Impossibility of the strong magnetic fields generation in an electron-positron plasma

TL;DR

This paper demonstrates that in an electron-positron plasma, including conditions like those in magnetars, magnetic field amplification via the studied mechanism is impossible, contradicting recent claims of such instability.

Contribution

The study provides a detailed calculation showing the antisymmetric photon polarization contribution vanishes, disproving the proposed magnetic field amplification mechanism in electron-positron plasmas.

Findings

No magnetic field instability in electron-positron plasma.

Seed magnetic fields are attenuated in a degenerate relativistic electron gas.

The proposed mechanism cannot explain strong magnetic fields in magnetars.

Abstract

We examine the issue whether a magnetic field can be amplified in a background matter consisting of electrons and positrons self-interacting within the Fermi model. For this purpose we compute the antisymmetric contribution to the photon polarization tensor in this matter having nonzero temperature and chemical potential. It is shown that this contribution is vanishing in the static limit. Then we study a particular case of a degenerate relativistic electron gas present in a magnetar. We demonstrate that a seed magnetic field is attenuated in this case. Thus, contrary to the recent claim, we show that there is no magnetic field instability in such a system, which can lead to the magnetic field growth. Therefore recently proposed mechanism cannot be used for the explanation of strong magnetic fields of magnetars.