Developing the QED plasma framework for magnetar magnetospheres

Magnetars -- neutron stars with magnetic fields of ~1e15 Gauss or greater -- do exist in the universe. These fields exceed the Schwinger (critical) field, hence quantum electrodynamics (QED) effects on magnetospheric plasmas cannot be ignored. Furthermore, advances in laser-plasma experiments bring would soon allow us to experimentally study ultra-magnetized plasmas too. Therefore, there is a great demand in systematic studies of the interplay of QED and plasma physics effects in ultra-strong-field environments. 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.