We show that the properties of the electron beam and bright x-rays produced by a laser wakefield accelerator can be predicted if the distance over which the laser self-focuses and compresses prior to self-injection is taken into account. A model based on oscillations of the beam inside a plasma bubble shows that performance is optimised when the plasma length is matched to the laser depletion length. With a 200~TW laser pulse this results in an x-ray beam with median photon energy of \unit[20]{ keV}, $> 6\times 10^{ 8}$ photons above \unit[1]{ keV} per shot and a peak brightness of $\unit[3 \times 10^{ 22}]{ photons~s^{ -1}mrad^{ -2}mm^{ -2} (0.1\% BW)^{ -1}}$.
Categories: physics.plasm-ph physics.acc-ph