Each successive generation of X-ray machines has opened up new frontiers in science, such as the first radiographs and the determination of the structure of DNA. State-of-the-art X-ray sources can now produce coherent high-brightness Xrays of greater than kiloelectronvolt energy and promise a new revolution in imaging complex systems on nanometre and femtosecond scales. Despite the demand, only a few dedicated synchrotron facilities exist worldwide, in part because of the size and cost of conventional (accelerator) technology 1 . Here we demonstrate the use of a new generation of laserdriven plasma accelerators 2 , which accelerate high-charge electron beams to high energy in short distances 3-5 , to produce directional, spatially coherent, intrinsically ultrafast beams of hard X-rays. This reduces the size of the synchrotron source from the tens of metres to the centimetre scale, simultaneously accelerating and wiggling the electron beam. The resulting X-ray source is 1,000 times brighter than previously reported plasma wigglers 6,7 and thus has the potential to facilitate a myriad of uses across the whole spectrum of light-source applications.There are a number of proposals to use extreme nonlinear interactions of the latest generation of high-power ultrashort-pulse laser systems to produce beams of high-energy photons with high brightness and short pulse duration. For example, high-order harmonic generation promises trains of coherent pulselets 8 and Compton scattering could extend energies into the γ -regime 9,10 . An alternative proposal has been the use of compact laser-plasma accelerators to drive sources of undulating/wiggling radiation 11 .These accelerators use the plasma wakefield generated by the passage of an intense laser pulse through an underdense plasma 12 . Such wakefields can have intrinsic fields of more than 1,000 times greater than the best achievable by conventional accelerator technology, and thus can accelerate particles to high energies in a fraction of the distance. Recently, it has been demonstrated that at high laser power, the wakefield can be driven to sufficient amplitude to be able to trap large numbers of particles (>100 pC) from the background plasma and accelerate them in a narrow energy spread beam 3-5 , now producing beams of electrons of gigaelectronvoltscale energy of the order of 1 cm (refs 13,14).Such electron sources are of interest to replace the accelerators that drive current synchrotron sources, and typically use multiple periods of alternately poled magnets (undulators or wigglers) to reinforce the synchrotron emission over a length of a few metres. The first demonstrations of wakefield-driven radiation using external wigglers have also been reported, though still being limited to optical or near-optical wavelengths and modest peak brightness 15,16 .However, the particles being accelerated in the plasma accelerator also undergo transverse (betatron) oscillations when subject to the focusing fields of the plasma wave. These oscillations occur at the betatron frequen...

Collisionless shocks can be produced as a result of strong magnetic fields in a plasma flow, and therefore are common in many astrophysical systems. The Weibel instability is one candidate mechanism for the generation of su ciently strong fields to create a collisionless shock. Despite their crucial role in astrophysical systems, observation of the magnetic fields produced by Weibel instabilities in experiments has been challenging. Using a proton probe to directly image electromagnetic fields, we present evidence of Weibelgenerated magnetic fields that grow in opposing, initially unmagnetized plasma flows from laser-driven laboratory experiments. Three-dimensional particle-in-cell simulations reveal that the instability e ciently extracts energy from the plasma flows, and that the self-generated magnetic energy reaches a few percent of the total energy in the system. This result demonstrates an experimental platform suitable for the investigation of a wide range of astrophysical phenomena, including collisionless shock formation in supernova remnants, large-scale magnetic field amplification, and the radiation signature from gamma-ray bursts.The magnetic fields required for collisionless shock formation in astrophysical systems may either be initially present, for example in supernova remnants or young galaxies 1 , or they may be selfgenerated in systems such as gamma-ray bursts (GRBs; ref. 2). In the case of GRB outflows, the intense magnetic fields are greater than those which can be seeded by the GRB progenitor or produced by misaligned density and temperature gradients (the Biermannbattery effect) 3,4 . It has long been known that instabilities can generate strong magnetic fields, even in the absence of seed fields. Weibel considered the development of an electromagnetic instability driven by the electron velocity anisotropy in a background of resting ions 5 . The signature of the instability is a pattern of current filaments stretched along the axis of symmetry of the electron motion. The process is quite general, and subsequent work has shown that such instabilities can be excited in both non-relativistic and relativistic shocks. This general nature makes the Weibel instability common in astrophysical systems [6][7][8] . The instability provides a mechanism by which the electromagnetic turbulence associated with the formation of collisionless shocks is fed by the flow anisotropy of the protons (and ions) stochastically reflecting off of the shock 9-11 , and leading ultimately to strong particle acceleration in GRB's (ref. 12).

The Rayleigh-Taylor (RT) instability occurs at an interface between two fluids of differing density during an acceleration. These instabilities can occur in very diverse settings, from inertial confinement fusion (ICF) implosions over spatial scales of [Formula: see text] cm (10-1,000 μm) to supernova explosions at spatial scales of [Formula: see text] cm and larger. We describe experiments and techniques for reducing ("stabilizing") RT growth in high-energy density (HED) settings on the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory. Three unique regimes of stabilization are described: () at an ablation front, () behind a radiative shock, and () due to material strength. For comparison, we also show results from nonstabilized "classical" RT instability evolution in HED regimes on the NIF. Examples from experiments on the NIF in each regime are given. These phenomena also occur in several astrophysical scenarios and planetary science [Drake R (2005) 47:B419-B440; Dahl TW, Stevenson DJ (2010) 295:177-186].

In diverse areas of science and technology, including inertial confinement fusion (ICF), astrophysics, geophysics, and engineering processes, turbulent mixing induced by hydrodynamic instabilities is of scientific interest as well as practical significance. Because of the fundamental roles they often play in ICF and other applications, three classes of hydrodynamic instability-induced turbulent flows—those arising from the Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instabilities—have attracted much attention. ICF implosions, supernova explosions, and other applications illustrate that these phases of instability growth do not occur in isolation, but instead are connected so that growth in one phase feeds through to initiate growth in a later phase. Essentially, a description of these flows must encompass both the temporal and spatial evolution of the flows from their inception. Hydrodynamic instability will usually start from potentially infinitesimal spatial perturbations, will eventually transition to a turbulent flow, and then will reach a final state of a true multiscale problem. Indeed, this change in the spatial scales can be vast, with hydrodynamic instability evolving from just a few microns to thousands of kilometers in geophysical or astrophysical problems. These instabilities will evolve through different stages before transitioning to turbulence, experiencing linear, weakly, and highly nonlinear states. The challenges confronted by researchers are enormous. The inherent difficulties include characterizing the initial conditions of such flows and accurately predicting the transitional flows. Of course, fully developed turbulence, a focus of many studies because of its major impact on the mixing process, is a notoriously difficult problem in its own right. In this pedagogical review, we will survey challenges and progress, and also discuss outstanding issues and future directions.