Ignition energy scaling of inertial confinement fusion targets

Abstract

ABSTRACT. Scaling of the ignition energy threshold Eig with the implosion velocity vim and isentrope parameter α of imploding spherical DT shells is investigated by performing one dimensional (1-D) hydrodynamic simulations of the implosion and hot spot formation dynamics. It is found that the a and b exponents in the power law approximation Eig ∝ α a v −b im depend crucially on the subset of initial configurations chosen to establish the scaling law. When the initial states are generated in the same way as in the Livermore study (W.K. Levedahl, J.D. Lindl, Nucl. Fusion 37 (1997) 165), the same scaling, Eig ∝ α 1.7 v −5.5 im , is recovered. If, however, the initial states are generated by rescaling the parent configuration according to the hydrodynamic similarity laws, a different scaling is obtained, Eig ∝ α 3.0 v −9.1 im , which is very close to the α 3 v −10 im dependence predicted by the simple isobaric model for assembled fuel states. The latter is more favourable than the Livermore scaling when rescaling the fusion capsules to higher implosion velocities, but requires the peak drive pressure to be increased as P ∝ v 5 im .

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

“…12 plots the entire data set of 2-D simulations in the plane of capsule yield versus the margin parameter from Eq. (6). That this form for the margin neatly aligns the entire data set (spanning different capsule scales, velocities, and perturbation fractions) onto a single ignition cliff is clearly evident.…”

“…IV, must first be accounted for. From the previous work on capsule ignition energy [3][4][5][6][7], it is known that the minimum ignition energy (and hence also the ignition margin) is a very strong function of the fuel entropy or adiabat. Ideally, then, if a power law fit is to be found for the margin as a function of the scale, velocity, and perturbation fraction, the entropy should be held constant across the various scales, velocities, and perturbation fractions.…”

“…In principle, these 1-D variations in the entropy may be compensated for in the 2-D data set using the scalings of the minimum ignition energy found in 1-D [3][4][5][6][7]. That is, since Eq.…”

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

“…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].…”