Dark and grey compressional dispersive Alfvén solitons in plasmas

Shukła, P. K.; Eliasson, Bengt; Stenflo, L.

doi:10.1063/1.3602463

Cited by 22 publications

(12 citation statements)

References 12 publications

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“…Later, extensive work was done to examine the properties of this mode; see, e.g., Refs. [4][5][6][7][8]. Some of these works incorporated the effect of electron-ion collisions, so a compressional dispersive Alfvén (CDA) wave exists.…”

Section: Introductionmentioning

confidence: 99%

Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas

2012

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It is shown that the dynamics of amplitude-modulated compressional dispersive Alfvénic (CDA) waves in a collisional megnetoplasma is governed by a complex Ginzburg-Landau (CGL) equation. The nonlinear dispersion relation for the modulational instability of the CDA waves is derived and investigated numerically. It is found that the growth rate of the modulational instability decreases (increases) with the increase of the normalized electron-ion collision frequency α (the plasma β). The modulational instability criterion for the CGL equation is defined precisely and investigated numerically. The region of the modulational instability becomes narrower with the increase of α and β, indicating that the system dissipates the wave energy by collisions, and a stable CDA wave envelope packet in the form of a hole will be a dominant localized pulse. For a collisionless plasma, i.e., α=0, the CGL equation reduces to the standard nonlinear Schrödinger (NLS) equation. The latter is used to investigate the modulational (in)stability region for the CDA waves in a collisionless magnetoplasma. It is shown that, within unstable regions, a random set of nonlinearly interacting CDA perturbations leads to the formation of CDA rogue waves. In order to demonstrate that the characteristics of the CDA rogue waves are influenced by the plasma β, the relevant numerical analysis of the appropriate nonlinear solution of the NLS equation is presented. The application of our investigation to space and laboratory magnetoplasmas is discussed.

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Section: Introductionmentioning

confidence: 99%

Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas

2012

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“…Nonthermal SWDSA waves with sheared wave magnetic field and finite density fluctuations could be excited by free energy sources contained in electron and proton beams, as well as in magnetic shear. The present investigation is thus complimentary to our previous model [13,19,27], which focused on the electron heating in the solar corona by long-wavelength (in comparison with i r ) dispersive shear Alfvén waves whose parallel wavelength is of the order of the ion-skin-depth c ,…”

Section: Introductionmentioning

confidence: 79%

“…A number of mechanisms for heating electrons in the solar coronal and solar wind plasmas has been proposed [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], involving acoustic, Alfvén and cyclotron wave heating, as well as those associated with microstructures and nanoflares. In deciding which particular model is relevant for explaining observations, it is important to understand the plasma conditions where the heating processes are taking place, as well as to identify the free energy sources available for the plasma heating, how the energy is transported into the region, and how the transported electromagnetic wave energy is dissipated efficiently [24].…”

Section: Introductionmentioning

confidence: 99%

Solar coronal electron heating by short-wavelength dispersive shear Alfvén waves

et al. 2015

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The electron heating of the solar coronal plasma has remained one of the most important problems in solar physics. An explanation of the electron heating rests on the identification of the energy source and appropriate physical mechanisms via which the energy can be channelled to the electrons. Our objective here is to present an estimate for the electron heating rate in the presence of finite amplitude short-wavelength (in comparison with the ion gyroradius) dispersive shear Alfvén (SWDSA) waves that propagate obliquely to the ambient magnetic field direction in the solar corona. Specifically, it is demonstrated that SWDSA waves can significantly contribute to the solar coronal electron heating via collisionless heating involving SWDSA wave-electron interactions.

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“…In this paper we use the method of double reduction to find the exact solutions of a Cubic nonlinear Schrödinger Partial Differential equation. Experiments on compressional dispersive Alven(CDA) waves have been done before on [13] and [14] where the relationship between CDA waves and the pertubations were analysed. Further in [14], the amplitude of the waves in a magnetic electronpositron plasma was discussed.…”

Section: Introductionmentioning

confidence: 99%

Reductions and exact solutions of a cubic Schrodinger Partial Differential Equation

Masemola¹,

Phidane²

2019

Preprint

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Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this method together the generalized fundamental theorem of double reduction. In particular, Noether symmetries and some associated conservation laws are constructed in our investigation to find exact solutions of higher order partial differential equations and complex partial differential equations.

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Dark and grey compressional dispersive Alfvén solitons in plasmas

Abstract: The amplitude modulation of compressional dispersive Alfvén (CDA) waves in a low-β plasma is considered. It is shown that the dynamics of modulated CDA waves is governed by a cubic nonlinear Schrödinger equation, which depicts the formation of a dark/grey envelope CDA soliton

Cited by 22 publications

References 12 publications

Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas

Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas

Solar coronal electron heating by short-wavelength dispersive shear Alfvén waves

Reductions and exact solutions of a cubic Schrodinger Partial Differential Equation

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