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Laser-driven free-electron lasers (LDFELs) replace magnetostatic undulators with the electromagnetic fields of a laser pulse. Because the undulator period is half the wavelength of the laser pulse, LDFELs can amplify x rays using lower electron energies and over shorter interaction lengths than a conventional free-electron laser. Here we show that a flying-focus pulse substantially reduces the energy required to reach high gain in an LDFEL by providing a highly uniform, high-intensity field over the entire interaction length. The flying-focus pulse features an intensity peak that travels in the opposite direction of its phase fronts. This enables an LDFEL configuration where an electron beam collides head-on with the phase fronts and experiences a near-constant undulator strength as it co-propagates with the intensity peak. Three-dimensional simulations of this configuration demonstrate the generation of megawatts of coherent x-ray radiation with 20 times less energy than a conventional laser pulse.

"Flying focus" techniques produce laser pulses with dynamic focal points that travels distances much greater than a Rayleigh length. The implementation of these techniques in laser-based applications requires the design of optical configurations that can both extend the focal range and structure the radial group delay. This article describes a method for designing optical configurations that produce ultrashort flying focus pulses with arbitrary-trajectory focal points. The method is illustrated by several examples that employ an axiparabola for extending the focal range and either a reflective echelon or a deformable mirror-spatial light modulator pair for structuring the radial group delay. The latter configuration enables rapid exploration and optimization of flying foci, which could be ideal for experiments.

The intensity peak of a "flying focus" travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an accurate description of the electromagnetic fields. Here we present exact analytical solutions to Maxwell's equations for the electromagnetic fields of a constant-velocity flying focus, generalized for arbitrary polarization and orbital angular momentum. The approach combines the complex source-point method, which transforms multipole solutions into beam-like solutions, with the Lorentz invariance of Maxwell's equations. Propagating the fields backward in space reveals the space-time profile that an optical assembly must produce to realize these fields in the laboratory. Comparisons with simpler paraxial solutions provide conditions for their reliable use when modeling a flying focus.

In nonlinear Thomson scattering, a relativistic electron reflects and re-radiates the photons of a laser pulse, converting optical light to x rays or beyond. While this extreme frequency conversion offers a promising source for probing high-energy-density materials and driving uncharted regimes of nonlinear quantum electrodynamics, conventional nonlinear Thomson scattering has inherent tradeoffs in its scaling with laser intensity. Here we discover that the ponderomotive control afforded by spatiotemporal pulse shaping enables novel regimes of nonlinear Thomson scattering that substantially enhance the scaling of the radiated power, emission angle, and frequency with laser intensity. By appropriately setting the velocity of the intensity peak, a spatiotemporally shaped pulse can increase the power radiated by orders of magnitude. The enhanced scaling with laser intensity allows for operation at significantly lower electron energies and can eliminate the need for a high-energy electron accelerator., Comment: 23 pages, 4 figures

Laser wakefield accelerators rely on the extremely high electric fields of nonlinear plasma waves to trap and accelerate electrons to relativistic energies over short distances. When driven strongly enough, plasma waves break, trapping a large population of the background electrons that support their motion. This limits the maximum electric field. Here we introduce a novel regime of plasma wave excitation and wakefield acceleration that removes this limit, allowing for arbitrarily high electric fields. The regime, enabled by spatiotemporal shaping of laser pulses, exploits the property that nonlinear plasma waves with superluminal phase velocities cannot trap charged particles and are therefore immune to wave breaking. A laser wakefield accelerator operating in this regime provides energy tunability independent of the plasma density and can accommodate the large laser amplitudes delivered by modern and planned high-power, short pulse laser systems.