The dynamics of charged particles in electromagnetic fields is an essential component of understanding the most extreme environments in our Universe. In electromagnetic fields of sufficient magnitude, radiation emission dominates the particle motion and effects of nonlinear quantum electrodynamics (QED) are crucial, which triggers electron-positron pair cascades and counterintuitive particle-trapping phenomena. As a result of recent progress in laser technology, high-power lasers provide a platform to create and probe such fields in the laboratory. With new large-scale laser facilities on the horizon and the prospect of investigating these hitherto unexplored regimes, we review the basic physical processes of radiation reaction and QED in strong fields, how they are treated theoretically and in simulation, the new collective dynamics they unlock, recent experimental progress and plans, as well as possible applications for high-flux particle and radiation sources. CONTENTS42 VI. Applications 43 A. Radiation generation 43 1. Electron-beam driven radiation sources 43 2. Laser-driven radiation sources 44 B. Positron sources 46 C. Polarized particle beams 46 D. Ion acceleration 47 VII. Outlook 48 A. Open questions 48 1. Theoretical questions 48 2. Simulation developments 49 B. Experimental programs 50 VIII. Conclusions 50 Acknowledgments 51 List of commonly used symbols 51 References 52

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Fermat’s principle is used to analyze the trajectories of light propagating in a radially inhomogeneous medium with a singularity in the center. It is found that the light trajectories are similar to those around a black hole, in the sense that there exists a critical radius within which the light cannot escape, but spirals into the singularity.

By using the quantum hydrodynamic and Maxwell equations, we derive nonlinear electronmagnetohydrodynamic (MHD), Hall-MHD, and dust Hall-MHD equations for dense quantum magnetoplasmas. The nonlinear equations include the electromagnetic, the electron pressure gradient, as well as the quantum electron tunneling and electron spin forces. They are useful for investigating a number of wave phenomena including linear and nonlinear electromagnetic waves, as well as threedimensional electromagnetic wave turbulence spectra arising from the mode coupling processes in dense magnetoplasmas.

Absorption covers the physical processes which convert intense photon flux into energetic particles when a high-power laser illuminates optically-thick matter. It underpins important petawatt-scale applications today, e.g., medical-quality proton beam production. However, development of ultrahigh-field applications has been hindered since no study so far has described absorption throughout the entire transition from the classical to the quantum electrodynamical (QED) regime of plasma physics. Here we present a model of absorption that holds over an unprecedented six orders-ofmagnitude in optical intensity and lays the groundwork for QED applications of laser-driven particle beams. We demonstrate 58% efficient γ-ray production at 1.8 × 10 25 W cm −2 and the creation of an anti-matter source achieving 4 × 10 24 positrons cm −3 , 10 6 × denser than of any known photonic scheme. These results will find applications in scaled laboratory probes of black hole and pulsar winds,γ-ray radiography for materials science and homeland security, and fundamental nuclear physics.