Generalized Measurable Ignition Criterion for Inertial Confinement Fusion

Py, Chang; Betti, R.; Bk, Spears; Ks, Anderson; Edwards, John; Fatenejad, Milad; Jd, Lindl; Rl, McCrory; Nora, R.; Shvarts, D.

doi:10.1103/physrevlett.104.135002

Cited by 78 publications

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References 16 publications

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“…Here we use the expression of Refs. [8,14,15] that is also related to the Livermore experimental ignition threshold factor (ITFx) [7,16,17]: where ρR is in g/cm 2 , the no-α neutron yield is in 10 16 , and the stagnating DT mass at bang time is in milligrams. The latter is often approximated with 1/2 of the unablated DT mass [8,15] …”

Section: The Higher Temperatures (Tmentioning

confidence: 99%

“…Based on analytic models and detailed numerical simulations [7,8], it was estimated that alpha-particle heating has led to a ∼2-2.5× enhancement of the fusion yield [6,8]. In the absence of alpha heating, the fusion yield from hydrodynamic compression alone would have been ∼ 4-5×10 15 . By extrapolating recent OMEGA results in size to match the 1.9 MJ of incident NIF laser energy, we find that the best-performing direct-drive OMEGA implosion to date would lead to a neutron yield of 4.5×10 16 neutrons and a level of alpha heating corresponding to about a 2× yield enhancement, similar to the indirect-drive HF targets at the same laser energy.…”

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confidence: 99%

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Core conditions for alpha heating attained in direct-drive inertial confinement fusion

et al. 2016

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It is shown that direct-drive implosions on the OMEGA laser have achieved core conditions that would lead to significant alpha heating at incident energies available on the National Ignition Facility (NIF) scale. The extrapolation of the experimental results from OMEGA to NIF energy assumes only that the implosion hydrodynamic efficiency is unchanged at higher energies. This approach is independent of the uncertainties in the physical mechanism that degrade implosions on OMEGA, and relies solely on a volumetric scaling of the experimentally observed core conditions. It is estimated that the current best-performing OMEGA implosion [Regan et al., Phys. Rev. Lett. 117, 025001 (2016)] extrapolated to a 1.9 MJ laser driver with the same illumination configuration and laser-target coupling would produce 125 kJ of fusion energy with similar levels of alpha heating observed in current highest performing indirect-drive NIF implosions. DOI: 10.1103/PhysRevE.94.011201 Inertial confinement fusion (ICF) [1] uses lasers or other drivers such as pulsed-power devices or particle accelerators to implode a shell of cryogenic deuterium and tritium (DT). Laser light can be directly incident on the capsule surface (direct drive) or converted into x-rays (indirect drive) through a high-Z enclosure (hohlraum). The shell is imploded to high velocities of hundreds km/s to achieve high central temperatures and areal densities [2]. The hot spot (∼5-10 keV) is a low-density (30-100 g/cm 3 ) core and is surrounded and tamped by a cold (200-500 eV) near Fermi-degenerate dense (300-1000 g/cm 3 ) fuel layer. Fusion alphas produced in the hot spot deposit their energy primarily through collisions with plasma electrons further enhancing the temperature and fusion reaction rate (alpha heating). Under certain conditions of pressure, temperature, and confinement time, alpha heating initiates a burn wave in the surrounding dense shell, leading to fusion energy outputs greatly exceeding the thermal and kinetic energy supplied to the DT fuel by the implosion [2]. Alpha heating is essential for ignition and energy gain in nuclear fusion.In this Rapid Communication we show that recent direct drive OMEGA implosions [3] have achieved core conditions that would lead to significant levels of alpha heating if reproduced at scales typical of the National Ignition Facility (NIF) [4]. At NIF scale, these direct drive targets would yield about 125 kJ of fusion energy, 5× the highest fusion output achieved to date in ICF. The level of alpha heating and yield amplification is predicted to be similar to that achieved with the 1.9 MJ indirect-drive NIF [4] high foot (HF) implosions [5]. These HF implosions have achieved record fusion yields of nearly 1016 neutrons or about 26 kJ of fusion energy [6], demonstrating significant levels of alpha heating. Based on analytic models and detailed numerical simulations [7,8], it was estimated that alpha-particle heating has led to a ∼2-2.5× enhancement of the fusion yield [6,8]. In the absence of alpha heating, the fusion ...

