A thermodynamic condition for ignition and burn-propagation in cryogenic layer inertially confined fusion implosions

A Lawson-like criterion for ignition (where self-heating dominates over all energy losses) in a dynamic implosion is developed, which accounts for asymmetry and for differences in an implosion x-ray confinement quality. It is shown that the thermodynamic ignition condition is equivalent to yield amplification levels of 16–32. Since negative pdV work of expansion after stagnation increases energy losses above that of x-ray and electron-conduction losses, the Lawson-like ignition criterion is necessary but not sufficient for igniting the hot spot to propagate into the DT fuel with sufficient vigor to generate high gain. A higher dimensional generalization of the Lawson-like criterion, which includes the cooling of the implosion upon disassembly, does provide the needed criteria, and it shows that significantly higher temperature is needed for very high levels of yield amplification compared to what traditional ignition metrics imply.