Analytic criteria for shock ignition of fusion reactions in a central hot spot

Ribeyre, X.; Tikhonchuk, V. T.; Breil, J.; Lafon, M.; Bel, E. Le

doi:10.1063/1.3646743

Cited by 23 publications

(28 citation statements)

References 16 publications

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“…We first make use of a result by Ribeyre et al [9] who give an approximation to the velocity of a Lagrangian fluid element following the passage of the spherical shock wave. This is used as a boundary condition in a 1D spherical fluid model [10], set to model an ideal fluid with no dissipation apart from the shock itself.…”

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confidence: 99%

Symmetry of Spherically Converging Shock Waves through Reflection, Relating to the Shock Ignition Fusion Energy Scheme

Davie

Evans

2013

Phys. Rev. Lett.

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We examine the properties of perturbed spherically imploding shock waves in an ideal fluid through the collapse, bounce, and development into an outgoing shock wave. We find broad conservation of the size and shape of ingoing and outgoing perturbations when viewed at the same radius. The outgoing shock recovers the velocity of the unperturbed shock outside the strongly distorted core. The results are presented in the context of the robustness of the shock ignition approach to inertial fusion energy. DOI: 10.1103/PhysRevLett.110.185002 PACS numbers: 52.57.Kk, 47.20.Ma, 47.40.Nm, 52.57.Fg Shock ignition [1] is a variant on fast ignition [2] of inertial fusion targets which improves target performance by burning the deuterium-tritium fuel on a lower adiabat (and therefore with less input energy) than is possible using central ignition [1]. Shock ignition occurs as the result of the temperature increase at the surface of collision of two shock waves. The ingoing ''ignition'' shock is the result of a rapid late time increase in driver power and the outgoing shock is the earlier ''compression'' shock. This compression shock converges, reflects at its minimum radius, and then expands before colliding with the ignition shock. Full radiation hydrodynamics calculations [3] show that shock ignition is reasonably tolerant of departures from spherical symmetry. This is perhaps surprising since it is known [4,5] that spherically converging shock waves are unstable to perturbations of their surface.The purpose of this Letter is to study an idealized problem relating to the compression shock, namely, the behavior of finite amplitude perturbations on a converging shock wave, to follow this shock through convergence, reflection at its minimum radius, and then into the expansion phase. We examine the underlying hydrodynamics with a uniform ideal gas, in the absence of heat conduction and other sources and sinks of energy. The relevance to shock ignition is that this approximates the behavior of the compression shock. Pure hydrodynamics is something of a worst case for these perturbed shocks-much of the additional physics will be dissipative and favor greater stability against perturbation growth. The results may also be of interest in the study of the symmetry of supernovae explosions with the proviso that the present work has no input of thermonuclear energy.Previous work has established that during convergence the shock is unstable to perturbations on its surface [4,5], and that during the subsequent blast wave the perturbations are likely to decay [6]. We show that the perturbations are transferred with little change through convergence into expansion, recovering their approximate ingoing form. This ability of the spherical shock waves to recover their ingoing form is at the root of the robustness of shock ignition.Analytic solutions for spherically symmetric converging shocks are used to validate the computer models for these shocks in 1D spherical and 2D axial symmetry. The 2D models then have small perturbations applied ...

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confidence: 99%

Symmetry of Spherically Converging Shock Waves through Reflection, Relating to the Shock Ignition Fusion Energy Scheme

Davie

Evans

2013

Phys. Rev. Lett.

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“…In these designs, shock pressures at shock launch time vary from $300 Mbar to $700 Mbar. The shocks are strongly amplified by spherical convergence by amounts that depend on the details of the implosion 813,816 and may reach pressures of the order of 1-3 Gbar at shock collision time. 809,816 The shock is further amplified by the shock collision.…”

Section: A One-dimensional Analysis and Simulationsmentioning

confidence: 99%

“…Betti et al indicated that a hot-spot pressure enhancement of 70% compared with that expected in typical hot-spot implosions can lead to a fourfold reduction in the energy required for ignition. Ribeyre et al 813 derived a criterion for ignition based on the strong-shock velocity and pre-spike fuel-assembly density and radius. One-dimensional theoretical models of shock propagation and shock collision in planar 814 and spherical 813,[815][816][817] geometries have characterized parameters for achieving maximum amplification of the hot-spot pressure.…”

Section: A One-dimensional Analysis and Simulationsmentioning

confidence: 99%

“…Ribeyre et al 813 derived a criterion for ignition based on the strong-shock velocity and pre-spike fuel-assembly density and radius. One-dimensional theoretical models of shock propagation and shock collision in planar 814 and spherical 813,[815][816][817] geometries have characterized parameters for achieving maximum amplification of the hot-spot pressure. A detailed analysis by Vallet et al 817 produced equations for shock and fluid-particle trajectories during shock convergence and reflection using a Guderley 818 solution with first-order corrections and characterized the effects of a finite shock Mach number.…”

