Burning plasma analysis for indirect drive implosions at the National Ignition Facility

In inertial confinement fusion, a spherical capsule of cryogenic DT is accelerated inward at a high velocity.  The final fuel assembly consists of a relatively low density ``hot spot” (where the deuterium and tritium fuse) confined by a cold and dense shell.  In the hot spot, one 3.5 MeV alpha particle is generated per fusion reaction which then deposits its energy back into the plasma, thereby increasing the temperature and the fusion reaction rate even more.  This feedback process is called ``alpha heating,'' and ignition is a direct consequence of this thermal instability. On the path toward ignition, the onset of a burning-plasma regime occurs when the hot spot has received more heating from alpha particle deposition than it has from pure hydrodynamic compression.  Progress toward the burning plasma regime is described by the parameter Q_α^hs  =alpha energy deposited in hot spot/ PdV work delivered to the hot spot and it can be related to the measurable Lawson parameter χ_α~(ρR)^0.61(Yield/M_stag)^0.34 where ρR is the shell’s areal density, Yield is the neutron yield, and M_stag is the mass which has been has been stagnated by the large hot spot pressure.  We discuss here how 2D asymmetries and uncertainties in the stagnated mass influence our ability to infer the burning plasma parameter in inertial fusion experiments on the National Ignition Facility.