[Paper Review] Electron-positron pair production in inhomogeneous electromagnetic fields

Christian Kohlfürst|arXiv (Cornell University)|Dec 18, 2015

Atomic and Molecular Physics26 references17 citations

TL;DR

This paper investigates electron-positron pair production in inhomogeneous electromagnetic fields using the Dirac-Heisenberg-Wigner (DHW) formalism in phase space. It identifies effective mass signatures and channel closing in momentum spectra, demonstrates enhanced particle yields in spatially focused fields, and shows that Lorentz invariants govern pair production in combined electric and magnetic fields, with non-monotonic frequency dependence and ponderomotive effects confirmed numerically.

ABSTRACT

The process of electron-positron pair production is investigated within the phase-space Wigner formalism. The similarities between atomic ionization and pair production for homogeneous, but time-dependent linearly polarized electric fields are examined mainly in the regime of multiphoton absorption (field-dependent threshold, above-threshold pair production). Characteristic signatures in the particle spectra are identified (effective mass, channel closing). The non-monotonic dependence of the particle yield on the carrier frequency is discussed as well. The investigations are then extended to spatially inhomogeneous electric fields. New effects arising due to the spatial dependence of the effective mass are discussed in terms of a semi-classical interpretation. An increase in the normalized particle yield is found for various field configurations. Pair production in inhomogeneous electric and magnetic fields is also studied. The influence of a time-dependent spatially inhomogeneous magnetic field on the momentum spectrum and the particle yield is investigated. The Lorentz invariants are identified to be crucial in order to understand pair production by strong electric fields in the presence of strong magnetic fields.

Motivation & Objective

• To extend the understanding of multiphoton pair production beyond homogeneous fields to spatially inhomogeneous configurations.
• To investigate the role of effective mass and ponderomotive forces in inhomogeneous electric fields using semi-classical and quantum kinetic methods.
• To analyze the influence of time-dependent, spatially inhomogeneous magnetic fields on pair production spectra and yields.
• To identify Lorentz invariants as key determinants of pair production in strong-field QED with combined E and B fields.
• To bridge theoretical models with experimental feasibility by adapting field configurations to realistic laser parameters.

Proposed method

• Employing the Dirac-Heisenberg-Wigner (DHW) formalism to describe pair production in phase space, enabling treatment of non-uniform and time-dependent fields.
• Using pseudo-spectral and pseudo-differential operator methods to solve the transport equations numerically with high accuracy.
• Applying an effective mass model to interpret momentum spectra and identify signatures such as channel closing.
• Implementing spatially localized electric fields to simulate laser focusing and study ponderomotive effects in 3+1 dimensions.
• Extending the analysis to time-dependent, spatially inhomogeneous magnetic fields and comparing results with homogeneous limits.
• Verifying consistency with Maxwell’s equations and Lorentz invariance in all configurations.

Experimental results

Research questions

• RQ1 How does spatial inhomogeneity of the electric field affect the effective mass and particle yield in electron-positron pair production?
• RQ2 What observable signatures, such as channel closing, can be identified in the momentum spectrum under inhomogeneous fields?
• RQ3 How do ponderomotive forces influence the particle momentum distribution in spatially focused fields?
• RQ4 What role do Lorentz invariants play in determining the pair production rate when strong electric and magnetic fields coexist?
• RQ5 How does the particle yield depend non-monotonically on the carrier frequency in inhomogeneous configurations?

Key findings

• The effective mass model successfully explains the oscillatory structure of the particle yield and peak positions in momentum space, confirming its relevance in inhomogeneous fields.
• A non-monotonic dependence of the normalized particle yield on the carrier frequency was observed, indicating complex interplay between field frequency and spatial focusing.
• Spatial focusing of the electric field leads to a measurable increase in the normalized particle yield, with signatures of relativistic ponderomotive forces appearing in the momentum spectrum.
• The concept of an effective field amplitude was validated, showing agreement between numerical DHW results and theoretical predictions in the multiphoton regime.
• In the presence of time-dependent, spatially inhomogeneous magnetic fields, the particle yield depends critically on the effective field strength, with results aligning with extrapolated homogeneous-field models for weak fields.
• Lorentz invariants were identified as the fundamental quantities governing pair production in combined E and B fields, with consistent results across different field configurations.