The term soliton has recently been coined to describe a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed. To date at least seven distinct wave systems, representing a wide range of applications in applied science, have been found to exhibit such solutions. This review paper covers the current status of soliton research, paying particular attention to the very important "inverse method" whereby the initial value problem for a nonlinear wave system can be solved exactly through a succession of linear calculations.

The soliton: A new concept in applied science

One of the scientific success stories of fusion research over the past decade is the development of the ExB shear stabilization model to explain the formation of transport barriers in magnetic confinement devices. This model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition. This concept has the universality needed to explain the edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines. More recently, this model has been applied to explain the further confinement improvement from H (high)-mode to VH (very high)-mode seen in some tokamaks, where the edge transport barrier becomes wider. Most recently, this paradigm has been applied to the core transport barriers formed in plasmas with negative or low magnetic shear in the plasma core. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to a higher energy state with reduced turbulence and transport when an additional source of free energy is applied to it. The transport decrease that is associated with ExB velocity shear effects also has significant practical consequences for fusion research. The fundamental physics involved in transport reduction is the effect of ExB shear on the growth, radial extent and phase correlation of turbulent eddies in the plasma. The same fundamental transport reduction process can be operational in various portions of the plasma because there are a number ways to change the radial electric field Er. An important theme in this area is the synergistic effect of ExB velocity shear and magnetic shear. Although the ExB velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of ExB velocity shear and facilitate turbulence stabilization.

/pdf/effects-of-e-b-velocity-shear-and-magnetic-shear-on-5f3wdz73f7.pdf

Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices

In this review we will focus on a topic of fundamental importance for both plasma physics and astrophysics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Ulysses’ high latitude observations and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD) turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.

/pdf/the-solar-wind-as-a-turbulence-laboratory-4mad4q4xdr.pdf

The Solar Wind as a Turbulence Laboratory

Complex (dusty) plasmas: current status, open issues, perspectives

A comprehensive overview is presented of recent observational and theoretical results on solar wind structures and fluctuations and magnetohydrodynamic waves and turbulence, with preference given to phenomena in the inner heliosphere. Emphasis is placed on the progress made in the past decade in the understanding of the nature and origin of especially small-scale, compressible and incompressible fluctuations. Turbulence models to describe the spatial transport and spectral transfer of the fluctuations in the inner heliosphere are discussed, and results from direct numerical simulations are dealt with. Intermittency of solar wind fluctuations and their statistical distributions are briefly investigated. Studies of the heating and acceleration effects of the turbulence on the background wind are critically surveyed. Finally, open questions concerning the origin, nature and evolution of the fluctuations are listed, and possible avenues and perspectives for future research are outlined.

MHD structures, waves and turbulence in the solar wind : observations and theories

A sharp transport barrier, accompanied by a bifurcated poloidal rotation and a radial electric field, is formed at the plasma edge by driving a radial current across the outer magnetic surfaces of a tokamak. A decrease in particle transport is observed for negative radial E fields. When the radial current is turned off, the E field and the rotation damp on a time scale comparable with the ion-ion collision time.

H -mode behavior induced by cross-field currents in a tokamak

The formation and propagation of ion-acoustic solitons are observed experimentally. The character of a solitary pulse is observed to follow the predictions of the Kortewegde Vries equation with respect to the shape and velocity of the soliton. The interaction between two solitons is modified significantly by dissipation. However, the nonlinear nature of the interactions is confirmed for solitons moving in the same direction. Solitons moving in the opposite direction and colliding have very little effect on each other.

Formation and Interaction of Ion-Acoustic Solitions

Observation of Collisionless Electrostatic Shocks

Magnetic pickup loops inserted into the Macrotor tokamak have shown a broad spectrum of oscillation in ${B}_{r}$ and ${B}_{p}$ up to $f\ensuremath{\approx}100$ kHz. The high-frequency ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}}_{r}$ have short radial and poloidal correlation lengths $Ll5$ cm, in contrast with the usual Mirnov oscillations with $f\ensuremath{\approx}7$ kHz and $L\ensuremath{\gg}5$ cm. The observed magnitude $\frac{\ensuremath{\Sigma}|{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}}_{r}|}{{B}_{T}}g{10}^{\ensuremath{-}5}$, where the summation extends over all $fg30$ kHz, is in the range in which such radial magnetic perturbations may be contributing to anomalous electron energy transport.

Small-Scale Magnetic Fluctuations Inside the Macrotor Tokamak.

The ion acoustic turbulence in the turbulent-heating experiment reported is excited by the ion-ion beam instability. Graphs are presented, showing the spatial evolution of the parallel ion beam energy and the spatial evolution of the ion acoustic turbulent wave spectrum. The observed characteristics of test waves in a turbulent beam-plasma imply that wave saturation is a dynamic balance between the emission of waves by the beam and the destruction or damping of wave coherence by the turbulent diffusion of particle orbits.

R. J. Taylor

Papers

H -mode behavior induced by cross-field currents in a tokamak

Formation and Interaction of Ion-Acoustic Solitions

Observation of Collisionless Electrostatic Shocks

Small-Scale Magnetic Fluctuations Inside the Macrotor Tokamak.

Ion heating via turbulent ion acoustic waves.