Theory of ignition and burn propagation in inertial fusion implosions

Abstract

A detailed analytic model is presented here to investigate the physics of burn propagation in inertially confined plasmas. The onset of ignition and burn propagation occurs when alpha heating of the hot spot causes rapid ablation of shell mass into the hot spot. This allows large energy gains to be achieved since most of the fuel mass is located in the shell. Here, we first present a comprehensive review of previous analytic models that have been used to describe the physics of hot-spot evolution and ignition; we then show that a proper description of a propagating burn wave requires a comprehensive model of hot spot and shell evolution that includes proper mass conservation in the shell, fusion reactivity, and fuel depletion. The analytic theory is in good agreement with detailed radiation-hydrodynamic simulations that predict the onset of burn propagation as occurring when the yield enhancement caused by alpha heating is between 15- and 25-fold, fα ∼ 1.4, where fα = alpha energy deposited/hot-spot energy at bang time, and the hot-spot burnup fraction is approximately 2%. We show that the definition of ignition is not sensitive to the alpha-particle stopping power nor asymmetries provided that the absorbed fraction of alpha particles θα is correctly accounted for. Finally, we use the results of 2-D simulations to show that even when θα is small and unknown (as is true in hot spots with mid modes that have significant leakage of alpha particles into the surrounding cold bubbles), one can still relate the experimentally measureable parameter χα53 to the yield amplification and the burning-plasma parameter Qαhs = alpha energy deposited/total input work delivered to the hot spot.