A generalized scaling law for the ignition energy of inertial confinement fusion capsules

Abstract

The minimum energy needed to ignite an inertial confinement fusion capsule is of considerable interest in the optimization of an inertial fusion driver. Recent computational work investigating this minimum energy has found that it depends on the capsule implosion history, in particular, on the capsule drive pressure. This dependence is examined using a series of LASNEX simulations to find ignited capsules which have different values of the implosion velocity, fuel adiabat and drive pressure. It is found that the main effect of varying the drive pressure is to alter the stagnation of the capsule, changing its stagnation adiabat, which, in turn, affects the energy required for ignition. To account for this effect a generalized scaling law has been devised for the ignition energy, Eign ∝ α 1.88±0.05 if v −5.89±0.12 P −0.77±0.03 . This generalized scaling law agrees with the results of previous work in the appropriate limits.

Integrated thermodynamic model for ignition target performance

“…This implies that the volume at peak velocity is 5 times greater than the design goal, and occurs at a radius of 233 m, rather than the simulated 133 m. This could occur with a higher than desired velocity for the first few microns of mass in the inner ice layer, which stagnate early and the stagnation shock arrives at the shell at a larger radius. Other consequences of this would be an 04001-p. 3 early shock flash, higher than expected temperature, lower than expected pressure, yield and r. All of these trends are observed in capsule implosions. A stronger than expected 5 th shock or significant shock mistiming (from LEH window ice) is the most likely cause of the problem.…”

“…To this end, we developed and applied a model to estimate the performance of an implosion and assess temperature, density, and composition distributions within the assembled core, solely from the experimental data taken during the shot. Using radiative, equation of state, nuclear fusion relations for relevant materials, and an approximation of pressure equilibrium within the hotspot [3], we derive a 3-dimensional representation of the capsule density and temperature profiles at stagnation, by predicting and optimizing fits to a broad set of x-ray and nuclear diagnostics. This model allows us to determine hotspot density, pressure, areal density ( r), total energy, and other ignition-relevant parameters not available from any single diagnostic.…”

Robustness studies of ignition targets for the National Ignition Facility in two dimensions

“…Note that some variation in the peak drive pressure, another variable found to contribute to the minimum ignition energy in 1-D [7], might also be expected from varying the peak flux. It was found, however, that such Finally, the third parameter entering the margin power law, the hot spot perturbation fraction, was scanned by applying a multiplier to the roughness of the inner surface of the DT ice.…”

“…Values as low as a = 1.7 and b = 5.5 [6,9] or as high as a = 3 and b = 10 [3] have been proposed for these exponents. The most recent values for these exponents (and arguably the most definitive since they include most of the relevant 1-D physical phenomena) are a = 1.88 ± 0.05 and b = 5.89 ± 0.12 as given by Herrmann et al [7]. Taking these values as approximating this minimum ignition energy requirement, the kinetic energy ignition margin in 1-D should be…”

“…Several authors [3][4][5][6][7][8] have published power laws for minimum energy for ignition of the form…”