Warm wave breaking of nonlinear plasma waves with arbitrary phase velocities

Abstract

A warm, relativistic fluid theory of a nonequilibrium, collisionless plasma is developed to analyze nonlinear plasma waves excited by intense drive beams. The maximum amplitude and wavelength are calculated for nonrelativistic plasma temperatures and arbitrary plasma wave phase velocities.The maximum amplitude is shown to increase in the presence of a laser field. These results set a limit to the achievable gradient in plasma-based accelerators.

Response to “Comment on ‘Wave-breaking limits for relativistic electrostatic waves in a one-dimensional warm plasma'” [Phys. Plasmas 14, 084701 (2007)]

“…In a recent Comment, 6 Schroeder, Esarey, and Shadwick argue that our paper 1 contains "several incorrect and misleading claims" and that their own paper on the same subject 5 provides a much better model for warm-plasma wave breaking than ours. In this Response we show that the claims in the Comment 6 lack foundation and are either wrong or irrelevant.…”

“…6 base this claim on the argument that Ref. 5 use the expressions w Ϸ n p 2 / h, T = h, so wT = n p 2 should always hold. However, Ref.…”

“…However, Ref. 5 uses different expressions for w and T , rendering the argument invalid. When inserting the expressions for w and T that are really used in Ref.…”

“…When inserting the expressions for w and T that are really used in Ref. 5, it is quickly found that the warm-plasma approximation does not satisfy Taub's inequality. This can be proven as follows.…”

“…In 1988, two different models were proposed to tackle this problem: one by Katsouleas and Mori 2 and one by Rosenzweig. 3 Slightly modified versions of the latter have also been presented by Sheng and Meyer-ter-Vehn 4 and by Schroeder et al 5 These models provide fundamentally different expressions for the wave-breaking limit in the regime ␥ 2 ␤ ӷ 1, where ␤ =3kT 0 / ͑m e c 2 ͒ and ␥ =1/ ͱ 1−v 2 . To our knowledge, no paper existed that succeeded in resolving this controversy until our paper was published.…”