TY - JOUR
T1 - Comment on "scalings for radiation from plasma bubbles" [Phys. Plasmas 17, 056708 (2010)]
AU - Corde, S.
AU - Stordeur, A.
AU - Malka, V.
PY - 2011/3/1
Y1 - 2011/3/1
N2 - 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 / γp2 + y′2 = R2 is solution of the equations of motion (in the bubble frame), within the approximation py ′2 / px ′2 1. In addition, he highlights that his result is different from the work of Kostyukov [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.
AB - 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 / γp2 + y′2 = R2 is solution of the equations of motion (in the bubble frame), within the approximation py ′2 / px ′2 1. In addition, he highlights that his result is different from the work of Kostyukov [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.
U2 - 10.1063/1.3566012
DO - 10.1063/1.3566012
M3 - Article
AN - SCOPUS:79953659857
SN - 1070-664X
VL - 18
JO - Physics of Plasmas
JF - Physics of Plasmas
IS - 3
M1 - 034701
ER -