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Description
When an electron interacts with an intense laser field, it is driven to relativistic velocities and emits radiation at integer multiples of the laser frequency (harmonics), thereby upconverting optical light into the extreme-ultraviolet or beyond. This process, known as the relativistic nonlinear Thomson scattering, is governed by the combined action of the electric and magnetic components of the laser field, both of which play a crucial role in determining the emitted radiation. Prior investigations of nonlinear Thomson scattering have considered a variety of electromagnetic beam configurations, including linearly, circularly, radially, and azimuthally polarized beams, as well as vortex beams.
Here, we consider relativistic emission driven by a toroidal pulse—an exact solution of Maxwell’s equations with unique properties. In contrast to Gaussian pulses, its spatial and temporal structures are intrinsically coupled and cannot be factorized into independent spatial and temporal profiles. The toroidal pulse exhibits a distinct toroidal topology: the magnetic field forms a doughnut-like structure around the propagation axis, while the electric field wraps along its surface, leading to a pronounced longitudinal component aligned with the direction of propagation. Thus, the toroidal pulse is also known as the flying electromagnetic doughnut. At the focal center, the toroidal pulse is characterized by a tightly localized, single-cycle electric field.
Our results suggest that at substantially lower pulse energies than those required for conventional Gaussian drivers, a toroidal pulse with peak field strength $E_0=10^{12}\,\text{V/m}$ ($a_0\approx0.2$) already leads to strongly directional radiation up to 150 eV, which corresponds to 100th harmonics of a $0.8$\textmu m laser. Our research offers new alternatives to UV and X-ray sources, high-harmonic generation, and advanced light–matter interaction studies.
| Keyword-1 | relativistic acceleration |
|---|---|
| Keyword-2 | High Harmonic Generation |