[en] Thomas has recently derived scaling laws for x-ray radiation from electrons accelerated in plasma bubbles, as well as a threshold for the self-injection of background electrons into the bubble [A. G. R. Thomas, Phys. Plasmas 17, 056708 (2010)]. To obtain this threshold, the equations of motion for a test electron are studied within the frame of the bubble model, where the bubble is described by prescribed electromagnetic fields and has a perfectly spherical shape. The author affirms that any elliptical trajectory of the form x^'2/γ_p²+y^'2=R² is solution of the equations of motion (in the bubble frame), within the approximation p_y^'2/p_x^'2<<1. In addition, he highlights that his result is different from the work of Kostyukov et al. [Phys. Rev. Lett. 103, 175003 (2009)], and explains the error committed by Kostyukov-Nerush-Pukhov-Seredov (KNPS). In this comment, we show that numerically integrated trajectories, based on the same equations than the analytical work of Thomas, lead to a completely different result for the self-injection threshold, the result published by KNPS [Phys. Rev. Lett. 103, 175003 (2009)]. We explain why the analytical analysis of Thomas fails and we provide a discussion based on numerical simulations which show exactly where the difference arises. We also show that the arguments of Thomas concerning the error of KNPS do not hold, and that their analysis is mathematically correct. Finally, we emphasize that if the KNPS threshold is found not to be verified in PIC (Particle In Cell) simulations or experiments, it is due to a deficiency of the model itself, and not to an error in the mathematical derivation.

[en] The x-ray emission in laser-plasma accelerators can be a powerful tool to understand the physics of relativistic laser-plasma interaction. It is shown here that the mapping of betatron x-ray radiation can be obtained from the x-ray beam profile when an aperture mask is positioned just beyond the end of the emission region. The influence of the plasma density on the position and the longitudinal profile of the x-ray emission is investigated and compared to particle-in-cell simulations. The measurement of the x-ray emission position and length provides insight on the dynamics of the interaction, including the electron self-injection region, possible multiple injection, and the role of the electron beam driven wakefield.