Development of a 3D Generalized Lawson ignition threshold metric and application to high yield NIF implosion data

The self-heating condition for an imploding hotspot require understanding the balance between mechanical work, heating via fusion reactions, and the radiative and conduction losses. A 3D generalized Lawson ignition threshold criterion is achieved when hotspot rho-r and temperature exceed critical values. In the presence of 3D shell rho-R asymmetry, loss of confinement in “thin” regions of the stagnated fuel increases expansion phase PdV work leading to loss of pressure, temperature, and alpha heating. Compared to conventional ignition metrics, the proper 3D metric requires both increased pressure and temperature for ignition to offset 3D loss in confinement, and places requirements on rho-r asymmetry and minimum rho-r. A potential flow solution to the 3D flows that develop near peak compression is derived and fit to observed hotspot and shell asymmetry data, to account for the expected thinning due to the evolution of the Rayleigh Taylor instability. This technique is applied to high yield implosion data from NIF, which exhibit significant 3D rho-r asymmetry, and is used to predict required improvements needed to achieve ignition.