Production and magnetic self-confinement of $e^-e^+$ plasma by an extremely intense laser pulse incident on a structured solid target

We propose an all-optical, single-laser-pulse scheme for generating dense, relativistic, strongly-magnetized electron-positron pair plasma. The scheme involves the interaction of an extremely intense ($I \gtrsim \SI{e24}{\watt/\cm^2}$) circularly polarized laser pulse with a solid-density target containing a conical cavity. Through full-scale three-dimensional particle-in-cell (PIC) simulations that account for quantum electrodynamical effects, it is shown that this interaction results in two significant outcomes: first, the generation of quasi-static axial magnetic fields reaching tens of gigagauss due to the inverse Faraday effect; and second, the production of large quantities of electron-positron pairs (up to $\num{e13}$) via the Breit-Wheeler process. The $e^-e^+$ plasma becomes trapped in the magnetic field and remains confined for hundreds of femtoseconds, far exceeding the laser timescale. The dependency of pair plasma parameters, as well as the efficiency of plasma production and confinement, is discussed in relation to the properties of the laser pulse and the target. Realizing this scheme experimentally would enable the investigation of physical processes relevant to extreme astrophysical environments.