Total yield of electron-positron pairs produced from vacuum in strong electromagnetic fields: validity of the locally constant field approximation

TL;DR

This paper critically assesses the validity of the locally constant field approximation (LCFA) for predicting electron-positron pair production in strong electromagnetic fields by comparing it with exact numerical methods across various field configurations.

Contribution

It provides a comprehensive numerical analysis to determine the parameter regimes where the LCFA is valid, challenging the conventional reliance on the Keldysh parameter.

Findings

LCFA's validity depends on specific field parameters.

The Keldysh parameter is not a reliable indicator of LCFA accuracy.

Numerical benchmarks identify regimes where LCFA can be confidently applied.

Abstract

The widely-used locally constant field approximation (LCFA) can be utilized in order to derive a simple closed-form expression for the total number of particles produced in the presence of a strong electromagnetic field of a general spatio-temporal configuration. A usual justification for this approximate approach is the requirement that the external field vary slowly in space and time. In this investigation, we examine the validity of the LCFA by comparing its predictions to the results obtained by means of exact nonperturbative numerical techniques. To benchmark the LCFA in the regime of small field amplitudes and low frequencies, we employ a semiclassical approach. As a reference, we consider a standing electromagnetic wave oscillating both in time and space as well as two spatially uniform field configurations: Sauter pulse and oscillating electric field. Performing a thorough numerical analysis, we identify the domain of the field parameters where the approximation is well justified. In particular, it is demonstrated that the Keldysh parameter is not a relevant quantity governing the accuracy of the LCFA.