to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Physics of shock waves and high-temperature hydrodynamic phenomena - Ya.B. Zeldovich and Yu.P. Raizer (translated from the Russian and then edited by Wallace D. Hayes and Ronald F. Probstein); Dover Publications, New York, 2002, 944 pp., $34.

Ignition is needed to make fusion energy a viable alternative energy source, but has yet to be achieved. A key step on the way to ignition is to have the energy generated through fusion reactions in an inertially confined fusion plasma exceed the amount of energy deposited into the deuterium-tritium fusion fuel and hotspot during the implosion process, resulting in a fuel gain greater than unity. Here we report the achievement of fusion fuel gains exceeding unity on the US National Ignition Facility using a 'high-foot' implosion method, which is a manipulation of the laser pulse shape in a way that reduces instability in the implosion. These experiments show an order-of-magnitude improvement in yield performance over past deuterium-tritium implosion experiments. We also see a significant contribution to the yield from α-particle self-heating and evidence for the 'bootstrapping' required to accelerate the deuterium-tritium fusion burn to eventually 'run away' and ignite.

https://materias.df.uba.ar/fc1a2014c1/files/2014/05/Hurricane-2014-Nature-Fuel-gain-exceeding-unity-in-an-inertially-confined-fusion-implosion.pdf

Fuel gain exceeding unity in an inertially confined fusion implosion

With the advent of high-energy-density (HED) experimental facilities, such as high-energy lasers and fast Z-pinch, pulsed-power facilities, millimeter-scale quantities of matter can be placed in extreme states of density, temperature, and/or velocity. This has enabled the emergence of a new class of experimental science, HED laboratory astrophysics, wherein the properties of matter and the processes that occur under extreme astrophysical conditions can be examined in the laboratory. Areas particularly suitable to this class of experimental astrophysics include the study of opacities relevant to stellar interiors, equations of state relevant to planetary interiors, strong shock-driven nonlinear hydrodynamics and radiative dynamics relevant to supernova explosions and subsequent evolution, protostellar jets and high Mach number flows, radiatively driven molecular clouds and nonlinear photoevaporation front dynamics, and photoionized plasmas relevant to accretion disks around compact objects such as black holes and neutron stars.

/pdf/experimental-astrophysics-with-high-power-lasers-and-z-2ws0p4rgie.pdf

Experimental astrophysics with high power lasers and Z pinches

Accurate x-ray scattering techniques to measure the physical properties of dense plasmas have been developed for applications in high energy density physics. This class of experiments produces short-lived hot dense states of matter with electron densities in the range of solid density and higher where powerful penetrating x-ray sources have become available for probing. Experiments have employed laser-based x-ray sources that provide sufficient photon numbers in narrow bandwidth spectral lines, allowing spectrally resolved x-ray scattering measurements from these plasmas. The backscattering spectrum accesses the noncollective Compton scattering regime which provides accurate diagnostic information on the temperature, density, and ionization state. The forward scattering spectrum has been shown to measure the collective plasmon oscillations. Besides extracting the standard plasma parameters, density and temperature, forward scattering yields new observables such as a direct measure of collisions and quantum effects. Dense matter theory relates scattering spectra with the dielectric function and structure factors that determine the physical properties of matter. Applications to radiation-heated and shock-compressed matter have demonstrated accurate measurements of compression and heating with up to picosecond temporal resolution. The ongoing development of suitable x-ray sources and facilities will enable experiments in a wide range of research areas including inertial confinement fusion,more » radiation hydrodynamics, material science, or laboratory astrophysics.« less

X-ray Thomson scattering in high energy density plasmas

A key demonstration on the path to inertial fusion energy is the achievement of high fusion yield (hundreds of MJ) and high target gain. Toward this goal, an indirect-drive high-yield inertial confinement fusion (ICF) target involving two Z-pinch x-ray sources heating a central secondary hohlraum is described by Hammer et al. [Phys. Plasmas 6, 2129 (1999)]. In subsequent research at Sandia National Laboratories, theoretical/computational models have been developed and an extensive series of validation experiments have been performed to study hohlraum energetics, capsule coupling, and capsule implosion symmetry for this system. These models have been used to design a high-yield Z-pinch-driven ICF target that incorporates the latest experience in capsule design, hohlraum symmetry control, and x-ray production by Z pinches. An x-ray energy output of 9MJ per pinch, suitably pulse-shaped, is sufficient for this concept to drive 0.3–0.5GJ capsules. For the first time, integrated two-dimensional (2D) hohlraum/ca...

Target design for high fusion yield with the double Z-pinch-driven hohlraum

http://absimage.aps.org/image/DPP06/MWS_DPP06-2006-000703.pdf

Target design for high fusion yield with the double Z-pinch-driven hohlraum.

