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 one to generalize the effective threshold condition of QED cascade onset. The generalized theory is applied to self-sustained 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 a self-sustained one. As an application, it would be also possible to produce this way bright collimated photon beams with up to GeV photon energies.

中文翻译：

---

通用电磁场中电子种子级联的开始

考虑了光学范围和任意配置的强电磁场中的 QED 级联。推导出关键电子量子动力学参数的短时依赖性的一般表达式，从而可以概括 QED 级联开始的有效阈值条件。广义理论应用于单个聚焦激光脉冲中的自持级联。根据数值模拟，如果使用 GeV 电子束作为种子，可以将普通级联转换为自持级联。作为一种应用，还可以通过这种方式产生具有高达 GeV 光子能量的明亮准直光子束。