Soliton Currents (Review)
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MA INVESTIGATIONS
Soliton Currents (Review) F. M. Trukhacheva, b, c, *, M. M. Vasilieva, b, and O. F. Petrova, b aJoint
Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412 Russia Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141701 Russia c Belarusian-Russian University, Mogilev, 212000 Belarus *e-mail: [email protected]
b
Received March 10, 2020; revised March 16, 2020; accepted March 30, 2020
Abstract—The theoretical and experimental results on plasma currents induced by acoustic-type solitons are generalized. Ion, electron, and dust-acoustic modes in plasma without magnetic field are considered in detail. It is shown that the generation of pulsed plasma currents with a significant direct component is an inherent property of solitons. The basic properties of soliton currents are established. DOI: 10.1134/S0018151X2004015X
CONTENTS Introduction 1. Soliton, general information 1.1. Linear theory, dispersion relation 1.2. Nonlinear theory, KdV equation 1.3. Nonlinear theory, Sagdeev pseudopotential 2. Plasma currents induced by ion-acoustic solitons 2.1. Derivation and analysis of the equation for currents 2.2. A group of solitons 2.3. Single-particle approximation 2.4. Ion-acoustic solitons. Trapped electrons 3. Electron and dust-acoustic modes 3.1. Electron-acoustic solitons 3.2. Dust-acoustic solitons. Experiment 3.3. Dust-acoustic solitons. Theory Conclusions References INTRODUCTION A soliton is a solitary nonlinear wave that exists due to the balance of nonlinearity and dispersion [1]. Solitary waves were first described by John Scott Russell [2, 3], who observed them on the surface of the water channel connecting Edinburgh with Glasgow in 1834. “I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped—not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course
along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel.” Russell also pointed to the invariance of solitons with respect to collisions with each other. Russell’s discovery was of practical importance and was used to optimize the shape of ships. The fundamental significance of the discovered phenomenon was revealed later. A theoretical model describing this phenomenon was built by Korteweg and de Vries [4] 50 years after Russell’s discovery. The key equation of the model is now called the KdV equation in their honor. Later
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