An intense laser pulse in a plasma can accelerate electrons [1][2][3][4] to GeV energies in centimetres [5][6][7] . Transverse betatron motion 8,9 in the plasma wake results in X-ray photons with an energy that depends on the electron energy, oscillation amplitude and frequency of the betatron motion [10][11][12] . Betatron X-rays from laser-accelerator electrons have hitherto been limited to spectra peaking between 1 and 10 keV (ref. 13). Here we show that the betatron amplitude is resonantly enhanced when electrons interact with the rear of the laser pulse 14,15 . At high electron energy, resonance occurs when the laser frequency is a harmonic of the betatron frequency, leading to a significant increase in the photon energy. 10 X-ray pulses from synchrotron sources have become immensely useful tools for investigating the structure of matter 17 , which has led to a huge international effort to construct light sources for many different scientific and technological applications. Synchrotrons are usually based on radio-frequency (RF) accelerating cavities that are limited to fields of 10-100 MV m −1 because of electrical breakdown, which results in very large and expensive devices.High-power lasers, on the other hand, have led to the development of many new areas of science, as diverse as inertial confinement fusion and laboratory astrophysics to the study of warm dense matter. However, they now have the potential to transform accelerator and light source technology. In the late 1970s, Tajima and Dawson 1 proposed harnessing the ponderomotive force associated with intense laser fields to excite plasma waves and form wake-like structures 18 (as behind a boat) that travel with a velocity close to the speed of light, c. The electrostatic forces of these charge density structures can rapidly accelerate particles to very high energies 6 ; where momentum is gained analogous to a surfer riding an ocean wave. Recent progress in the development of laser wakefield accelerators (LWFAs) has enabled electron beams to be accelerated with unprecedented acceleration gradients 2-4 , three orders of magnitude higher than in RF cavities, thus reducing a 100 m long GeV accelerator to centimetres in length 6 . The LWFA can now produce high-quality electron beams with low emittance, ε n , of the order 1π mm mrad 19 , small energy spread 20 , δγ /γ 1%, where γ is the Lorenz factor, and high charge 4 , Q = 10-100 pC. At high laser intensities, in the so-called blowout regime 21 , the LWFA structure has an approximately spherical bubble shape with a radius of R ≈ 2 √ a 0 c/ω p , which is primarily determined by the normalized laser vector potential, a 0 = eA/m e c 2 and the plasma frequency, ω p = √ 4π n p e 2 /m e , where n p is the plasma density, e, the electron charge and m e , the electron mass 22 . The plasma wave is efficiently driven when the laser pulse duration is approximately a plasma period. Micrometre-long electron bunches that extend only a fraction of the plasma wavelength, λ p = 2πc/ω p , are self-injected and accelerate...

Progress in laser wakefield accelerators indicates their suitability as a driver of compact free-electron lasers (FELs). High brightness is defined by the normalized transverse emittance, which should be less than 1π mm mrad for an x-ray FEL. We report high-resolution measurements of the emittance of 125 MeV, monoenergetic beams from a wakefield accelerator. An emittance as low as 1.1±0.1π mm mrad is measured using a pepper-pot mask. This sets an upper limit on the emittance, which is comparable with conventional linear accelerators. A peak transverse brightness of 5×10¹⁵ A m⁻¹ rad⁻¹ makes it suitable for compact XUV FELs.

Self-injection in a laser-plasma wakefield accelerator is usually achieved by increasing the laser intensity until the threshold for injection is exceeded. Alternatively, the velocity of the bubble accelerating structure can be controlled using plasma density ramps, reducing the electron velocity required for injection. We present a model describing self-injection in the short-bunch regime for arbitrary changes in the plasma density. We derive the threshold condition for injection due to a plasma density gradient, which is confirmed using particle-in-cell simulations that demonstrate injection of subfemtosecond bunches. It is shown that the bunch charge, bunch length, and separation of bunches in a bunch train can be controlled by tailoring the plasma density profile.

The laser-plasma wakefield accelerator is a compact source of high brightness, ultra-short duration electron bunches. Self-injection occurs when electrons from the background plasma gain sufficient momentum at the back of the bubble-shaped accelerating structure to experience sustained acceleration. The shortest duration and highest brightness electron bunches result from self-injection close to the threshold for injection. Here we show that in this case injection is due to the localized charge density build-up in the sheath crossing region at the rear of the bubble, which has the effect of increasing the accelerating potential to above a critical value. Bunch duration is determined by the dwell time above this critical value, which explains why single or multiple ultra-short electron bunches with little dark current are formed in the first bubble. We confirm experimentally, using coherent optical transition radiation measurements, that single or multiple bunches with femtosecond duration and peak currents of several kiloAmpere, and femtosecond intervals between bunches, emerge from the accelerator.