Quantum-electrodynamical birefringence vanishing in a thermal relativistic pair plasma

Quantum electrodynamical (QED) birefringence in a thermal relativistic pair plasma with the presence of the strong crossed field: E0 ⊥ B0, is proposed and investigated. We clarify the coupling relationship and competition between the QED effect and the plasma collective effect and find the critical condition that makes the birefringence vanish. In a relative weak electromagnetic field, the birefringence is dominated by the coupling of the QED-effect, the collective effect and the E0 × B0 drift effect. In a relative strong electromagnetic field, we obtain the formulations stating the competition between the QED effect and the collective effect and then the critical conditions so that they are canceled with each other and the birefringence vanishes. With our results, a new possible scheme is proposed to estimate the thickness of the magnetosphere in a millisecond pulsar and the plasma density of a pulsar, if the magnetic field is known beforehand.