The PSI Positron Production experiment, known as P\textsuperscript{3} or \textit{P-cubed}, is a proof-of-principle positron source and capture system that can greatly improve the state-of-the-art positron yield. The P\textsuperscript{3} project is led by the Paul Scherrer Institute in Switzerland, and addresses the long-standing challenge faced by conventional injector facilities to generate, capture, and damp the emittance of high-current positron beam, which is a major limiting factor for the feasibility of future electron-positron colliders. P\textsuperscript{3} follows the same basic principles as its predecessors, utilizing a positron source driven by pair-production and an RF linac with a high-field solenoid focusing system. However, it incorporates pioneering technology, such as high-temperature superconducting solenoids, that can outperform significantly the present positron capture efficiency rates. The P\textsuperscript{3} experiment will be hosted at PSI's SwissFEL, and will serve as the positron source test facility of CERN's FCC-ee. This paper outlines the concept, technology, infrastructure, physics studies and diagnostics of P\textsuperscript{3}.

The Future Circular Collider (FCC-ee) is designed to explore the Z and W± bosons, along with the Higgs boson and top quark, achieving exceptionally high luminosity. In order to minimize the energy lost per turn due to Synchrotron Radiation (SR) we explore the use of Nested Magnets (NMs) into the arcs cell. For this, it is necessary to explore the possible combinations of the different magnet types in the cell, namely: dipoles, quadrupoles and sextupoles. Specifications in terms of strength and alignment tolerances are reviewed in this paper.