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It is known that strong electric fields produce electron and positron pairsfrom the vacuum, and due to the back-reaction these pairs oscillate back andforth coherently with the alternating electric fields in time. We study thisphenomenon in spatially inhomogeneous and bound electric fields by integratingthe equations of energymomentum and particle-number conservations and Maxwellequations. The space and time evolutions of the pair-induced electric field,electric charge- and currentdensities are calculated. The results show thatnon-vanishing electric charge-density and the propagation of pair-inducedelectric fields, differently from the case of homogeneous and unbound electricfields. The space and time variations of pair-induced electric charges andcurrents emit an electromagnetic radiation. We obtain the narrow spectrum andintensity of this radiation, whose peak {\omega}peak locates in the regionaround 4 KeV for electric field strength \sim Ec. We discuss their relevancesto both the laboratory experiments for electron and positron pair-productionsand the astrophysical observations of compact stars with an electromagneticstructure.

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