Relativistic Spherical Wake Wave in Plasma. Relativistic focusing spherical mirror and Schwinger pair production

We report on the analytic and computer simulation study of a relativistic spherical wake wave. Such a wave in the breaking regime, traveling towards the center is able to reflect and focus the incoming radiation and up-shifting its frequency. The reflected and focused electromagnetic pulse can have such high intensity, that it is able to create $e^+e^-$ pairs via Schwinger process.