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Raman or Brillouin amplification of a laser beam in plasma has long been seen as a way to reach multi-PW powers in compact laser systems. However, no significant plasma-based Raman amplification of a laser pulse beyond 0.1 TW has been achieved in nearly 20 years, and only one report of Brillouin amplification beyond 1 TW. In this paper, we reveal novel non-linear criteria for the initial seed pulse that will finally open the door to efficient Raman and Brillouin amplification to petawatt powers and Joule-level energies. We show that the triple product of the coupling constant    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\Gamma $$\end{document}   Γ, seed pulse duration    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\tau $$\end{document}   τand seed pulse amplitude  a  for the Raman seed pulse (or    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$a^{2/3}$$\end{document}    a   2  /  3for Brillouin) must exceed a specific minimum threshold for efficient amplification. We also analyze the plasma-based Raman and Brillouin amplification experiments to date, and show that the seed pulses used in nearly all experiments are well below our new threshold, which explains the poor efficiency obtained in them. Finally, we analyze a recent Brillouin amplification experiment that used increased seed pulse power to obtain Joule-level amplification, and find excellent agreement with our theory.

New criteria for efficient Raman and Brillouin amplification of laser beams in plasma