  It was suggested [A. R. Bell & J. G. Kirk, PRL 101, 200403 (2008)] 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 we apply to the case of the standing wave
created by two circularly polarized lasers and demonstrate that it allows to
predict the particle yield for the full range of intensity able to generate an
avalanche. We account for the damping of the growth rate due to pair migration
from the region of prolific generation and show that above a threshold in
intensity, this effect is negligible. The growth rate calculation allows us to
predict when abundant pair production will induce a back-reaction on the
generating field due to plasma collective effects and screening. Our model
shows excellent agreement with self-consistent PIC simulations and can be
applied to study the generation of electron-positron pair avalanches in
realistic field configurations to plan future experiments at
ultra-high-intensity laser facilities.
