Eur. Phys. J. Plus (2025) 140: 771
https://doi.org/10.1140/epjp/s13360-025-06652-y

Regular Article

Pair production in multi-pulse trains electric fields with temporal oscillation

¹ School of Mathematics and Physics, Lanzhou Jiaotong University, 730070, Lanzhou, China
² Key Laboratory of Beam Technology of the Ministry of Education, and School of Physics and Astronomy, Beijing Normal University, 100875, Beijing, China
³ School of Mathematics and Physics, Xinjiang Hetian College, 848000, Hetian, China
⁴ Institute of Radiation Technology, Beijing Academy of Science and Technology, 100875, Beijing, China

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Received: 12 March 2025
Accepted: 12 July 2025
Published online: 17 August 2025

Abstract

Pair production in multi-pulse trains electric fields with temporal oscillation, including strong but slowly varying, weak but rapidly changing, and combined electric fields, is studied in the quantum kinetic framework. We investigate the influences of the pulse number on pair production and the enhancement effect of temporal oscillation on the particle number density. In the full momentum space scenario, the momentum spectra are sensitive to temporal oscillation causing various interference effects for different pulse numbers of the external field. The number density increases by at least one order of magnitude when the pulse number is ten-fold increased. For the longitudinal momentum distribution, it is found that the momentum spectra exhibit a quasi-monoenergetic structure for large pulse numbers. Within our studied pulse number range, the number density is enhanced by nearly one order of magnitude with increasing pulse number. Additionally, an optimal pulse number parameter is determined for the ratio of the number density in the combined electric field. Furthermore, for both longitudinal momentum distribution and full momentum space, the particle number density in both the combined field and the weak but rapidly changing field is increased by more than one order of magnitude compared with the results of electric fields with only envelopes.