  Laser-driven plasma accelerators can generate accelerating gradients three
orders of magnitude larger than radio-frequency accelerators and have achieved
beam energies above 1 GeV in centimetre long stages. However, the pulse
repetition rate and wall-plug efficiency of plasma accelerators is limited by
the driving laser to less than approximately 1 Hz and 0.1% respectively. Here
we investigate the prospects for exciting the plasma wave with trains of
low-energy laser pulses rather than a single high-energy pulse. Resonantly
exciting the wakefield in this way would enable the use of different
technologies, such as fibre or thin-disc lasers, which are able to operate at
multi-kilohertz pulse repetition rates and with wall-plug efficiencies two
orders of magnitude higher than current laser systems. We outline the
parameters of efficient, GeV-scale, 10-kHz plasma accelerators and show that
they could drive compact X-ray sources with average photon fluxes comparable to
those of third-generation light source but with significantly improved temporal
resolution. Likewise FEL operation could be driven with comparable peak power
but with significantly larger repetition rates than extant FELs.
