Electromagnetic field solver for QED polarization in super-strong magnetic fields of magnetars and laser plasmas

Superstrongly magnetized plasmas play a crucial role in extreme environments of magnetars and laboratory laser experiments, demanding a comprehensive understanding of how quantum electrodynamic (QED) effects influence plasma behavior. Earlier analytical and semi-analytical calculations have shown that QED effects can significantly modify the plasma polarization mode behavior around magnetars. In this work, we present the first electromagnetic field solver that is valid in the range from B→0 to beyond the Schwinger limit. QED vacuum polarization in superstrong magnetic fields is modeled with nonlinear Maxwell equations. We show that electromagnetic waves in simulations follow the analytical solutions well and reproduce the birefringence effects of electromagnetic wave modes between the O and X polarizations of perpendicular electromagnetic waves and those between L and R polarizations of parallel waves. This new framework can be applied to kinetic as well as other types of computer simulations. The solver's key advantage lies in its versatility, allowing it to be used in gyro-motion, gyro-center, and gyro-kinetic simulations, which do not resolve the cyclotron motion, or in plasma studies with ground-level Landau quantization.