Advancing plasma accelerator science: Insights from the EuPRAXIA Doctoral Network

The EuPRAXIA Doctoral Network (EuPRAXIA-DN) trains the next generation of scientists in plasma-based accelerator technologies, addressing challenges in laser-plasma interactions, advanced beam diagnostics, and novel applications. This contribution highlights progress made in three critical areas: ) real‑time characterization of capillary discharge plasmas to stabilize laser‑wakefield accelera-tion, (ii) femtosecond‑precision X‑band low‑level RF (LLRF) control for the compact EuPRAX-IA@SPARC_LAB injector, and (iii) active‑plasma‑lens (APL)–based beam transport enabling extreme‑ultraviolet free‑electron‑laser (EUV‑FEL) operation within four me-ters of undulator. The innovative training elements with-in the network, such as the EuPRAXIA School on Plasma Accelerators held in Rome in April 2024 and upcoming EuPRAXIA Camps, are also discussed. It is shown how these foster knowledge exchange and skill development for the network's Fellows and the wider plasma accelera-tor community.