Response to “Comment on ‘Scalings for radiation from plasma bubbles’ ” [Phys. Plasmas 18, 034701 (2011)]

Thomas, Alexander George Roy (2011) Response to “Comment on ‘Scalings for radiation from plasma bubbles’ ” [Phys. Plasmas 18, 034701 (2011)]. Physics of Plasmas, 18 (3): 034702. ISSN 1070-664X

Abstract

In the preceding Comment, Corde, Stordeur, and Malka claim that the trapping threshold derived in my recent paper is incorrect. Their principal argument is that the elliptical orbits I used are not exact solutions of the equation of motion in the fields of the bubble. The original paper never claimed this—rather I claimed that the use of elliptical orbits was a reasonable approximation, which I based on observations from particle-in-cell simulations. Integration of the equation of motion for analytical expressions for idealized bubble fields (either analytically [I. Kostyukov, E. Nerush, A. Pukhov, and V. Seredov, Phys. Rev. Lett. 103, 175003 (2009)] or numerically [S. Corde, A. Stordeur, and V. Malka, “Comment on ‘Scalings for radiation from plasma bubbles,’ ” Phys. Plasmas 18, 034701 (2011)]) produces a trapping threshold wholly inconsistent with experiments and full particle-in-cell (PIC) simulations (e.g., requiring an estimated laser intensity of a0∼30a0∼30 for ne∼1019 cm−3ne∼1019 cm−3). The inconsistency in the particle trajectories between PIC and the numeric model used by the comment authors arises due to the fact that the analytical fields are only approximately true for “real” plasma bubbles, and lack certain key features of the field structure. Two possible methods of resolution to this inconsistency are either to find ever more complicated but accurate models for the bubble fields or to find approximate solutions to the equations of motion that capture the essential features of the self-consistent electron trajectories. The latter, heuristic approach used in my recent paper produced a threshold that is better matched to experimental observations. In this reply, I will also revisit the problem and examine the relationship between bubble radius and electron momentum at the point of trapping without reference to a particular trajectory. Original article: Physics of Plasmas 23, 034701 (2011) Original article: Physics of Plasmas 17, 056708 (2010)