  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/{\gamma}_p^2 +
y'^2 = R^2 is solution of the equations of motion (in the bubble frame), within
the approximation p'_y^2/p'_x^2 \ll 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.