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Section: The Higher Temperatures (Tmentioning

confidence: 99%

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confidence: 99%

Core conditions for alpha heating attained in direct-drive inertial confinement fusion

et al. 2016

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“…In this letter, we consider yield amplifications ≤ 10 that are of most interest for current implosions on the NIF and characterstic of a subignited burning plasma. Using a simple model of the hot spot and shell dynamics (alpha heating model), we find the burning-plasma conditions for ICF and show that the fusion yield enhancement due to alpha heating depends only on the Lawson parameter [6,7] through a universal curve valid for direct and indirect drive ICF. It is shown that the alpha-heating model results agree with radiation-hydrodynamics simulations.…”

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Alpha Heating and Burning Plasmas in Inertial Confinement Fusion

et al. 2015

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“…Here I discuss a minimal model of ignition, simple enough for intuitive understanding, and its quantification by means of the partial derivatives (2). It is not meant to be a realistic description of the actual ignition of flammable gases or an inertial fusion capsule, although such capsules are a well-known and well-quantified example of a design problem with a steep cliff (Chang, et al 2010 Fig. 4).…”

Section: A Determinate Model: Ignitionmentioning

confidence: 99%

“…The first is the ignition of a flammable gas mixture by a small spark. This is a simple model of the more complex problem of ignition of a laser fusion capsule (Chang, et al 2010;Lindl, et al 2011;Haan, et al 2011;Edwards, et al 2011). The second is the well-known problem of plastic failure of a ductile material in tension (Ugural and Fenster 2011).…”

Section: Review Of Literaturementioning

confidence: 99%

Quantifying “cliffs” in design space

Katz

2014

Journal of Engineering, Design and Technology

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Purpose: This paper studies the regions of parameter space of engineering design in which performance is sensitive to design parameters. Some of these parameters (for example, the dimensions and compositions of components) constitute the design, but others are intrinsic properties of materials or Nature. The paper is concerned with narrow regions of parameter space, "cliffs", in which performance (some measure of the final state of a system, such as ignition or non-ignition of a flammable gas, or failure or non-failure of a ductile material subject to tension) is a sensitive function of the parameters. In these regions performance is also sensitive to uncertainties in the parameters. This is particularly important for intrinsically indeterminate systems, those whose performance is * email:katz@wuphys.wustl.edu, 1 not predictable from measured initial conditions and is not reproducible.Design/methodology/approach: We develop models of ignition of a flammable mixture and of failure in plastic flow under tension. We identify and quantify cliffs in performance as functions of the design parameters. These cliffs are characterized by large partial derivatives of performance parameters with respect to the design parameters and with respect to the uncertainties in the model. We calculate and quantify the consequences of small random variations in the parameters of indeterminate systems.Findings: We find two qualitatively different classes of performance cliffs. In one class, performance is a sensitive function of the parameters in a narrow range that separates wider ranges in which it is insensitive. In the other class, the final state is not defined for parameter values outside some range, and performance is a sensitive function of the parameters as they approach their limiting values. We find that sensitivity of performance to control (design) parameters implies that it is also sensitive to other parameters, some of which may not be known, and to uncertainties of the initial state that are not under the control of the designer. Near or on a cliff performance is degraded. It is also less predictable and less reproducible.Practical implications: Frequently, design optimization or cost minimization leads to choices of engineering design parameters near cliffs. The sensitivity of performance to uncertainty that we find in those regimes implies that caution and extensive empirical experience are required to assure reliable functioning. Because cliffs are defined as behavior on the threshold of failure, this is a reflection of the tradeoff between optimization and margin of safety, and implies the importance of ensuring that margins and uncertainties are quantified. The implications extend far beyond the model systems we consider to engineering systems in general.Originality/value: Many of these considerations have been part of the informal culture of engineering design, but they were not formalized until the methodology of "Quantification of Margins and Uncertainty" was developed in recent years. Although this met...

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Generalized Measurable Ignition Criterion for Inertial Confinement Fusion

Cited by 78 publications

References 16 publications

Core conditions for alpha heating attained in direct-drive inertial confinement fusion

Core conditions for alpha heating attained in direct-drive inertial confinement fusion

Alpha Heating and Burning Plasmas in Inertial Confinement Fusion

Quantifying “cliffs” in design space

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