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We show that the properties of the electron beam and bright x-rays producedby a laser wakefield accelerator can be predicted if the distance over whichthe laser self-focuses and compresses prior to self-injection is taken intoaccount. A model based on oscillations of the beam inside a plasma bubble showsthat performance is optimised when the plasma length is matched to the laserdepletion length. With a 200~TW laser pulse this results in an x-ray beam withmedian photon energy of \unit[20]{keV}, $> 6\times 10^{8}$ photons above\unit[1]{keV} per shot and a peak brightness of $\unit[3 \times10^{22}]{photons~s^{-1}mrad^{-2}mm^{-2} (0.1\% BW)^{-1}}$.

Bright X-ray radiation from plasma bubbles in an evolving laser wakefield accelerator