On QED plasma framework*

Ultra-magnetized plasmas where the magnetic field strength exceeds the Schwinger (critical) field become of great scientific interest, thank 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 that are present in ultra-strong-field environments affect plasma dynamics. Interestingly, magnetars -- neutron stars with magnetic fields of ~1e15 Gauss or greater -- do exist and QED effects on their magnetospheric plasma cannot be ignored. In particular, Maxwell's equations become nonlinear in the strong-QED regime. This effect has neither been incorporated in plasma codes, nor systematically considered in theoretical studies. Here we present the `QED plasma framework' which will allow for such studies. We present the derivation of the general equation of linear plasma modes in QED-plasma with arbitrarily strong magnetic field. We also precent an illustrative example of low-frequency modes in the ultra-magnetized cold plasma. These results can be important for understanding of a magnetospheric pair plasma of a magnetar and for future laser-plasma experiments.