Radiation by a laser-driven flying-focus electron wave packet

TL;DR

This paper derives an exact solution for a focused electron wave packet in an electromagnetic plane wave, analyzing its radiation emission and potential experimental signatures of a laser-driven flying-focus electron wave packet.

Contribution

It provides the first exact solution for a focused electron wave packet with a moving focus in an electromagnetic plane wave, and analyzes its radiation spectrum both analytically and numerically.

Findings

Broader angular distribution of emitted radiation when focused beyond a Compton wavelength.

Reduced photon yield in the transverse plane for flying-focus wave packets.

Potential experimental signature of laser-driven flying-focus electron wave packets.

Abstract

An exact solution of the Dirac equation in the presence of an arbitrary electromagnetic plane wave is found, which corresponds to a focused electron wave packet, with the focus of the wave packet moving at the speed of light in the opposite direction of the average momentum of the electron wave packet (unless the plane wave is so intense to reflect the electron). The photon spectrum emitted by such an electron wave packet in the presence of a linearly-polarized plane wave is studied both analytically and numerically. The spectrum is also compared with the one emitted by a single-momentum, plane-wave electron in the case of the electron being initially counter-propagating (on average for the flying-focus case) with the plane wave and within the locally-constant field approximation. It is found that if the electron flying-focus wave packet is focused beyond a Compton wavelength, the angular distribution of the emitted radiation along the magnetic field of the electromagnetic plane wave is broader than for an electron with definite momentum. Corresponding the maximum value of the photon yield on the transverse plane is smaller in the flying-focus electron case. This could represent an experimental signature of a laser-driven flying-focus electron wave packet.