Laser wakefield accelerators (LWFAs) produce extremely high gradients enabling compact accelerators and radiation sources, but face design limitations, such as dephasing, occurring when trapped electrons outrun the accelerating phase of the wakefield. Here we combine spherical aberration with a novel cylindrically symmetric echelon optic to spatiotemporally structure an ultra-short, high-intensity laser pulse that can overcome dephasing by propagating at any velocity over any distance. The ponderomotive force of the spatiotemporally shaped pulse can drive a wakefield with a phase velocity equal to the speed of light in vacuum, preventing trapped electrons from outrunning the wake. Simulations in the linear regime and scaling laws in the bubble regime illustrate that this dephasingless LWFA can accelerate electrons to high energies in much shorter distances than a traditional LWFA-a single 4.5 m stage can accelerate electrons to TeV energies without the need for guiding structures. Forty years ago, Tajima and Dawson recognized that the axial electric fields of ponderomotively driven plasma waves far surpass those of conventional radiofrequency accelerators [1], launching the field of 'advanced accelerators'-disruptive concepts that promise smaller-scale, cheaper accelerators for high energy physics experiments and advanced light sources [2,3]. Since their seminal paper, a number of theoretical breakthroughs [4-7] and experimental demonstrations [8-14] of laser wakefield acceleration (LWFA) have made rapid progress toward that goal. Experiments recurrently achieve record-breaking electron energy gains underscored by the recent observation of a 7.8 GeV energy gain in only 20 cm [15]. In spite of this impressive progress, traditional LWFA faces a key design limitation of electrons outrunning the accelerating phase of the wakefield or dephasing.In traditional LWFA, a near-collimated laser pulse, either through channel or selfguiding, produces a ponderomotive force that travels subluminally at the group velocity (

Flying focus is a technique that uses a chirped laser beam focused by a highly chromatic lens to produce an extended focal region within which the peak laser intensity can propagate at any velocity. When that intensity is high enough to ionize a background gas, an ionization wave will track the intensity isosurface corresponding to the ionization threshold. We report on the demonstration of such ionization waves of arbitrary velocity. Subluminal and superluminal ionization fronts were produced that propagated both forward and backward relative to the ionizing laser. All backward and all superluminal cases mitigated the issue of ionization-induced refraction that typically inhibits the formation of long, contiguous plasma channels.

A high-intensity laser pulse propagating through a medium triggers an ionization front that can accelerate and frequency-upshift the photons of a second pulse. The maximum upshift is ultimately limited by the accelerated photons outpacing the ionization front or the ionizing pulse refracting from the plasma. Here we apply the flying focus-a moving focal point resulting from a chirped laser pulse focused by a chromatic lens-to overcome these limitations. Theory and simulations demonstrate that the ionization front produced by a flying focus can frequency-upshift an ultrashort optical pulse to the extreme ultraviolet over a centimeter of propagation. An analytic model of the upshift predicts that this scheme could be scaled to a novel table-top source of spatially coherent x-rays.A growing number of scientific fields rely critically on high intensity, high-repetition rate sources of extreme ultraviolet (XUV) radiation (wavelengths < 120 nm). These sources provide highresolution imaging for high energy density physics and nanotechnology [1,2], fine-scale material ablation for nanomachining, spectrometry, and photolithography [3][4][5], and ultrafast pump/probe techniques for fundamental studies in atomic and molecular physics [6][7][8]. While XUV sources have historically been challenging to produce, methods including nonlinear frequency mixing [9], high harmonic generation [10,11], and XUV lasing or line emission in metal-vapor and noble-gas plasmas [5,12] have demonstrated promising results. Despite their successes, each of these methods introduces tradeoffs in terms of tunability, spatial coherence, divergence, or efficiency [5,[9][10][11][12]. Photon acceleration offers an alternative method for tunable XUV production that could lessen or even eliminate these tradeoffs.Photon acceleration refers to the frequency upshift of light in response to a refractive index that decreases in time [13,14]. In analogy to charged particle acceleration, the increase in photon energy, i.e. frequency, accompanies an increase in group velocity. In the context of an electromagnetic pulse, the leading phase fronts experience a higher index than adjacent, trailing phase fronts, which manifests as a local phase velocity that increases over the duration of the pulse.The trailing phase front, on account of its higher phase velocity, gradually catches up with the