A comprehensive alpha-heating model for inertial confinement fusion

Abstract

A comprehensive model is developed to study alpha-heating in inertially confined plasmas. It describes the time evolution of a central low-density hot spot confined by a compressible shell, heated by fusion alphas, and cooled by radiation and thermal losses. The model includes the deceleration, stagnation, and burn phases of inertial confinement fusion implosions, and is valid for sub-ignited targets with ≤10× amplification of the fusion yield from alpha-heating. The results of radiation-hydrodynamic simulations are used to derive realistic initial conditions and dimensionless parameters for the model. It is found that most of the alpha energy (∼90%) produced before bang time is deposited within the hot spot mass, while a small fraction (∼10%) drives mass ablation off the inner shell surface and its energy is recycled back into the hot spot. Of the bremsstrahlung radiation emission, ∼40% is deposited in the hot spot, ∼40% is recycled back in the hot spot by ablation off the shell, and ∼20% leaves the hot spot. We show here that the hot spot, shocked shell, and outer shell trajectories from this analytical model are in good agreement with simulations. A detailed discussion of the effect of alpha-heating on the hydrodynamics is also presented.