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

Analysis of the x-ray diffraction signal for the alpha-epsilon transition in shock-compressed iron: Simulation and experiment

Recent published work has shown that the phase change of shock-compressed iron along the [001] direction does transform to the [hexagonal close-packed (hcp)] phase similar to the case for static measurements. This article provides an in-depth analysis of the experiment and nonequilibrium molecular dynamics simulations, using x-ray diffraction in both cases to study the crystal structure upon transition. Both simulation and experiment are consistent with a compression and shuffle mechanism responsible for the phase change from body-centered cubic to hcp. Also both show a polycrystalline structure upon the phase transition, due to the four degenerate directions in which the phase change can occur. © 2006 The American Physical Society

Multiple film plane diagnostic for shocked lattice measurements

Laser-based shock experiments have been conducted in thin Si and Cu crystals at pressures above the Hugoniot elastic limit. In these experiments, static film and x-ray streak cameras recorded x rays diffracted from lattice planes both parallel and perpendicular to the shock direction. These data, showed uniaxial compression of Si(100) along the shock direction and three.-dimensional compression of Cu(100). In the case of the Si diffraction, there was a multiple wave structure observed, which may be due to a one-dimensional phase transition or a time variation in the shock pressure. A new film-based detector has been developed for these in situ dynamic diffraction experiments. This large-angle detector consists of three film cassettes that are positioned to record x rays diffracted from a shocked crystal anywhere within a full pi steradian. It records x rays that are diffracted from multiple lattice planes both parallel and at oblique angles with respect to the shock direction. It is a time-integrating measurement, but time-resolved data may be recorded using a short duration laser pulse to create the diffraction source x rays. This new instrument,has been fielded at the OMEGA and Janus lasers to study single-crystal materials shock compressed by direct laser irradiation. In these experiments, a multiple wave structure was observed on many different lattice planes in Si. These data provide information on, the structure under compression. (C) 2003 American Institute of Physics

High-pressure, high-strain-rate lattice response of shocked materials

Laser-based shock experiments have been conducted in thin Si and Cu crystals at pressures above the published Hugoniot Elastic Limit (HEL) for these materials. In situ x-ray diffraction has been used to directly measure the response of the shocked lattice during shock loading. Static film and x-ray streak cameras recorded x rays diffracted from lattice planes both parallel and perpendicular to the shock direction. In addition, experiments were conducted using a wide-angle detector to record x rays diffracted from multiple lattice planes simultaneously. These data showed uniaxial compression of Si (100) along the shock direction and three-dimensional compression of Cu (100). In the case of the Si diffraction, there was a multiple wave structure observed. This is evaluated to determine whether there is a phase transition occurring on the time scale of the experiments, or the HEL is much higher than previously reported. Results of the measurements are presented. (C) 2003 American Institute of Physics

Picosecond X-ray diffraction studies of shocked single crystals - art. no. 62610T

The past few years have seen a rapid growth in the development and exploitation of X-ray diffraction on ultra-fast time-scales. One area of physics which has benefited particularly from these advances is the the field of shock-waves. Whilst it has been known for many years that crystalline matter, subjected to uniaxial shock compression, can undergo plastic deformation and, for certain materials, polymorphic phase transformations, it has hitherto not been possible to observe the rearrangement of the atoms on the pertinent timescales. We have used laser-plasma generated X-rays to study how single crystals of metals (copper and iron) react to uniaxial shock compression, and observed rapid plastic flow (in the case of copper), and directly observed the famous alpha-epsilon transition in Iron. These studies have been complemented by large-scale multi-million atom molecular dynamics simulations, yielding significant information on the underlying physics

Picosecond X-ray diffraction studies of shocked single crystals

The past few years have seen a rapid growth in the development and exploitation of X-ray diffraction on ultrafast time-scales. One area of physics which has benefited particularly from these advances is the the field of shock-waves. Whilst it has been known for many years that crystalline matter, subjected to uniaxial shock compression, can undergo plastic deformation and, for certain materials, polymorphic phase transformations, it has hitherto not been possible to observe the rearrangement of the atoms on the pertinent timescales. We have used laser-plasma generated X-rays to study how single crystals of metals (copper and iron) react to uniaxial shock compression, and observed rapid plastic flow (in the case of copper), and directly observed the famous alpha-epsilon transition in Iron. These studies have been complemented by large-scale multi-million atom molecular dynamics simulations, yielding significant information on the underlying physics

