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 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>

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.

scholarly journals On global stability of thin ionized disks immersed in an external magnetic field

2008 ◽  
Vol 4 (S259) ◽  
pp. 111-112
Author(s):  
Edward Liverts ◽  
Michael Mond
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Global Stability ◽  
Initial Perturbation ◽  
Mhd Equations ◽  
Growth Time ◽  
Initial Value ◽  
Finite Systems ◽  
The Individual ◽  
Thin Disks

AbstractThe problem of the global stability of rotating magnetized thin disks is considered. The appropriate boundary value problem (BVP) of the linearized MHD equations is solved by employing the WKB approximation to describe the dynamical development of an initial perturbation. The eigenfrequencies as well as eigenfunctions are explicitly obtained and are verified numerically. The importance of considering the initial value problem (IVP) as well as the question of global stability for finite systems is emphasized and discussed in detail. It is further shown that thin enough disks are stable (global stability) but as their thickness grows increasing number of unstable modes participate in the solution of the IVP. However it is demonstrated that due to the localization of the initial perturbation the growth time of the instability may be significantly longer than the calculated inverse growth rate of the individual unstable eigenfunctions.

scholarly journals Resonant absorption of kink oscillations in coronal flux tubes with continuous magnetic twist

2019 ◽  
Vol 490 (2) ◽  
pp. 1644-1651 ◽  
Author(s):  
Zanyar Ebrahimi ◽  
Karam Bahari
Keyword(s):  
Magnetic Field ◽  
Resonant Absorption ◽  
Realistic Model ◽  
Mhd Equations ◽  
Flux Tubes ◽  
Kink Mode ◽  
Background Magnetic Field ◽  
Inhomogeneous Density ◽  
Kink Wave ◽  
Kink Waves

ABSTRACT There are observational evidences for the existence of twisted magnetic field in the solar corona. Here, we have investigated resonant damping of the magnetohydrodynamic (MHD) kink waves in magnetic flux tubes. A realistic model of the tube with continuous magnetic twist and radially inhomogeneous density profile has been considered. We have obtained the dispersion relation of the kink wave using the solution to the linear MHD equations outside the density inhomogeneity and the appropriate connection formula to the solutions across the thin transitional boundary layer. The dependence of the oscillation frequency and damping rate of the waves on the twist parameter and longitudinal wavenumber has been investigated. For the flux tube parameters considered in this paper, we obtain rapid damping of the kink waves comparable to the observations. In order to justify this rapid damping, depending on the sign of the azimuthal kink mode number, $m=+1$ or $-1$, the background magnetic field must have left- or right-handed twisted profile, respectively. For the model considered here, the resonant absorption occurs only when the twist parameter is in a range specified by the density contrast.

Parametric excitation of magnetoacoustic waves by a pump magnetic field in a high-β plasma

1977 ◽  
Vol 17 (1) ◽  
pp. 93-103 ◽  
Author(s):  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Parametric Excitation ◽  
Acoustic Waves ◽  
Magnetic Pressure ◽  
Gas Pressure ◽  
Alfven Wave ◽  
Fast Wave ◽  
Magnetoacoustic Waves ◽  
Background Magnetic Field ◽  
The Waves

The parametric excitation of slow, intermediate (Alfvén) and fast magneto-acoustic waves by a modulated spatially non-uniform magnetic field in a plasma with a finite ratio of gas pressure to magnetic pressure is considered. The waves are excited in pairs, either pairs of the same mode, or a pair of different modes. The growth rates of the instabilities are calculated and compared with the known result for the Alfvén wave in a zero gas pressure plasma. The only waves that are found not to be excited are the slow plus fast wave pair, and the intermediate plus slow or fast wave pair (unless the waves have a component of propagation direction perpendicular to both the background magnetic field and the direction of non-uniformity of the field).

scholarly journals On the differential system govering flows in magnetic field with data inLp

1998 ◽  
Vol 21 (2) ◽  
pp. 299-305 ◽  
Author(s):  
Fengxin Chen ◽  
Ping Wang ◽  
Chaoshun Qu
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Boundary Conditions ◽  
Differential System ◽  
Existence And Uniqueness ◽  
Mhd Equations ◽  
The Earth ◽  
Initial And Boundary Conditions ◽  
Time Existence ◽  
The Magnetic Field

In this paper we study the system governing flows in the magnetic field within the earth. The system is similar to the magnetohydrodynamic (MHD) equations. For initial data in spaceLp, we obtained the local in time existence and uniqueness ofweak solutions of the system subject to appropriate initial and boundary conditions.

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