Section: A One-dimensional Analysis and Simulationsmentioning

confidence: 99%

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Direct-drive inertial confinement fusion: A review

et al. 2015

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The direct-drive, laser-based approach to inertial confinement fusion (ICF) is reviewed from its inception following the demonstration of the first laser to its implementation on the present generation of high-power lasers. The review focuses on the evolution of scientific understanding gained from target-physics experiments in many areas, identifying problems that were demonstrated and the solutions implemented. The review starts with the basic understanding of laser–plasma interactions that was obtained before the declassification of laser-induced compression in the early 1970s and continues with the compression experiments using infrared lasers in the late 1970s that produced thermonuclear neutrons. The problem of suprathermal electrons and the target preheat that they caused, associated with the infrared laser wavelength, led to lasers being built after 1980 to operate at shorter wavelengths, especially 0.35 μm—the third harmonic of the Nd:glass laser—and 0.248 μm (the KrF gas laser). The main physics areas relevant to direct drive are reviewed. The primary absorption mechanism at short wavelengths is classical inverse bremsstrahlung. Nonuniformities imprinted on the target by laser irradiation have been addressed by the development of a number of beam-smoothing techniques and imprint-mitigation strategies. The effects of hydrodynamic instabilities are mitigated by a combination of imprint reduction and target designs that minimize the instability growth rates. Several coronal plasma physics processes are reviewed. The two-plasmon–decay instability, stimulated Brillouin scattering (together with cross-beam energy transfer), and (possibly) stimulated Raman scattering are identified as potential concerns, placing constraints on the laser intensities used in target designs, while other processes (self-focusing and filamentation, the parametric decay instability, and magnetic fields), once considered important, are now of lesser concern for mainline direct-drive target concepts. Filamentation is largely suppressed by beam smoothing. Thermal transport modeling, important to the interpretation of experiments and to target design, has been found to be nonlocal in nature. Advances in shock timing and equation-of-state measurements relevant to direct-drive ICF are reported. Room-temperature implosions have provided an increased understanding of the importance of stability and uniformity. The evolution of cryogenic implosion capabilities, leading to an extensive series carried out on the 60-beam OMEGA laser [Boehly et al., Opt. Commun. 133, 495 (1997)], is reviewed together with major advances in cryogenic target formation. A polar-drive concept has been developed that will enable direct-drive–ignition experiments to be performed on the National Ignition Facility [Haynam et al., Appl. Opt. 46(16), 3276 (2007)]. The advantages offered by the alternative approaches of fast ignition and shock ignition and the issues associated with these concepts are described. The lessons learned from target-physics and implosion experiments are taken into account in ignition and high-gain target designs for laser wavelengths of 1/3 μm and 1/4 μm. Substantial advances in direct-drive inertial fusion reactor concepts are reviewed. Overall, the progress in scientific understanding over the past five decades has been enormous, to the point that inertial fusion energy using direct drive shows significant promise as a future environmentally attractive energy source.

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“…4 We provide an outline here of the construction of the symmetric piston, a more complete explanation can be found in Davie and Evans. 4 We first make use of a result by Ribeyre et al 13 who give an approximation to the velocity of a Lagrangian fluid element following the passage of a strong, spherically converging shock wave. This is used as a boundary condition in a 1D spherical fluid model, 14 set to follow an ideal fluid with no dissipation apart from the shock itself.…”

Section: Code Initialisation For Spherically Converging Shocksmentioning

confidence: 99%

Stability of shocks relating to the shock ignition inertial fusion energy scheme

2014

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Motivated by the shock ignition approach to improve the performance of inertial fusion targets, we make a series of studies of the stability of shock waves in planar and converging geometries. We examine stability of shocks moving through distorted material and driving shocks with nonuniform pressure profiles. We then apply a fully 3D perturbation, following this spherically converging shock through collapse to a distorted plane, bounce and reflection into an outgoing perturbed, broadly spherical shock wave. We find broad shock stability even under quite extreme perturbation. V C 2014 AIP Publishing LLC. [http://dx

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Analytic criteria for shock ignition of fusion reactions in a central hot spot

Cited by 23 publications

References 16 publications

Symmetry of Spherically Converging Shock Waves through Reflection, Relating to the Shock Ignition Fusion Energy Scheme

Symmetry of Spherically Converging Shock Waves through Reflection, Relating to the Shock Ignition Fusion Energy Scheme

Direct-drive inertial confinement fusion: A review

Stability of shocks relating to the shock ignition inertial fusion energy scheme

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