We investigate a new regime for betatron x-ray emission that utilizes kilojoule-class picosecond lasers to drive wakes in plasmas. When such laser pulses with intensities of ∼5×10^{18} W/cm^{2} are focused into plasmas with electron densities of ∼1×10^{19} cm^{-3}, they undergo self-modulation and channeling, which accelerates electrons up to 200 MeV energies and causes those electrons to emit x rays. The measured x-ray spectra are fit with a synchrotron spectrum with a critical energy of 10-20 keV, and 2D particle-in-cell simulations were used to model the acceleration and radiation of the electrons in our experimental conditions.