Electron-positron pair production in external electric fields varying both in space and time

Abstract

The Schwinger mechanism of electron-positron pair production in the presence of strong external electric fields is analyzed numerically for the case of one-and two-dimensional field configurations where the external field depends both on time and one spatial coordinate. In order to provide this analysis, a new efficient numerical approach is developed. The number of particles created is obtained numerically and also compared with the analytical results for several exactly solvable one-dimensional backgrounds. For the case of two-dimensional field configurations the effects of the spatial finiteness are examined, which confirms their importance and helps us to attest our approach further. The corresponding calculations are also performed for several more interesting and nontrivial combinations of temporal and spatial inhomogeneities. Finally, we discuss the case of a spatially periodic external field when the approach is particularly productive. The method employed is described in detail.

Dynamically assisted Schwinger effect beyond the spatially-uniform-field approximation

“…Finally, we stress that the spatial dependence of the external background in the context of Schwinger pair production was considered so far in a very few studies [16,17,20,[26][27][28]. We expect that multidimensional inhomogeneities should be significant for a much broader class of possible scenarios.…”

“…This approach was described in detail in Refs. [19,20]. As a result, our computations provide the number density of electrons (positrons) produced per unit volume:…”

Photon emission in strong fields beyond the locally-constant field approximation

“…Taking into account the periodicity of the external field (13), one can represent the in one-particle solutions of the Dirac equation in the following form (see, e.g., Refs. [29][30][31]):…”

Pulse shape optimization for electron-positron production in rotating fields

“…This increases the pair production rate and reduces the ex- * francois.fillion@emt.inrs.ca † hebenstreit@itp.unibe.ch ‡ denis.gagnon@emt.inrs.ca § steve.maclean@emt.inrs.ca ponential suppression owing to the combination of tunnelling and multiphoton effects. Most theoretical calculations that investigate the effect of the laser pulse shape on the pair density have considered homogeneous fields, although some spatial effects have also been studied recently [22][23][24][25][26]. Even for the simpler homogeneous but oscillating electric field with an envelope, it is far from trivial to understand the pair spectrum and to find an optimal configuration due to time-domain quantum interferences.…”