Materials science under extreme conditions of pressure and strain rate

Solid-state dynamics experiments at very high pressures and strain rates are becoming possible with high-power laser facilities, albeit over brief intervals of time and spatially small scales. To achieve extreme pressures in the solid state requires that the sample be kept cool, with T-sample < T-melt. To this end, a shockless, plasma-piston "drive" has been developed on the Omega laser, and a staged shock drive was demonstrated on the Nova laser. To characterize the drive, velocity interferometer measurements allow the high pressures of 10 to 200 GPa (0.1 to 2 Mbar) and strain rates of 10(6) to 10(8) s(-1) to be determined. Solid-state strength in the sample is inferred at these high pressures using the Rayleigh-Taylor (RT) instability as a "diagnostic." Lattice response and phase can be inferred for single-crystal samples from time-resolved X-ray diffraction. Temperature and compression in polycrystalline samples can be deduced from extended X-ray absorption fine-structure (EXAFS) measurements. Deformation mechanisms and residual melt depth can be identified by examining recovered samples. We will briefly review this new area of laser-based materials-dynamics research, then present a path forward for carrying these solid-state experiments to much higher pressures, P > 10(3) GPa (10 Mbar), on the National Ignition Facility (NIF) laser at Lawrence Livermore National Laboratory

Picosecond X-ray diffraction from laser-shocked copper and iron

In situ X-ray diffraction allows the determination of the structure of transient states of matter. We have used laser-plasma generated X-rays to study how single crystals of metals (copper and iron) react to uniaxial shock compression. We find that copper, as a face-centred-cubic material, allows rapid generation and motion of dislocations, allowing close to hydrostatic conditions to be achieved on sub-nanosecond timescales. Detailed molecular dynamics calculations provide novel information about the process, and point towards methods whereby the dislocation density might be measured during the passage of the shock wave itself. We also report on recent experiments where we have obtained diffraction images from shock-compressed single-crystal iron. The single crystal sample transforms to the hcp phase above a critical pressure, below which it appears to be uniaxially compressed bcc, with no evidence of plasticity. Above the transition threshold, clear evidence for the hcp phase can be seen in the diffraction images, and via a mechanism that is also consistent with recent multi-million atom molecular dynamics simulations that use the Voter-Chen potential-We believe these data to be of import, in that they constitute the first conclusive in situ evidence of the transformed structure of iron during the passage of a shock wave

Finite element analysis of idealised unit cell cancellous structure based on morphological indices of cancellous bone

Human bones can be categorised into one of two types—the compact cortical and the porous cancellous. Whilst the cortical is a solid structure macroscopically, the structure of cancellous bone is highly complex with plate-like and strut-like structures of various sizes and shapes depending on the anatomical site. Reconstructing the actual structure of cancellous bone for defect filling is highly unfeasible. However, the complex structure can be simplified into an idealised structure with similar properties. In this study, two idealised architectures were developed based on morphological indices of cancellous bone: the tetrakaidecahedral and the prismatic. The two architectures were further subdivided into two types of microstructure, the first consists of struts only and the second consists of a combination of plates and struts. The microstructures were transformed into finite element models and displacement boundary condition was applied to all four idealised cancellous models with periodic boundary conditions. Eight unit cells extracted from the actual cancellous bone obtained from micro-computed tomography were also analysed with the same boundary conditions. Young’s modulus values were calculated and comparison was made between the idealised and real cancellous structures. Results showed that all models with a combination of plates and struts have higher rigidity compared to the one with struts only. Values of Young’s modulus from eight unit cells of cancellous bone varied from 42 to 479 MPa with an average of 234 MPa. The prismatic architecture with plates and rods closely resemble the average stiffness of a unit cell of cancellous bone