Vacuum Channeling Radiation by Relativistic Electrons in a Transverse Field of a Laser-Based Bessel Beam

Relativistic electrons counterpropagating through the center of a radially polarized $J_1$ optical Bessel beam in vacuum will emit radiation in a manner analogous to the channeling radiation that occurs when charged particles traverse through a crystal lattice. However, since this interaction occurs in vacuum, problems with scattering of the electrons by the lattice atoms are eliminated. Contrary to inverse Compton scattering, the emitted frequency is also determined by the amplitude of the laser field, rather than only by its frequency. Adjusting the value of the laser field permits the tuning of the emitted frequency over orders of magnitude, from terahertz to soft X rays. High flux intensities are predicted ($\sim 100\mathrm{MW}/{\mathrm{cm}}^2$). Extended interaction lengths are feasible due to the diffraction-free properties of the Bessel beam and its radial field, which confines the electron trajectory within the center of the Bessel beam.

Figure 1

A radially polarized $J_1(x)$ Bessel optical beam, the intensity cross section of which is illustrated in the main frame, counterpropagates against a narrow beam of electrons. For stable transverse motion, the diameter of the electron beam is smaller than the distance between the first lobes of the $J_1(x)$ Bessel beam; see vertical dashed (green) lines, $|x|<1.841$. In this range, the transverse motion of the electrons is determined by the initial conditions and the effective potential, illustrated in the inset at right. As the electrons oscillate transversely back and forth, they generate “channeling” radiation.

Figure 2

Predicted emission characteristics in the forward direction for channeling radiation in vacuum as a function of the Bessel beam field (see text for values of other parameters). (a) Emission wavelength. (b) Emitted flux.