Plasma modes in QED super-strong magnetic fields of magnetars and laser plasmas

Ultra-magnetized plasmas, where the magnetic field strength exceeds the Schwinger field of about B_Q ~ 4 x 10¹³ gauss, become of great scientific interest, thanks to the current advances in laser-plasma experiments and astrophysical observations of magnetar emission. These advances demand better understanding of how quantum electrodynamics (QED) effects influence collective plasma phenomena. In particular, Maxwell's equations become nonlinear in the strong-QED regime. Here we present the 'QED plasma framework' which will allow one to systematically explore collective phenomena in a QED-plasma with arbitrarily strong magnetic field. Further, we illustrate the framework by exploring low-frequency modes in the ultra-magnetized, cold, electron-positron plasmas. These results should be important for understanding of a magnetospheric pair plasma of a magnetar and for laboratory laser-plasma experiments in the QED regime.