Theory of Hydro-Equivalent Ignition for Inertial Fusion and Its Applications to OMEGA and the National Ignition Facility

Introduction In inertial confinement fusion (ICF),1 a spherical capsule is illuminated either directly with laser light2 or indirectly within x rays generated by laser irradiation of the walls of a container (hohlraum) enclosing the capsule.3 The capsule consists of a cryogenic layer of deuterium and tritium (DT) frozen onto the inner surface of a spherical shell of ablator material. Photons are absorbed in the coronal plasma surrounding the shell via inverse bremsstrahlung, and the energy is thermally conducted to the surface of the shell, causing it to ablate. The ablating mass creates an equal and opposite force that causes the remaining shell material to implode. This mechanism is typically known as the “rocket effect.” The imploding shell attains a peak implosion velocity before converting a fraction of its kinetic energy into internal energy upon stagnation. The compressed core of an ICF capsule consists of a low-density (tens of g/cm3) and high-temperature (several keV’s) DT plasma (the hot spot) surrounded by a dense (hundreds of g/cm3) and cold (hundreds of eV’s) DT shell. If the thermal energy and areal density of the hot spot are large enough, the alpha particles generated from fusion reactions deposit their energy within the hot spot, triggering a thermal runaway process called “thermonuclear ignition.” A robust ignition would launch an alpha-driven burn wave in the surrounding dense fuel, leading to a significant fusion-energy output. The resulting energy gain (target gain = fusion energy/ laser energy on target) depends on the shell’s areal density (tR), which determines the fraction of fuel burned (U) according to the expression R R 7 g/cm g/cm 2 2 t t U = + ` j (Ref. 4). The shell’s areal density is a critical parameter for the onset of ignition since it provides the inertial confinement for the hot-spot pressure.