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G igaelectron volt (GeV) electron accelerators are essential to synchrotron radiation facilities and free-electron lasers, and as modules for high-energy particle physics. Radiofrequency-based accelerators are limited to relatively low accelerating fields (10−50 MV m −1), requiring tens to hundreds of metres to reach the multi-GeV beam energies needed to drive radiation sources, and many kilometres to generate particle energies of interest to high-energy physics. Laser-wakefield accelerators 1,2 produce electric fields of the order 10-100 GV m −1 enabling compact devices. Previously, the required laser intensity was not maintained over the distance needed to reach GeV energies, and hence acceleration was limited to the 100 MeV scale 3-5. Contrary to predictions that petawatt-class lasers would be needed to reach GeV energies 6,7 , here we demonstrate production of a high-quality electron beam with 1 GeV energy by channelling a 40 TW peak-power laser pulse in a 3.3-cm-long gas-filled capillary discharge waveguide 8,9. Although it is straightforward to achieve acceleration gradients of 10−100 GV m −1 in laser-wakefield accelerators 1,2 , until recently the electron beams (e-beams) from such accelerators had energies <200 MeV with 100% energy spread 10. A breakthrough improvement in energy spread was obtained in 2004 by three groups 3-5 by interacting intense laser pulses with millimetre-scale gas jets to generate 70-200 MeV beams with percent level energy spread. For example, by using relatively large spot sizes, r s = 18 μm (1/e 2 radius of the laser intensity profile), 170 MeV e-beams were produced in 1-2-mm-long gas jets with the order of 0.5 nC bunch charge using 30 fs, 30 TW laser pulses 5. Using a 2-mm-long preformed plasma channel 2 in a gas jet to guide the driving laser beam 4,11,12 , enabled the production of 85 MeV e-beams containing 0.3 nC bunch charge, with only 9 TW of laser peak power. To scale laser-driven accelerators to GeV electron energies and beyond, two approaches had been proposed: (1) operate in initially uniform plasmas 7,13 with petawatt (PW)-scale lasers and large laser spot sizes, or (2) channel guide the laser beam over centimetre-scale distances 2,14,15. Without guiding (for example, without self-focusing or preformed channels), the laser-plasma interaction length is

An overview is given of the physics issues relevant to the plasma wakefield accelerator, the plasma beat-wave accelerator, the laser wakefield accelerator, including the self-modulated regime, and wakefield accelerators driven by multiple electron or laser pulses. Basic properties of linear and nonlinear plasma waves are discussed, as well as the trapping and acceleration of electrons in the plasma wave. Formulas are presented for the accelerating field and the energy gain in the various accelerator configurations. The propagation of the drive electron or laser beams is discussed, including limitations imposed by key instabilities and methods for optically guiding laser pulses. Recent experimental results are summarized.

Guiding of relativistically intense laser pulses with peak power of 0.85 PW over 15 diffraction lengths was demonstrated by increasing the focusing strength of a capillary discharge waveguide using laser inverse Bremsstrahlung heating. This allowed for the production of electron beams with quasi-monoenergetic peaks up to 7.8 GeV, double the energy that was previously demonstrated. Charge was 5 pC at 7.8 GeV and up to 62 pC in 6 GeV peaks, and typical beam divergence was 0.2 mrad.

Multi-GeV electron beams with energy up to 4.2 GeV, 6% rms energy spread, 6 pC charge, and 0.3 mrad rms divergence have been produced from a 9-cm-long capillary discharge waveguide with a plasma density of ≈7×10¹⁷ cm⁻³, powered by laser pulses with peak power up to 0.3 PW. Preformed plasma waveguides allow the use of lower laser power compared to unguided plasma structures to achieve the same electron beam energy. A detailed comparison between experiment and simulation indicates the sensitivity in this regime of the guiding and acceleration in the plasma structure to input intensity, density, and near-field laser mode profile.