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.

💡 Research Summary

This paper presents a comprehensive theoretical study of wave propagation in ultra‑relativistic electron‑positron (pair) plasmas that are immersed in magnetic fields approaching or exceeding the QED critical (Schwinger) field (B_Q\simeq4\times10^{13}) G. The authors extend the “QED‑plasma” formalism introduced in their earlier “Paper I” to the regime where the plasma temperature is far above the electron rest‑mass energy ((\Theta=k_BT/m_ec^2\gg1)), i.e., the ultra‑relativistic limit.

The analysis begins by constructing the linear wave equation that incorporates both the plasma dielectric response and the nonlinear QED vacuum susceptibilities. The vacuum coefficients (C_\delta, C_\epsilon,) and (C_\mu) are functions of the field strength; in the weak‑field limit they scale as ((B/B_Q)^2), while in the strong‑field limit (C_\epsilon\propto B/B_Q), (C_\delta\propto\ln(B/B_Q)), and (C_\mu) saturates to a constant. The plasma susceptibility tensor (\chi^{\rm plasma}_{ij}) contains the usual transverse and longitudinal components, an off‑diagonal term (g) proportional to the charge‑non‑neutrality (\Delta n/n), and a longitudinal function (Q(\omega,k)) that encodes the kinetic (temperature) effects.

A one‑dimensional Maxwell‑Jüttner distribution is assumed for the particle momenta. In the ultra‑relativistic limit the modified Bessel function simplifies, and the kinetic function (Q) can be approximated in two regimes:

• Case I ((|1-\omega^2/k_z^2c^2|\gg\Theta^{-2})): (Q\approx \omega_{p}^{*2}\Theta/