymeric material, Somos Watershed XC11122, that is used 3D printed stereolithography parts. A Us–up relationship was determined to be Us = 2.93 us + 1.73 mm/μs through traditional PDV. Slope and sound speed values determined from x-ray imaging methods varied 11% from PDV measurements. Each method yielded a Hugoniot with densities similar to poly(methyl methacrylate) (PMMA). The similarity shows the viability of such analyses for dynamic properties and Hugoniot data. The performance and analysis of both PDV and dynamic x-ray measurements are laid out in this work. Comparing PDV and x-ray imaging highlights distinct advantages and disadvantages among each method. PDV provides less uncertainty for velocity measurements, however x-ray imaging is more spatially resolved allowing for shock steadiness observations of value when studying heterogeneous materials. Additionally, x-ray imaging provides greater insight into the shape and heterogeneity of the shock front as well as uniaxial strain state (1D zone) assumptions