# Effects of finite spatial extent on Schwinger pair production

## TL;DR

This paper investigates how the finite spatial size of electric fields influences electron-positron pair production, revealing that smaller spatial extents weaken temporal signatures and introduce new features, affecting overall yields and assistance mechanisms.

## Contribution

It provides a numerical analysis of spatial inhomogeneity effects on pair production using the Dirac-Heisenberg-Wigner formalism, highlighting novel behaviors in small spatial regimes.

## Key findings

- Signatures of temporal fields weaken with decreasing spatial extent.
- Novel features emerge in pair production at extremely small spatial scales.
- Assistance in particle production increases in highly inhomogeneous regimes.

## Abstract

Electron-positron pair production from vacuum in external electric fields with space and time dependencies is studied numerically using real time Dirac-Heisenberg-Wigner formalism. The influence of spatial focusing scale of the electric field on momentum distribution and the total yield of the particles is examined by considering standing wave mode of the electric field with different temporal configurations. With the decrease of spatial extent of the external field, signatures of the temporal field are weaken in the momentum spectrum. Moreover, in the extremely small spatial extent, novel features emerge due to the combined effects of both temporal and spatial variations. We also find that for dynamically assisted particle production, while the total particle yield drops significantly in small spatial extents, the assistance mechanism tends to increase in these highly inhomogeneous regimes, where the slow and fast pulses are affected differently by the overall spatial inhomogeneity.