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Thomas has recently derived scaling laws for X-ray radiation from electronsaccelerated in plasma bubbles, as well as a threshold for the self-injection ofbackground electrons into the bubble [A. G. R. Thomas, Phys. Plasmas 17, 056708(2010)]. To obtain this threshold, the equations of motion for a test electronare studied within the frame of the bubble model, where the bubble is describedby prescribed electromagnetic fields and has a perfectly spherical shape. Theauthor affirms that any elliptical trajectory of the form x'^2/{\gamma}_p^2 +y'^2 = R^2 is solution of the equations of motion (in the bubble frame), withinthe approximation p'_y^2/p'_x^2 \ll 1. In addition, he highlights that hisresult is different from the work of Kostyukov et al. [Phys. Rev. Lett. 103,175003 (2009)], and explains the error committed byKostyukov-Nerush-Pukhov-Seredov (KNPS). In this comment, we show thatnumerically integrated trajectories, based on the same equations than theanalytical work of Thomas, lead to a completely different result for theself-injection threshold, the result published by KNPS [Phys. Rev. Lett. 103,175003 (2009)]. We explain why the analytical analysis of Thomas fails and weprovide a discussion based on numerical simulations which show exactly wherethe difference arises. We also show that the arguments of Thomas concerning theerror 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 inPIC (Particle In Cell) simulations or experiments, it is due to a deficiency ofthe model itself, and not to an error in the mathematical derivation.

Comment on "Scalings for radiation from plasma bubbles" [Phys. Plasmas 17, 056708 (2010)]