  Higher-order tree-level processes in strong laser fields, i.e. cascades, are
in general extremely difficult to calculate, but in some regimes the dominant
contribution comes from a sequence of first-order processes, i.e. nonlinear
Compton scattering and nonlinear Breit-Wheeler pair production. At high
intensity the field can be treated as locally constant, which is the basis for
standard particle-in-cell codes. However, the locally-constant-field (LCF)
approximation and these particle-in-cell codes cannot be used when the
intensity is only moderately high, which is a regime that is experimentally
relevant. We have shown that one can still use a sequence of first-order
processes to estimate higher orders at moderate intensities provided the field
is sufficiently long. An important aspect of our new "gluing" approach is the
role of the spin/polarization of intermediate particles, which is more
nontrivial compared to the LCF regime.
