  QED cascades in a strong electromagnetic field of optical range and arbitrary
configuration are considered. A general expression for short-time dependence of
the key electron quantum dynamical parameter is derived, allowing to generalize
the effective threshold condition of QED cascade onset. The generalized theory
is applied to selfsustained cascades in a single focused laser pulse. According
to numerical simulations, if a GeV electron bunch is used as a seed, an
ordinary cascade can be converted into the selfsustained one. As an
application, it would be also possible to produce this way bright collimated
photon beams with up to GeV photon energies.
