scholarly journals Dispersive MHD waves and alfvenons in charge non-neutral plasmas

2008 ◽  
Vol 15 (4) ◽  
pp. 681-693 ◽  
Author(s):  
K. Stasiewicz ◽  
J. Ekeberg
Keyword(s):  
Soliton Solutions ◽  
Theoretical Models ◽  
Mhd Waves ◽  
Space Plasmas ◽  
Charge Effects ◽  
Novel Technique ◽  
Solitary Structures ◽  
Spatial Dimensions ◽  
Electric Potentials ◽  
Linear And Nonlinear

Abstract. Dispersive properties of linear and nonlinear MHD waves, including shear, kinetic, electron inertial Alfvén, and slow and fast magnetosonic waves are analyzed using both analytical expansions and a novel technique of dispersion diagrams. The analysis is extended to explicitly include space charge effects in non-neutral plasmas. Nonlinear soliton solutions, here called alfvenons, are found to represent either convergent or divergent electric field structures with electric potentials and spatial dimensions similar to those observed by satellites in auroral regions. Similar solitary structures are postulated to be created in the solar corona, where fast alfvenons can provide acceleration of electrons to hundreds of keV during flares. Slow alfvenons driven by chromospheric convection produce positive potentials that can account for the acceleration of solar wind ions to 300–800 km/s. New results are discussed in the context of observations and other theoretical models for nonlinear Alfvén waves in space plasmas.

scholarly journals Darboux transformation for classical acoustic spectral problem

2003 ◽  
Vol 2003 (49) ◽  
pp. 3123-3142 ◽  
Author(s):  
A. A. Yurova ◽  
A. V. Yurov ◽  
M. Rudnev
Keyword(s):  
Spectral Problem ◽  
Inhomogeneous Medium ◽  
Darboux Transformation ◽  
Maxwell Equations ◽  
Soliton Solutions ◽  
Moutard Transformation ◽  
Acoustic Problem ◽  
Spatial Dimensions ◽  
Dielectric Permitivity ◽  
Harry Dym Equation

We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows steps similar to those for the Schrödinger operator. However, there is no one-to-one correspondence between the two problems. The technique developed enables one to construct new families of integrable potentials for the acoustic problem, in addition to those already known. The acoustic problem produces a nonlinear Harry Dym PDE. Using the technique, we reproduce a pair of simple soliton solutions of this equation. These solutions are further used to construct a new positon solution for this PDE. Furthermore, using the dressing-chain approach, we build a modified Harry Dym equation together with its LA pair. As an application, we construct some singular and nonsingular integrable potentials (dielectric permitivity) for the Maxwell equations in a 2D inhomogeneous medium.

Oblique nonlinear Alfvén waves in strongly magnetized beam plasmas. Part 2. Soliton solutions and integrability

1993 ◽  
Vol 50 (3) ◽  
pp. 457-476 ◽  
Author(s):  
Bernard Deconinck ◽  
Peter Meuris ◽  
Frank Verheest
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Mhd Waves ◽  
Displacement Current ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

Oblique propagation of MHD waves in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation, and hence requires a new approach to solitary-wave solutions, integrability and related problems. The new equation is shown to be integrable by the use of the prolongation method, and by finding a sufficient number of conservation laws, and possesses bright and dark soliton solutions, besides possible periodic solutions.

scholarly journals Excitation of kinetic Alfvén turbulence by MHD waves and energization of space plasmas

2004 ◽  
Vol 11 (5/6) ◽  
pp. 535-543 ◽  
Author(s):  
Y. Voitenko ◽  
M. Goossens
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Energy Transport ◽  
Plasma Heating ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Space Plasmas ◽  
Small Scale ◽  
The Magnetic Field ◽  
Dissipation Range

Abstract. There is abundant observational evidence that the energization of plasma particles in space is correlated with an enhanced activity of large-scale MHD waves. Since these waves cannot interact with particles, we need to find ways for these MHD waves to transport energy in the dissipation range formed by small-scale or high-frequency waves, which are able to interact with particles. In this paper we consider the dissipation range formed by the kinetic Alfvén waves (KAWs) which are very short- wavelengths across the magnetic field irrespectively of their frequency. We study a nonlocal nonlinear mechanism for the excitation of KAWs by MHD waves via resonant decay AW(FW)→KAW1+KAW2, where the MHD wave can be either an Alfvén wave (AW), or a fast magneto-acoustic wave (FW). The resonant decay thus provides a non-local energy transport from large scales directly in the dissipation range. The decay is efficient at low amplitudes of the magnetic field in the MHD waves, B/B0~10-2. In turn, KAWs are very efficient in the energy exchange with plasma particles, providing plasma heating and acceleration in a variety of space plasmas. An anisotropic energy deposition in the field-aligned degree of freedom for the electrons, and in the cross-field degrees of freedom for the ions, is typical for KAWs. A few relevant examples are discussed concerning nonlinear excitation of KAWs by the MHD wave flux and consequent plasma energization in the solar corona and terrestrial magnetosphere.

