Does pair cascade absorption cap the attainable laser intensity
In plain words
If a few seed electrons start an avalanche, the resulting pair plasma could absorb the laser before it reaches full focus. The question is whether this sets a hard ceiling on how intense a focused laser can get.
Precise statement
Fedotov, Narozhny, Mourou and Korn (2010) argued that cascades seeded by a single pair deplete the laser field and limit the attainable focused field to far below $E_{S} \sim 4.4e13\ \mathrm{statvolt/cm}$. Determine the maximal attainable peak field in a vacuum focus as a function of input power ($10\text{-}100\ \mathrm{PW}$, multi-beam dipole focusing), including seeding by residual gas, by target debris and by pairs created from vacuum, and decide whether ultrahigh vacuum, pulse shaping or tight focusing lifts the limit.
What would settle it
3D QED particle-in-cell simulations with realistic seeding and pulse shapes giving the saturated peak field, tested by measuring focal intensity or gamma-ray yield at increasing power.