On plasma modes in a strong-field plasma in magnetars

Magnetars -- the strongly magnetized neutron stars -- have the surface field stronger than the Schwinger field. In such an environment, Maxwell's equations become nonlinear due to QED effects. Magnetar magnetospheres also contain substantial amounts of plasma. Thus, there is great interest in understanding how plasma modes are modified in a super-strong field. Here we derive the general equations describing QED plasma linear modes. We discuss the properties of the low-frequency modes, for which the transitions between the Landau levels can be safely neglected. The results can be important for understanding of propagation of radio and other low-frequency waves in a magnetar magnetosphere and, perhaps, for unraveling the origin of fast radio bursts.