scholarly journals Stability of the 3D incompressible MHD equations with horizontal dissipation in periodic domain

2021 ◽  
Vol 6 (11) ◽  
pp. 11837-11849
Author(s):  
Ruihong Ji ◽  
◽  
Ling Tian ◽  
Keyword(s):  
Magnetic Field ◽  
Stability Problem ◽  
Stability Result ◽  
Mhd Equations ◽  
Periodic Domain ◽  
Magnetic Diffusion ◽  
Partial Dissipation ◽  
Background Magnetic Field ◽  
The Stability ◽  
Incompressible Mhd

<abstract><p>The stability problem on the magnetohydrodynamics (MHD) equations with partial or no dissipation is not well-understood. This paper focuses on the 3D incompressible MHD equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the stability of perturbations near the steady solution given by a background magnetic field in periodic domain. The new stability result presented here is among few stability conclusions currently available for ideal or partially dissipated MHD equations.</p></abstract>

scholarly journals Global stability solution of the 2D MHD equations with mixed partial dissipation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yana Guo ◽  
Yan Jia ◽  
Bo-Qing Dong
Keyword(s):  
Magnetic Field ◽  
Global Stability ◽  
Mhd Equations ◽  
Bootstrap Argument ◽  
Partial Dissipation ◽  
Background Magnetic Field ◽  
Mhd System

<p style='text-indent:20px;'>This paper is devoted to understanding the global stability of perturbations near a background magnetic field of the 2D magnetohydrodynamic (MHD) equations with partial dissipation. We establish the global stability for the solutions of the nonlinear MHD system by the bootstrap argument.</p>

scholarly journals On the Stability of Incompressible MHD Modes in Magnetic Cylinder with Twisted Magnetic Field and Flow

2018 ◽  
Vol 866 (2) ◽  
pp. 86 ◽  
Author(s):  
Oleg Cheremnykh ◽  
Viktor Fedun ◽  
Yu. Ladikov-Roev ◽  
Gary Verth
Keyword(s):  
Magnetic Field ◽  
The Stability ◽  
Incompressible Mhd

An exact solution in the stability of m. h. d. Couette flow

1972 ◽  
Vol 327 (1569) ◽  
pp. 269-278 ◽  
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Couette Flow ◽  
Stability Problem ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Mhd Stability ◽  
Arbitrary Magnetic Field ◽  
The Stability ◽  
Conducting Cylinders

The MHD stability problem for dissipative Couette flow in a narrow gap between corotating, conducting cylinders with an axial magnetic field is solved exactly. Results are presented for an arbitrary magnetic field; in particular, previous results on the zero and infinite magnetic field limits are verified.

Magnetosonic solitons in space plasmas: dark or bright solitons?

2007 ◽  
Vol 73 (6) ◽  
pp. 981-992 ◽  
Author(s):  
O. A. POKHOTELOV ◽  
O.G. ONISHCHENKO ◽  
M. A. BALIKHIN ◽  
L. STENFLO ◽  
P. K. SHUKLA
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Velocity Distribution Function ◽  
Mhd Equations ◽  
Space Plasmas ◽  
Ion Distribution ◽  
Loss Cone ◽  
Solitary Solution ◽  
Background Magnetic Field ◽  
The Magnetic Field

AbstractThe nonlinear theory of large-amplitude magnetosonic (MS) waves in highβ space plasmas is revisited. It is shown that solitary waves can exist in the form of ‘bright’ or ‘dark’ solitons in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion, which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived.It takes into account general plasma equilibria, such as the Dory–Guest–Harris (DGH) or Kennel–Ashour-Abdalla (KA) loss-cone equilibria, as well as distributions with a power-law velocity dependence that can be modelled by κdistributions. It is shown that in a bi-Maxwellian plasma the dispersion is negative, i.e. the phase velocity decreases with an increase of the wavenumber. This means that the solitary solution in this case has the form of a ‘bright’ soliton with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas, such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall–MHD equations are reviewed. The relevance of our theoretical results to existing satellite wave observations is outlined.

Instability of ion–ion hybrid waves in current-carrying collisional plasmas with two ion species

1979 ◽  
Vol 22 (1) ◽  
pp. 59-70 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Magnetic Field ◽  
Electrostatic Waves ◽  
Hybrid Frequency ◽  
Background Magnetic Field ◽  
Field Aligned Current ◽  
The Stability ◽  
Hybrid Waves ◽  
Simple Equations ◽  
Ion Species

The stability of electrostatic waves propagating at large angles with respect to the background magnetic field is studied in collisional, fully ionized plasmas with two types of ion species and carrying a field-aligned current. By considering plasmas with ma/mb ≪ Nb/Na ≪ mb/ma where m and N denote mass and density respectively and subscripts a and b refer to the two ion species, a complicated dispersion relation is reduced to two simple equations for the determination of the real and imaginary parts of the frequency. It is found that, under appropriate conditions, an instability occurs at frequencies slightly above but very close to the ion–ion hybrid frequency. The growth rate scales directly as the electron–ion collisional frequency.

Magnetic Field

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Background Field ◽  
Magnetohydrodynamic Equations ◽  
Electrically Conducting ◽  
Background Magnetic Field ◽  
Nonlinear Simulations ◽  
Uniform Background ◽  
The Stability ◽  
2D Model

This chapter focuses on magnetoconvection, which refers to thermal convection of an electrically conducting fluid within a background magnetic field maintained by some external mechanism. It first provides a brief overview of magnetohydrodynamics and the magnetohydrodynamic equations before explaining how to make a 2D model of magnetic field. In this approach, the case of a uniform vertical background field and the case of a uniform horizontal background field are both considered. The chapter then describes how one could simulate a case of a uniform background field that is tilted relative to both the vertical and horizontal axes. It also considers what can be learned about the stability and structure of magnetoconvection and the dispersion relation for magneto-gravity waves from analytical analyses without the nonlinear terms. Finally, it discusses nonlinear simulations of magnetoconvection in a box with impermeable side boundaries, along with magnetoconvection with a horizontal background field and an arbitrary background field.

A cosmic-ray-driven plasma instability

1989 ◽  
Vol 41 (1) ◽  
pp. 89-95 ◽  
Author(s):  
G. P. Zank
Keyword(s):  
Magnetic Field ◽  
Cosmic Rays ◽  
Thermal Plasma ◽  
Cosmic Ray ◽  
Mhd Equations ◽  
Mutual Interaction ◽  
Shock Acceleration ◽  
Wave Effects ◽  
The Stability

The stability of the MHD equations describing the mutual interaction of cosmic rays, thermal plasma, magnetic field and Alfvén waves used in cosmic-ray-shock acceleration theory (e.g. McKenzie & Völk 1982) is analysed for linear compressive instabilities. It is found that the inclusion of wave effects implies that the forward propagating sub-Alfvénic mode is unstable on wavelength scales greater than 1 parsec. The role of the instability in astrophysical models is considered.

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