Thermonuclear ignition and the onset of propagating burn in inertial fusion implosions

Separating ignition of the central hot spot from propagating burn in the surrounding dense fuel is crucial to conclusively assess the achievement of ignition in inertial confinement fusion (ICF). We show that the transition from hot spot ignition to the onset of propagating burn occurs when the alpha heating within the hot spot has amplified the fusion yield by 15× to 25× with respect to the compression-only case without alpha energy deposition. This yield amplification corresponds to a value of the fractional alpha energy f_{α}≈1.4 (f_{α}=0.5 alpha energy/hot spot energy). The parameter f_{α} can be inferred in ICF experiments by measuring the neutron yield, hot spot size, temperature, and burn width. This ignition threshold is measurable and applicable to all ICF implosions of deuterium and tritium targets both direct and indirect drive. The results of this Rapid Communication can be used to set the goals of the ICF effort with respect to the first demonstration of thermonuclear ignition.