Eigenmodes in an ultra-relativistic ultra-magnetized pair QED-plasma

Ultra-relativistic quantum-electrodynamic (QED) plasmas, characterized by magnetic field strengths approaching and even exceeding the Schwinger field of approximately $B_{Q} \approx 4 \times 10^{13}$ gauss, hold significant interest for laser-plasma experiments and astrophysical observations of neutron stars and magnetars. In this study, we investigate the joint modification of normal plasma modes in ultra-relativistic electron-positron plasmas, both charge neutral and non-neutral, by the super-strong magnetic field and plasma relativistic temperature. Our analysis shows that the most substantial modification concerns the reduction of the plasma frequency cutoff, resulting in relativistic and field-induced transparency. Additionally, we observe a temperature-independent modification of the index of refraction of electromagnetic waves, which coincides with the behavior observed in a cold QED plasma.