Nonlinear wave collapse and strong turbulence

TLDR

Wave self‑focusing, collapse, and strong nonlinear turbulence are central phenomena in diverse wave systems, with Langmuir waves in unmagnetized plasmas serving as a primary illustrative example and extensions to optics, solid‑state, magnetized, and oceanic waves discussed. The review aims to synthesize the main concepts of wave collapse and strong turbulence, highlight open questions, and suggest future research directions. The authors present an introductory overview of linear wave physics and nonlinear wave‑wave interactions, then develop a detailed theoretical framework for wave collapse and strong turbulence, supported by numerical simulations and experimental studies in plasma, laser, and beam‑plasma contexts. Over the past decade, theory and experimental realizations of wave collapse and strong turbulence have progressed rapidly, yet several fundamental questions remain unresolved.

Abstract

The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions.