Electron-positron pair production in external electric fields varying both in space and time

TL;DR

This paper develops a new numerical method to analyze electron-positron pair production in complex, space- and time-dependent electric fields, validating it against known solutions and exploring effects of spatial finiteness and periodicity.

Contribution

A novel efficient numerical approach for studying pair production in multidimensional, inhomogeneous electric fields is introduced and validated against analytical solutions.

Findings

Numerical results agree with analytical solutions for 1D backgrounds.

Spatial finiteness significantly affects pair production.

The method is effective for complex, nontrivial field configurations.

Abstract

The Schwinger mechanism of electron-positron pair production in the presence of strong external electric fields is analyzed numerically for the case of one- and two-dimensional field configurations where the external field depends both on time and one spatial coordinate. In order to provide this analysis, a new efficient numerical approach is developed. The number of particles created is obtained numerically and also compared with the analytical results for several exactly solvable one-dimensional backgrounds. For the case of two-dimensional field configurations the effects of the spatial finiteness are examined, which confirms their importance and helps us to attest our approach further. The corresponding calculations are also performed for several more interesting and nontrivial combinations of temporal and spatial inhomogeneities. Finally, we discuss the case of a spatially periodic external field when the approach is particularly productive. The method employed is described in detail.