“…Betatron radiations are generated when the relativistic electrons perform transverse oscillations, referred to "betatron oscillations," due to the transverse focusing forces of the wakefiled, 12 resonant oscillations in the laser field, 13,14 and the unstable evolution of the bubble structure which is mentioned above. 6 The characteristics of the betatron radiation, such as photon flux, photon energy spectrum, angular distribution and the brilliance, are determined by the characteristics of the accelerated electron beam, such as beam charge, energy spectrum, amplitude of transverse oscillations, and beam duration, [15][16][17] and hence depend on the dynamic evolution of the wakefield. Therefore, by studying the characteristics of the betatron radiation, we can retrieve the behaviors of the electron beams, and, in principle, we can reconstruct the process of the bubble dynamic evolution.…”