When a highly relativistic electron is injected off-axis into an ion channel, the restoring force of the radial field of the ions will cause the electron to accelerate towards the axis, overshoot, and begin to undergo oscillations about the ioncolumn axis at a characteristic frequency; the betatron frequency. This so-called betatron motion will cause the electron to radiate hard x-rays in the forward direction. In two recent experiments at the Stanford Linear Accelerator Center (SLAC), betatron x-rays in the 1-20kV range and in the 1-50MV range were produced with an electron beam with an energy of 28.5 GeV for ion densities of about 1 × 1014 cm-3 and 1 × 1017cm-3, respectively. To make such an x-ray source more compact, the 3km long SLAC linac would be replaced by a source of electrons from a Laser Wakefield accelerator (LWFA). To increase the efficiency of converting laser into photons at high photon energies, we propose adding a second stage where the LWFA electrons radiate via a second ion channel, independent of the accelerating process. This two stage concept allows one to control the critical frequency of the emitted radiation as well as the efficiency of the process.