Volkov States and Non-linear Compton Scattering in Short and Intense Laser Pulses

TL;DR

The paper surveys high-intensity QED in short laser pulses, framing the problem with plane-wave backgrounds and defining key parameters $a_0$, $b_0$, $\chi_e$, and the dephasing $a_0^2\Delta\phi$. It develops the Dirac-Furry formalism using Volkov states and the Dirac-Volkov propagator, yielding strong-field Feynman rules for processes like non-linear Compton scattering. A central result is the short-pulse broadening of non-linear Compton spectra due to laser bandwidth and ponderomotive effects, contrasted with the Zel'dovich-level structure in infinite monochromatic waves; the spectrum broadening can be mitigated by chirped pulses, enabling bright, narrowband hard gamma sources. The work connects classical dynamics, exact quantum solutions in a plane-wave background, and practical spectroscopic control, contributing to both fundamental strong-field QED and potential applications in high-energy photon sources.

Abstract

The collision of ultra-relativistic electron beams with intense short laser pulses makes possible to study QED in the high-intensity regime. Present day high-intensity lasers mostly operate with short pulse durations of several tens of femtoseconds, i.e. only a few optical cycles. A profound theoretical understanding of short pulse effects is important not only for studying fundamental aspects of high-intensity laser matter interaction, but also for applications as novel X- and gamma-ray radiation sources. In this article we give a brief overview of the theory of high-intensity QED with focus on effects due to the short pulse duration. The non-linear spectral broadening in non-linear Compton scattering due to the short pulse duration and its compensation is discussed.

Figures (8)

• Figure 1: Contour plot of (the real part of) the scalar and tensor projections of the Ritus matrices $E_p(x)$ in the ($z$-$t$) plane for a circularly polarized laser pulse with $a_0=2$ and pulse duration $\Delta\phi=20$.
• Figure 2: Contour plot of a normalized scalar Volkov wave packet in the ($t$-$z$) plane. For comparison, the classical trajectory is depicted as solid black curve. The laser pulse propagates between the two black dotted lines.
• Figure 3: Spectral components of the Volkov state with a small (large) range of spectral components $\ell$ contributing in the left (right) panels. In the left panel the black vertical lines indicate the positions of the Zel'dovich levels at $\ell = n+\frac{ma_0^2}{8\omega\gamma}$ in the case of an infinite monochromatic plane wave. One can make a clear connection between these Zel'dovich levels and the peaks in the Volkov spectrum for a pulsed field. In the right panel a large number of spectral components contribute the width of each level is larger than their separation which makes a clear identification of individual Zel'dovich levels difficult.
• Figure 4: The light-front momentum component $\pi^-$ along the classical trajectory of an electron in a short laser pulse as a function of the laser phase $\phi = \omega x^+$ (left panel) is compared to the spectral component $\mathrsfs K_+(\ell)$ of the Volkov state in the same pulse (right panel). The electron counterpropagates the laser pulse with initial energy of $1$ GeV at an angle of $\theta = 2/\gamma$. Other parameters are as follows: (a) $a_0 = 1$, $\Delta\phi = 8$, linear polarization; (b) $a_0 = 5$, $\Delta\phi=8$, linear polarization; (c) $a_0=5$, $\Delta\phi = 8$, circular polarization; (d) $a_0=5$, $\Delta\phi = 12$, linear polarization.
• Figure 5: Strong-field Feynman diagrams in the Furry picture for Non-linear Compton scattering (a) and Non-linear Double Compton scattering (b). Double lines represent laser dressed electron wave functions and propagators for external and internal lines, respectively.