We have developed wire-array $z$-pinch scaling relations for plasma-physics and inertial-confinement-fusion (ICF) experiments. The relations can be applied to the design of $z$-pinch accelerators for high-fusion-yield $(\ensuremath{\sim}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{GJ∕shot})$ and inertial-fusion-energy $(\ensuremath{\sim}3\phantom{\rule{0.3em}{0ex}}\mathrm{GJ∕shot})$ research. We find that $({\ensuremath{\delta}}_{a}∕{\ensuremath{\delta}}_{\mathrm{RT}})\ensuremath{\propto}{(m∕\ensuremath{\ell})}^{1∕4}{(R\ensuremath{\Gamma})}^{\ensuremath{-}1∕2}$, where ${\ensuremath{\delta}}_{a}$ is the imploding-sheath thickness of a wire-ablation-dominated pinch, ${\ensuremath{\delta}}_{\mathrm{RT}}$ is the sheath thickness of a Rayleigh-Taylor-dominated pinch, $m$ is the total wire-array mass, $\ensuremath{\ell}$ is the axial length of the array, $R$ is the initial array radius, and $\ensuremath{\Gamma}$ is a dimensionless functional of the shape of the current pulse that drives the pinch implosion. When the product $R\ensuremath{\Gamma}$ is held constant the sheath thickness is, at sufficiently large values of $m∕\ensuremath{\ell}$, determined primarily by wire ablation. For an ablation-dominated pinch, we estimate that the peak radiated x-ray power ${P}_{r}\ensuremath{\propto}{(I∕{\ensuremath{\tau}}_{i})}^{3∕2}R\ensuremath{\ell}\ensuremath{\Phi}\ensuremath{\Gamma}$, where $I$ is the peak pinch current, ${\ensuremath{\tau}}_{i}$ is the pinch implosion time, and $\ensuremath{\Phi}$ is a dimensionless functional of the current-pulse shape. This scaling relation is consistent with experiment when $13\phantom{\rule{0.3em}{0ex}}\mathrm{MA}\ensuremath{\leqslant}I\ensuremath{\leqslant}20\phantom{\rule{0.3em}{0ex}}\mathrm{MA}$, $93\phantom{\rule{0.3em}{0ex}}\mathrm{ns}\ensuremath{\leqslant}{\ensuremath{\tau}}_{i}\ensuremath{\leqslant}169\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$, $10\phantom{\rule{0.3em}{0ex}}\mathrm{mm}\ensuremath{\leqslant}R\ensuremath{\leqslant}20\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$, $10\phantom{\rule{0.3em}{0ex}}\mathrm{mm}\ensuremath{\leqslant}\ensuremath{\ell}\ensuremath{\leqslant}20\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$, and $2.0\phantom{\rule{0.3em}{0ex}}\mathrm{mg}∕\mathrm{cm}\ensuremath{\leqslant}m∕\ensuremath{\ell}\ensuremath{\leqslant}7.3\phantom{\rule{0.3em}{0ex}}\mathrm{mg}∕\mathrm{cm}$. Assuming an ablation-dominated pinch and that $R\ensuremath{\ell}\ensuremath{\Phi}\ensuremath{\Gamma}$ is held constant, we find that the x-ray-power efficiency ${\ensuremath{\eta}}_{x}\ensuremath{\equiv}{P}_{r}∕{P}_{a}$ of a coupled pinch-accelerator system is proportional to ${({\ensuremath{\tau}}_{i}{P}_{r}^{7∕9})}^{\ensuremath{-}1}$, where ${P}_{a}$ is the peak accelerator power. The pinch current and accelerator power required to achieve a given value of ${P}_{r}$ are proportional to ${\ensuremath{\tau}}_{i}$, and the requisite accelerator energy ${E}_{a}$ is proportional to ${\ensuremath{\tau}}_{i}^{2}$. These results suggest that the performance of an ablation-dominated pinch, and the efficiency of a coupled pinch-accelerator system, can be improved substantially by decreasing the implosion time ${\ensuremath{\tau}}_{i}$. For an accelerator coupled to a double-pinch-driven hohlraum that drives the implosion of an ICF fuel capsule, we find that the accelerator power and energy required to achieve high-yield fusion scale as ${\ensuremath{\tau}}_{i}^{0.36}$ and ${\ensuremath{\tau}}_{i}^{1.36}$, respectively. Thus the accelerator requirements decrease as the implosion time is decreased. However, the x-ray-power and thermonuclear-yield efficiencies of such a coupled system increase with ${\ensuremath{\tau}}_{i}$. We also find that increasing the anode-cathode gap of the pinch from $2\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}4\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ increases the requisite values of ${P}_{a}$ and ${E}_{a}$ by as much as a factor of 2.

Theoretical z-pinch scaling relations for thermonuclear-fusion experiments

A quasianalytic model of the dynamic hohlraum is presented. Results of the model are compared to both experiments and full numerical simulations with good agreement. The computational simplicity of the model allows one to find the behavior of the hohlraum radiation temperature as a function of the various parameters of the system and thus find optimum parameters as a function of the driving current. The model is used to investigate the benefits of ablative standoff and quasispherical Z pinches.

/pdf/scaling-and-optimization-of-the-radiation-temperature-in-2njn0skr1q.pdf

Scaling and optimization of the radiation temperature in dynamic hohlraums

Simulations of a double Z-pinch hohlraum, relevant to the high-yield inertial-confinement-fusion concept, predict that through geometry design the time-integrated P 2 Legendre mode drive asymmetry can be systematically controlled from positive to negative coefficient values. Studying capsule elongation, recent experiments on Z confirm such control by varying the secondary hohlraum length. Since the experimental trend and optimum length are correctly modeled, confidence is gained in the simulation tools; the same tools predict capsule drive uniformity sufficient for high-yield fusion ignition.

Roger Alan Vesey

Papers

Target design for high fusion yield with the double Z-pinch-driven hohlraum

Target design for high fusion yield with the double Z-pinch-driven hohlraum.

Theoretical z-pinch scaling relations for thermonuclear-fusion experiments

Scaling and optimization of the radiation temperature in dynamic hohlraums

Demonstration of radiation symmetry control for inertial confinement fusion in double Z-pinch hohlraums.