Re-examining the effect of low and intermediate mode number perturbations on Ignition Metrics Scaling Laws

We re-examine the way 2/3D effects on scaling laws for ignition metrics, such as the generalized Lawson Criterion (GLC) and the Ignition Threshold Factor (ITF). These scaling laws were derived for 1D symmetrical case and 2/3D perturbations [Hann et al. PoP 2010; Lindl et al., PoP 2014; Betti et al., PoP 2010]. The main cause for the difference between the 1D and the 2/3D scaling laws in those works, is heat conduction losses from the hot-spot bubbles to the cold shell [Kishony and Shvarts, PoP 2001]. This ``dry out'' of the bubbles is the dominant mechanism for intermediate mode number perturbations (6\textless l\textless 40) and can be described as an effective 1D implosion. However, for low mode number perturbations (l$\le $6), heat conduction loss does not fully ``dry out'' the bubbles and an additional mechanism- residual kinetic energy (RKE) [Kirtcher PoP 2014; Gu et al., PoP 2014] does reduce the hydrodynamic coupling efficiency from the imploding cold shell to the hot spot. These two effects do not have an effective 1D analogue and therefore needs a more complicated model. A consistent extension of the ignition metrics for l$\le $6, accounting for both energy loss mechanisms, will be presented and compared with previous models and results.