Microinstabilities in plasmas-non-linear effects

Abstract

This review attempts to bring together and present in as coherent a manner as possible the wide range of non-linear kinetic phenomena which occur in a plasma. The extent to which the theory has been borne out by experiment is indicated in detail and in several instances it is convenient to catalogue the results.While the main thrust of laboratory plasma physics has been associated with magnetic containment fusion, there has been the recent emergence of laser heating as an alternative path to fusion, and the refinement of measurements in the ionosphere and magnetosphere means that there has been a parallel development of interest in non-linear processes. For this reason this review attempts to cover fundamental aspects rather than those which are specific to one situation.The processes considered range from resonant three-wave interactions in homogeneous and inhomogeneous plasmas to situations in which the plasma parameters themselves vary as a result of the interactions under consideration. The understanding of most processes is now reasonably complete but general statements about which non-linear process will dominate are still difficult to make and the goal of describing the properties of any particular turbulent plasma still lies ahead.

Higher-order rogue wave solutions of the three-wave resonant interaction equation via the generalized Darboux transformation

“…In this paper, we assume x to be the evolution variable, and t is the second independent variable. For concrete physical contexts, equation (1) can describe the propagation and mixing of waves with different frequencies in weakly nonlinear dispersive media [15,16], and it is of also elementary application in nonlinear optics [17], fluid dynamics [18], plasma physics [19], solid state physics [20], and so forth. Over recent years, there have been a substantial number of reports for equation (1), such as the inverse scattering transformation studied by Kaup [17], the Darboux transformation (DT) and multi-soliton solutions given by Zhou [21], and the finite dimensional Hamiltonian system and algebrogeometric solutions derived by Geng and Wu et al [22,23].…”

Rogue Waves Emerging from the Resonant Interaction of Three Waves

“…Indeed, this system describes the propagation and mixing of waves in weakly nonlinear and dispersive media. Applications of the TWRI system have been found in fluid dynamics (capillary-gravity waves, internal gravity waves, surface and internal waves) [29,30], in optics (parametric amplification, frequency conversion, stimulated Raman and Brillouin scattering) [31,32], in plasmas (plasma instability, laser-plasma interactions, radio frequency heating) [33,34], and in solid-state physics and acoustics [35].…”

Resonant Drift-Wave Coupling Modified by Nonlinear Separatrix Dissipation

“…This nondissipative nonlinearity gives rise to a plethora of mode couplings and instabilities which have been broadly studied. Specifically, the 3-wave parametric instability, which shows late-time energy sloshing and mode recurrences, has been analyzed theoretically [1,2], but less so experimentally.…”