Effect of super-Gaussian pulse shape on pair production in chirped electric field with spatial inhomogeneity

TL;DR

The paper investigates vacuum $e^{+}e^{-}$ pair production in spatially inhomogeneous, chirped electric fields with super-Gaussian pulse shapes using the Dirac-Heisenberg-Wigner formalism. It computes equal-time Wigner functions to obtain reduced momentum spectra and total yields, examining how the envelope exponent $l$ influences these observables in both high- and low-frequency regimes. A semiclassical turning-point analysis clarifies the origin of oscillations and peak structures in the momentum spectra, revealing that larger $l$ generally enhances yields and shapes the spectra, with nuanced dependence on chirp and spatial scale. The findings offer practical guidance for optimizing external-field profiles to maximize vacuum-pair production and inform future experimental designs.

Abstract

Pair production in spatially inhomogeneous chirped electric fields with super-Gaussian pulse shape is investigated using the Dirac-Heisenberg-Wigner formalism, and the effect of super-Gaussian pulse shapes on the reduced momentum spectrum and the reduced total yield of created particles is mainly concerned. It is found that with the variation of the super-Gaussian envelope exponent, the momentum spectrum exhibits the more pronounced oscillations, shifting and broadening. The total yield of created particles increases monotonically with the increase of the super-Gaussian envelope exponent in the high-frequency fields with small chirp and low-frequency fields with any chirp. Meanwhile, the total yield of created particles under the super-Gaussian pulse electric fields is approximately twice that produced with the usual Gaussian pulse envelope. These results can provide theoretical guidance for optimizing the form of external field to enhance the vacuum pair production rate.

Figures (9)

• Figure 1: Reduced momentum spectrum for different super-Gaussian envelope exponents in the high-frequency electric fields with $\lambda= 1000~\mathrm{m}^{-1}$. The other field parameters are $E_{0}=0.5E_\mathrm{cr}$, $\omega=0.7~\mathrm{m}$ and $\tau=45~\mathrm{m}^{-1}$.
• Figure 2: Reduced momentum spectrum for different super-Gaussian envelope exponents in the high-frequency electric fields with $\lambda= 10~ \mathrm{m}^{-1}$. The other field parameters are the same as in Fig. \ref{['fig:1']}.
• Figure 3: Reduced momentum spectrum for different super-Gaussian envelope exponents in the high-frequency electric fields with $\lambda=2.5~ \mathrm{m}^{-1}$. The other field parameters are the same as in Fig. \ref{['fig:1']}.
• Figure 4: Reduced total yield dependence on spatial scales for different super-Gaussian envelope exponents in the high-frequency electric fields. The chirp values are $b=0.1\omega/\tau$ for (a) and $b=0.5\omega/\tau$ for (b), respectively.
• Figure 5: Reduced momentum spectrum for different super-Gaussian envelope exponents in the low-frequency electric fields with $\lambda=500~\mathrm{m}^{-1}$. The other field parameters are $E_{0}=0.5E_\mathrm{cr}$, $\omega=0.1~\mathrm{m}$ and $\tau=25~\mathrm{m}^{-1}$.