Scaling LWFA-based betatron emission to the 1PW level

We review the results obtained with the INRS laser system on the scaling of X-ray sources based on laser wake-field acceleration (LWFA) of electrons. We have successfully generated stable propagation in gas jets of a relativistic pulse through self-guiding on length well larger than the classical LWFA dephasing and depletion lengths, generating very intense beams of hard X-rays with 200TW on target. Our experimental scaling law obtained for the photon yield is presented and the level of X-ray emission in a 30keV-40keV band at the 1PW laser peak power level, now available at several laser facilities, is estimated.