Optical bright, dark and dipole solitons with derivative nonlinearity in the presence of parity-time-symmetric lattices

2020 ◽  
Vol 34 (16) ◽  
pp. 2050174
Author(s):  
Asad Zubair ◽  
Nauman Raza
Keyword(s):  
Nonlinear Medium ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Arbitrary Power ◽  
Derivative Term ◽  
Linear And Nonlinear ◽  
New Formula ◽  
Singular Soliton ◽  
Engineering Scheme

This paper deals with the study of optical solitons in the presence of new linear and nonlinear parity-time [Formula: see text]-symmetric modulation lattices. The nonlinear medium is a derivative term with arbitrary power. Inverse engineering scheme is utilized to retrieve bright, dark, dipole and singular soliton solutions. These solutions are presented for four new [Formula: see text]-symmetric potentials. The results reveal that optical bright, dark and dipole solitons can exist for those new physical settings.

scholarly journals Determination of wave vectors using the phase differencing method

2013 ◽  
Vol 31 (9) ◽  
pp. 1611-1617 ◽  
Author(s):  
S. N. Walker ◽  
I. Moiseenko
Keyword(s):  
Wave Packet ◽  
Correlation Length ◽  
Coherence Length ◽  
Low Frequency ◽  
Plasma Waves ◽  
Mhd Waves ◽  
Space Plasmas ◽  
The Waves ◽  
Theoretical Results

Abstract. Due to the collisionless nature of space plasmas, plasma waves play an important role in the redistribution of energy between the various particle populations in many regions of geospace. In order to fully comprehend such mechanisms it is necessary to characterise the nature of the waves present. This involves the determination of properties such as wave vector k. There are a number of methods used to calculate k based on the multipoint measurements that are now available. These methods rely on the fact that the same wave packet is simultaneously observed at two or more locations whose separation is small in comparison to the correlation length of the wave packet. This limitation restricts the analysis to low frequency (MHD) waves. In this paper we propose an extension to the phase differencing method to enable the correlation of measurements that were not made simultaneously but differ temporally by a number of wave periods. The method is illustrated using measurements of magnetosonic waves from the Cluster STAFF search coil magnetometer. It is shown that it is possible to identify wave packets whose coherence length is much less than the separation between the measurement locations. The resulting dispersion is found to agree with theoretical results.

Pseudo-three-dimensional convective cell motion in a magnetized plasma

1984 ◽  
Vol 31 (2) ◽  
pp. 231-238 ◽  
Author(s):  
P. K. Shukla ◽  
M. Y. Yu
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Mode Coupling ◽  
Three Dimensional ◽  
Convective Cell ◽  
Magnetized Plasma ◽  
Space Plasmas ◽  
Linear And Nonlinear ◽  
Convective Cells ◽  
Cell Motion

Linear and nonlinear mechanisms for generating convective cells with finite but small parallel (to the external magnetic field B0) wavelength are presented. The problems of mode-coupling as well as quasi-steady nonlinear mode structures are analytically studied. Possible applications in space plasmas are discussed.

Nonlinear effects in photothermal-optical-beam-deflection imaging

1986 ◽  
Vol 64 (9) ◽  
pp. 1269-1275 ◽  
Author(s):  
Grover C. Wetsel Jr. ◽  
James B. Spicer
Keyword(s):  
Thermal Effects ◽  
Nonlinear Optical ◽  
Nonlinear Effects ◽  
Theoretical Models ◽  
Optical Beam ◽  
Beam Deflection ◽  
Nonlinear Phenomena ◽  
Contrast Mechanisms ◽  
High Purity Aluminum ◽  
Linear And Nonlinear

Nonlinear phenomena have been observed during photothermal-optical-beam-deflection imaging experiments on samples of both high-purity aluminum and aluminum alloys. Evidence for nonlinear optical and thermal effects have been measured. Theoretical models have been developed as aids in understanding the different contrast mechanisms observed in linear and nonlinear photothermal images.

Parallel solitary Alfvén waves in warm multi-species beam-plasma systems. Part 2. Anisotropic pressures

1992 ◽  
Vol 47 (1) ◽  
pp. 25-37 ◽  
Author(s):  
Frank Verheest
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Soliton Solutions ◽  
Mhd Waves ◽  
Beam Plasma ◽  
Electric And Magnetic Fields ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Ion Species ◽  
Anisotropic Pressures

A nonlinear treatment is given for MHD waves that propagate parallel to the external magnetic field in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts. Both the wave electric and magnetic fields obey a derivative nonlinear Schrödinger equation. Soliton solutions are discussed, in particular for plasmas with two ion species.

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