Onset of electron-seeded cascades in generic electromagnetic fields

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.