Growth Rate of Self-Sustained QED Cascades Induced by Intense Lasers

It was suggested [] that an avalanche of electron-positron pairs can be triggered in the laboratory by a standing wave generated by intense laser fields. Here, we present a general solution to the long-standing problem of the avalanche growth rate calculation. We provide a simple formula that accounts for the damping of the growth rate due to pair and photon migration from the region of prolific generation. We apply our model to a variety of 3D field configurations including focused laser beams and show that (i) the particle yield for the full range of intensity able to generate an avalanche can be predicted, (ii) a critical intensity threshold due to migration is identified, and (iii) the effect of migration is negligible at a higher intensity and the local growth rate dominates. Excellent agreement with Monte Carlo and self-consistent particle-in-cell simulations is shown. The growth rate calculation allows us to predict when abundant pair production will induce a backreaction on the generating field due to plasma collective effects and screening. Our model can be applied to study the generation of electron-positron pair avalanches in realistic fields to plan future experiments at ultrahigh-intensity laser facilities.