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

TL;DR

This paper critically examines Thomas's scaling laws for plasma bubble radiation and self-injection thresholds, revealing discrepancies with numerical simulations and clarifying the validity of previous analytical and computational models.

Contribution

The authors demonstrate that Thomas's analytical results for electron trajectories and injection thresholds are inconsistent with numerical simulations, highlighting limitations of the analytical approach.

Findings

Numerical simulations contradict Thomas's self-injection threshold.

Thomas's analytical assumptions lead to incorrect trajectory predictions.

Kostyukov et al.'s analysis remains mathematically correct, but its applicability is questioned.

Abstract

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.