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

Turbulent dynamos that exponentially amplify initially small, seed magnetic fields are crucial in magnetizing the Galaxy and beyond. Until now, the ideal environment for turbulent dynamos to grow has been difficult to recreate. In a new approach, we leverage the long pulse capability of the OMEGA-EP laser to recreate the highly conductive and inviscid (Re m $ 5500; Pr m տ 1) growth environment of the turbulent dynamo within the magnetized plasma jet ablated from a simple cone target of CH plastic. In 3-D FLASH simulations of our scheme, we find that the ideal dynamo environment is a typically $1 mm 3 , տ 1:5 keV hot spot where the laser beams intersect to produce maximum direct heating of the jet plasma. The dynamo environment is maintained from the onset of steady flows through the $10 ns length of the laser pulse. For a plasma vorticity of 0.3-3.0 ns-1 and a dynamo active over $5 ns, the magnetic energy increases on an exponential trajectory by more than a decade. Fourier analysis reveals that the dynamo progressively saturates up to E B =E K $ 20% from small scales k տ 30 cm À1 to large in the time it is sustained. We find robust agreement between the evolution of magnetic energy spectra extracted from the FLASH physics simulation and that derived from synthetic sheath-accelerated proton deflectometry images, thereby demonstrating that the dynamo activity can be quantified in a real experiment.

A planar laser pulse propagating in vacuum can exhibit an extremely large ponderomotive force. This force, however, cannot impart net energy to an electron: As the pulse overtakes the electron, the initial impulse from its rising edge is completely undone by an equal and opposite impulse from its trailing edge. Here we show that planar-like "flying focus" pulses can break this symmetry, imparting relativistic energies to electrons. The intensity peak of a flying focus-a moving focal point resulting from a chirped laser pulse focused by a chromatic lens-can travel at any subluminal velocity, forwards or backwards. As a result, an electron can gain enough momentum in the rising edge of the intensity peak to outrun and avoid the trailing edge.Accelerating the intensity peak can further boost the momentum gain. Theory and simulations demonstrate that these dynamic intensity peaks can backwards accelerate electrons to the MeV energies required for radiation and electron diffraction probes of high energy density materials.Vacuum laser acceleration (VLA) exploits the large electromagnetic fields of highintensity laser pulses to accelerate electrons to relativistic energies over short distances [1][2][3][4][5][6][7][8][9][10][11][12].The field of an intense pulse can far surpass that in conventional radio-frequency (RF) or advanced plasma-based accelerators, and the underlying interaction-involving only an electron and the electromagnetic field-has an appealing simplicity. RF accelerators routinely improve beam quality and achieve unprecedented energies, but their low damage threshold constrains the maximum accelerating field. This necessitates physically and economically immense structures to accelerate electrons to the energies necessary for high energy density probes, radiation sources such as free electron lasers, or high-energy physics experiments [13][14][15][16]. Wakefield accelerators, on the other hand, employ plasma to sustain accelerating fields nearly 1000x that of RF accelerators [17][18][19][20][21][22][23]. The use of plasma, however, comes with its own set of challenges, such as tuning the laser or electron beam parameters to the plasma conditions, avoiding a myriad of instabilities, and creating long uniform plasma channels [24,25].

Spatiotemporal control over the intensity of a laser pulse has the potential to enable or revolutionize a wide range of laser-based applications that currently suffer from the poor flexibility offered by conventional optics. Specifically, these optics limit the region of high intensity to the Rayleigh range and provide little to no control over the trajectory of the peak intensity. Here, we introduce a nonlinear technique for spatiotemporal control, the “self-flying focus,” that produces an arbitrary trajectory intensity peak that can be sustained for distances comparable to the focal length. The technique combines temporal pulse shaping and the inherent nonlinearity of a medium to customize the time and location at which each temporal slice within the pulse comes to its focus. As an example of its utility, simulations show that the self-flying focus can form a highly uniform, meter-scale plasma suitable for advanced plasma-based accelerators.

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