Breit-Wheeler process in very short electromagnetic pulses

The generalized Breit-Wheeler process, i.e., the emission of $e^{+}{e}^{-}$ pairs off a probe photon propagating through a polarized short-pulsed electromagnetic (e.g., laser) wave field, is analyzed. We show that the production probability is determined by the interplay of two dynamical effects. The first one is related to the shape and duration of the pulse and the second one is the nonlinear dynamics of the interaction of $e^{\pm }$ with the strong electromagnetic field. The first effect manifests itself most clearly in the weak-field regime, where the small field intensity is compensated by the rapid variation of the electromagnetic field in a limited space-time region, which intensifies the few-photon events and can enhance the production probability by orders of magnitude compared to an infinitely long pulse. Therefore, short pulses may be considered as a powerful amplifier. The nonlinear dynamics in the multiphoton Breit-Wheeler regime plays a decisive role at large field intensities, where effects of the pulse shape and duration are less important. In the transition regime, both effects must be taken into account simultaneously. We provide suitable expressions for the $e^{+}{e}^{-}$ production probability for kinematic regions which can be used in transport codes.

Figure 1

Pulse envelope $f\left(\varphi \right)$ (top panels) and the product $f\left(\varphi \right)\cos \varphi$ (middle and bottom panels) as a function of the invariant phase $\varphi$. The left and right panels correspond to the one- and two-parameter envelope functions, respectively. The top and the middle panels exhibit an ultrashort pulse with the number of oscillations less than one, $N=0.5$, while the bottom panels are for a short pulse with $N=5$.

Figure 2

Square of the Fourier transforms of envelope functions for a subcycle pulse with $N=0.5$. (Left) The solid and dashed curves depict the hyperbolic secant and Gaussian shapes, respectively. (Right) The solid, dot-dashed, and dashed curves show the symmetrized Fermi shape for $b/\Delta =0.1$, 0.3, and 0.5, respectively.

Figure 3

The probability $W$ of $e^{+}{e}^{-}$ production as a function of the subthreshold parameter $\zeta$ for one-parameter envelope functions for an ultrashort pulse with $N=0.5$. The solid and dashed curves correspond to numerical calculations with the hyperbolic secant and Gaussian shapes, respectively. The symbols “star” and “plus” are for the approximation (19). The thin solid curves marked by dots correspond to IPA. The left and right panels are for ${\xi }^2={10}^{-2}$ and ${10}^{-4}$, respectively.

Figure 4

The same as in Fig. 3 but for symmetrized Fermi shape envelope. The solid, dot-dashed, and dashed lines are for $b/\Delta =0.1$, 0.3 and 0.5, respectively. The corresponding approximate solutions are shown by symbols “+”, “$\times$”, and “$*$”, respectively.

Figure 5

(Left) The differential production probability as a function of the azimuthal angle ${\varphi }_e$ of the electron emission. (Right) The anisotropy (26) for the hyperbolic secant (solid curves) and Gaussian (dashed curves) shapes. For ${\xi }^2=0.1$ and $\zeta =4$.

Figure 6

The partial probability $w\left(l\right)$ defined in (13) at ${\varphi }_0=0$ and $\pi$ shown by solid and dashed curves, respectively, for the symmetrized Fermi envelope shape. The left panel corresponds to small values of $b/\Delta =$0.01 and 0.1, while the right panel is for $b/\Delta =0.5$. For ${\xi }^2=0.1$ and $\zeta =4$.

Figure 7

The same as in Fig. 5 but for the symmetrized Fermi shape. The solid, dot-dashed, and dashed curves are for $b/\Delta =0.1$, 0.3, and 0.5, respectively. For ${\xi }^2=0.1$ and $\zeta =4$.

Figure 8

The function ${\mathcal{P}}_0\left(\varphi \right)$ defined in (29) with (solid curves) and without (dashed curves) the term (30) for $\Delta =\pi N$ with $N=2$ and 5, shown in the left and right panels, respectively. The term (30) is shown separately by dot-dashed curves.

Figure 9

The partial probability $w\left(l\right)$ defined in (33) as a function of $l$ at $u=1$. The solid and dashed curves correspond to the beam size $\Delta =\pi N$, with $N=2$ and 10, respectively. The left and right panels exhibit results for the envelopes with hyperbolic secant and symmetrized Fermi shapes, respectively. For $\xi ={10}^{-4}$ and $\zeta =0.5$

Figure 10

The same as in Fig. 9 but for the subthreshold region at $\zeta =1.25$.

Figure 11

The total probability $W$ of the $e^{+}{e}^{-}$ pair production as a function of $\zeta$ for short pulses with $\Delta =\pi N$ for $N=2$, 5, and 10, as indicated in the legend. The thin solid curves marked by dots depict the IPA result. The left and right panels correspond to the hyperbolic secant and symmetrized Fermi envelope shapes, respectively.

Figure 12

The total probability $W$ of the $e^{+}{e}^{-}$ pair production as a function of $\zeta$ for one- and two-parameter envelope shapes (dashed and solid curves are for hyperbolic secant and symmetrized Fermi shapes, respectively). The thin solid curves marked by dots depict the IPA result. The left and right panels correspond to the number of oscillation in a pulse $N=2$ and 10, respectively.

Figure 13

The total probability of $e^{+}{e}^{-}$-pair production for two envelope shapes (dashed and solid curves are for hyperbolic secant and symmetrized Fermi shapes, respectively). The thin solid curves marked by dots are the result of IPA. (Left) The total probability as a function of $\zeta$ at ${\xi }^2=1$. (Right) The total probability as a function of ${\xi }^2$ at $\zeta =4$.

Figure 14

The differential probability of $e^{+}{e}^{-}$-pair production as a function of ${\varphi }_e={\varphi }_0$ at $\zeta =4$ and $N=2$.

Figure 15

The total probability $W$ of the $e^{+}{e}^{-}$ pair production as a function of ${\xi }^2$ for various values of $\zeta$. (Left) Results of FPA for not-too-large values of ${\xi }^2$ (curves marked by “stars” in “FPA” sections) and the asymptotic probability (45) for large values of ${\xi }^2$ (sections labeled by “asymptotic”) at $\zeta =2$, 4, and 6. (Right) The asymptotic probability (45) for various values of $\zeta$ as indicated in the legend.