“…We calculate the betatron spectra according to the following method: we set the driving laser power, the laser wavelength (0.8 µm), and the plasma density, which, according to [18], determine the blowout radius r b (1) and (2), the accelerated charge (equation 10) and the energy (6). The electrons are injected at the back of the ionic cavity with an initial distance r 0 that we set equal to 0.2 × r b , according to previous source size measurements [21]. The initial axial and radial momenta of the injected electrons are set to γ g and γ g /2, respectively (where γ g is the Lorentz factor associated with the velocity of the ionic cavity), such that the trapping condition γ > γ g holds.…”