Electron-positron pair oscillation in spatially inhomogeneous electric fields and radiation

TL;DR

This paper investigates electron-positron pair oscillations in spatially inhomogeneous electric fields, revealing unique charge distributions and radiation emissions, with implications for laboratory and astrophysical phenomena.

Contribution

It extends the understanding of pair oscillations to inhomogeneous fields by analyzing their space-time evolution and resulting electromagnetic radiation.

Findings

Non-zero charge densities and propagating electric fields observed.

Electromagnetic radiation emitted with a narrow spectrum around 4 keV.

Results relevant for laboratory pair production and astrophysical observations.

Abstract

It is known that strong electric fields produce electron and positron pairs from the vacuum, and due to the back-reaction these pairs oscillate back and forth coherently with the alternating electric fields in time. We study this phenomenon in spatially inhomogeneous and bound electric fields by integrating the equations of energymomentum and particle-number conservations and Maxwell equations. The space and time evolutions of the pair-induced electric field, electric charge- and currentdensities are calculated. The results show that non-vanishing electric charge-density and the propagation of pair-induced electric fields, differently from the case of homogeneous and unbound electric fields. The space and time variations of pair-induced electric charges and currents emit an electromagnetic radiation. We obtain the narrow spectrum and intensity of this radiation, whose peak {\omega}peak locates in the region around 4 KeV for electric field strength \sim Ec. We discuss their relevances to both the laboratory experiments for electron and positron pair-productions and the astrophysical observations of compact stars with an electromagnetic structure.