QED cascades in extreme focusing

We investigate the onset and development of the electron-positron cascade, seeded by tenuous gas electrons, during a collision of two tightly focused laser pulses. The results reveal that the laser pulse polarization plays a critical role in reaching cascade pair production. Contrary to traditionally considered linear or circular polarization, we utilize radially polarized laser beams, which provide a restoring force that acts in the opposite direction to the one in which the seed electrons have been previously ejected. Therefore, this feature guarantees the cascade seeding even if the seed electrons were previously expelled from the center of the focal plane. As a consequence, the laser power required for a cascade development is 100x (80x) lower compared to the case of circular (linear) polarization of tightly focused laser pulses. In other words, the threshold intensity for the onset of the electron-positron cascade is two orders of magnitude lower than that in the case of circular or linear polarization. Moreover we show, that considering 4- or 6-beam collision (total laser energy is fixed), the number of created electron-positron pairs is even higher.