A new decay channel for compressional Alfvén waves in plasmas

AbstractWe present a new efficient wave decay channel involving nonlinear interactions between a compressional Alfvén wave, a kinetic Alfvén wave, and a modified ion sound wave in a magnetized plasma. It is found that the wave coupling strength of the ideal magnetohydrodynamic (MHD) theory is much increased when the effects due to the Hall current are included in a Hall–MHD description of wave–wave interactions. In particular, with a compressional Alfvén pump wave well described by the ideal MHD theory, we find that the growth rate is very high when the decay products have wavelengths of the order of the ion thermal gyroradius or shorter, in which case they must be described by the Hall–MHD equations. The significance of our results to the heating of space and laboratory plasmas as well as for the Solar corona and interstellar media are highlighted.

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Axisymmetric Magnetohydrodynamic Equilibria without a Wall

Zeitschrift für Naturforschung A ◽

10.1515/zna-1993-1201 ◽

1993 ◽

Vol 48 (12) ◽

pp. 1131-1150

Author(s):

D. Lortz ◽

W. Haimerl

Keyword(s):

Magnetic Field ◽

Homogeneous Magnetic Field ◽

Mhd Equations ◽

External Current ◽

Flux Function ◽

Plasma Torus ◽

Ideal Magnetohydrodynamic ◽

Axisymmetric Configuration ◽

A Current ◽

The Ideal

Abstract Starting from the ideal magnetohydrodynamic (MHD) equations, we consider the following axisymmetric configuration: a current-carrying plasma torus in a homogeneous magnetic field that is aligned parallel to the torus axis. At a certain field strength this configuration is in equilibrium without need of external current singularities such as wires or walls.The magnetic flux function is expanded in small inverse aspect ratio. The geometry of this configuration is completely determined to second order as a function of the profile parameters.

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DYNAMO EFFECTS IN MAGNETIZED IDEAL PLASMA COSMOLOGIES

International Journal of Modern Physics A ◽

10.1142/s0217751x08039542 ◽

2008 ◽

Vol 23 (11) ◽

pp. 1697-1710 ◽

Cited By ~ 1

Author(s):

KOSTAS KLEIDIS ◽

APOSTOLOS KUIROUKIDIS ◽

DEMETRIOS PAPADOPOULOS ◽

LOUKAS VLAHOS

Keyword(s):

Magnetic Field ◽

Cosmological Model ◽

Homogeneous Magnetic Field ◽

Mhd Equations ◽

Cosmological Perturbations ◽

Gravitational Instabilities ◽

Ideal Magnetohydrodynamic ◽

The Magnetic Field ◽

Ideal Plasma ◽

The Ideal

The excitation of cosmological perturbations in an anisotropic cosmological model and in the presence of a homogeneous magnetic field has been studied, using the ideal magnetohydrodynamic (MHD) equations. In this case, the system of partial differential equations which governs the evolution of the magnetized cosmological perturbations can be solved analytically. Our results verify that fast-magnetosonic modes propagating normal to the magnetic field, are excited. But, what is most important, is that, at late times, the magnetic-induction contrast(δB/B) grows, resulting in the enhancement of the ambient magnetic field. This process can be particularly favored by condensations, formed within the plasma fluid due to gravitational instabilities.

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Structures of reconnection layers based on the ideal magnetohydrodynamic equations

Journal of Plasma Physics ◽

10.1017/s0022377800017645 ◽

1994 ◽

Vol 51 (3) ◽

pp. 381-398

Author(s):

Wenlong Dai ◽

Paul R. Woodward

Keyword(s):

Numerical Simulations ◽

Quantitative Agreement ◽

Mhd Equations ◽

Riemann Solver ◽

Magnetohydrodynamic Equations ◽

One Dimensional ◽

Ideal Mhd ◽

Ideal Magnetohydrodynamic ◽

The One ◽

The Ideal

A Riemann solver is used, and a set of numerical simulations are performed, to study the structures of reconnection layers in the approximation of the one- dimensional ideal MHD equations. Since the Riemann solver may solve general Riemarin problems, the model used in this paper is more general than those in previous investigations on this problem. Under the conditions used in the previous investigations, the structures we obtained are the same. Our numerical simulations show quantitative agreement with those obtained through the Riemann solver.

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Remarks on the parallel propagation of small-amplitude dispersive Alfvénic waves

Nonlinear Processes in Geophysics ◽

10.5194/npg-6-169-1999 ◽

1999 ◽

Vol 6 (3/4) ◽

pp. 169-178 ◽

Cited By ~ 21

Author(s):

S. Champeaux ◽

D. Laveder ◽

T. Passot ◽

P. L. Sulem

Keyword(s):

Nonlinear Dynamics ◽

Speed Of Sound ◽

Small Amplitude ◽

Modulational Instability ◽

Wave Train ◽

Nonlinear Effects ◽

Mhd Equations ◽

Alfven Wave ◽

Expected Time ◽

Hall Mhd

Abstract. The envelope formalism for the description of a small-amplitude parallel-propagating Alfvén wave train is tested against direct numerical simulations of the Hall-MHD equations in one space dimension where kinetic effects are neglected. It turns out that the magnetosonic-wave dynamics departs from the adiabatic approximation not only near the resonance between the speed of sound and the Alfvén wave group velocity, but also when the speed of sound lies between the group and phase velocities of the Alfvén wave. The modulational instability then does not anymore affect asymptotically large scales and strong nonlinear effects can develop even in the absence of the decay instability. When the Hall-MHD equations are considered in the long-wavelength limit, the weakly nonlinear dynamics is accurately reproduced by the derivative nonlinear Schrödinger equation on the expected time scale, provided no decay instabilities are present. The stronger nonlinear regime which develops at later time is captured by including the coupling to the nonlinear dynamics of the magnetosonic waves.

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Alfven wave interactions within the Hall-MHD description

Journal of Plasma Physics ◽

10.1017/s0022377813000640 ◽

2013 ◽

Vol 79 (5) ◽

pp. 909-911 ◽

Cited By ~ 5

Author(s):

G. BRODIN ◽

L. STENFLO

Keyword(s):

Alfven Wave ◽

Coupling Coefficients ◽

Wave Interactions ◽

Wave Coupling ◽

Mhd Model ◽

Model Equations ◽

Hall Mhd

AbstractWe show that comparatively simple expressions for the Alfven wave coupling coefficients can be deduced from the well-known Hall-magnetohydrodynamics (MHD) model equations.

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Global well-posedness of the full compressible Hall-MHD equations

Advances in Nonlinear Analysis ◽

10.1515/anona-2020-0178 ◽

2021 ◽

Vol 10 (1) ◽

pp. 1235-1254

Author(s):

Qiang Tao ◽

Canze Zhu

Keyword(s):

Global Solution ◽

Large Time ◽

Initial Temperature ◽

Large Time Behavior ◽

Initial Energy ◽

Mhd Equations ◽

Well Posedness ◽

Time Behavior ◽

Magnetohydrodynamic Flows ◽

Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

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