On the effect of time-dependent inhomogeneous magnetic fields on the particle momentum spectrum in electron-positron pair production

TL;DR

This paper investigates how time-dependent inhomogeneous magnetic fields influence the particle momentum spectrum in electron-positron pair production, using the Dirac-Heisenberg-Wigner formalism and numerical methods.

Contribution

It introduces a detailed analysis of magnetic field effects on pair production spectra within the quantum kinetic framework and discusses numerical solution techniques for the Wigner functions.

Findings

Magnetic fields significantly alter the particle momentum distribution.

Signature patterns of Schwinger and multiphoton pair production are identified.

Numerical methods effectively solve the integro-differential equations for Wigner functions.

Abstract

Electron-positron pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied within the Dirac-Heisenberg-Wigner formalism (quantum kinetic theory) through computing the corresponding Wigner functions. The focus is on discussing the particle momentum spectrum regarding signatures of Schwinger and multiphoton pair production. Special emphasis is put on studying the impact of a strong dynamical magnetic field on the particle distribution functions. As the equal-time Wigner approach is formulated in terms of partial integro-differential equations an entire section of the manuscript is dedicated to present numerical solution techniques applicable to Wigner function approaches in general.