Linear Visco-Resistive Computations of Magnetohydrodynamic Waves: II. Viscous Effects

1994 ◽  
Vol 144 ◽  
pp. 506-508
Author(s):  
R. Erdélyi ◽  
M. Goossens
Keyword(s):  
Stress Tensor ◽  
Resonant Absorption ◽  
Mhd Waves ◽  
Larmor Radius ◽  
Coronal Loops ◽  
Viscous Effects ◽  
Viscous Stress Tensor ◽  
Magnetohydrodynamic Waves ◽  
Finite Larmor Radius ◽  
Viscosity Coefficients

AbstractResonant absorption of MHD waves in coronal loops is studied in linear, viscous MHD. Viscosity is described by Braginskii’s viscosity stress tensor. The dependence of the process of resonant absorption on the viscosity coefficients is studied. The compressive viscosity and viscosity due to the finite Larmor radius do not produce absorption. Shear viscosity produces absorption and is a viable candidate for heating coronal loops. The width of the dissipation layer is found to be proportional to, whereη1is the shear viscous coefficient of the full viscous stress tensor.

Linear Visco-Resistive Computations of Magnetohydrodynamic Waves: I. The Code and Test Cases

1994 ◽  
Vol 144 ◽  
pp. 503-505
Author(s):  
R. Erdélyi ◽  
M. Goossens ◽  
S. Poedts
Keyword(s):  
Resonant Absorption ◽  
Numerical Code ◽  
Mhd Waves ◽  
Test Cases ◽  
Numerical Accuracy ◽  
Element Discretization ◽  
Flux Tubes ◽  
Magnetohydrodynamic Waves ◽  
Viscosity Coefficients ◽  
Magnetic Flux Tubes

AbstractThe stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. Our computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code.

Damping of magnetohydrodynamic waves by resonant absorption in the solar atmosphere

2005 ◽  
Vol 364 (1839) ◽  
pp. 433-446 ◽  
Author(s):  
M Goossens ◽  
J Andries ◽  
I Arregui
Keyword(s):  
Resonant Absorption ◽  
Mhd Waves ◽  
Coronal Loops ◽  
Two Dimensional ◽  
Heliospheric Observatory ◽  
Magnetohydrodynamic Waves ◽  
One Dimensional ◽  
Magnetic Structures ◽  
Different Types ◽  
Kink Waves

In the last decade we have been overwhelmed by an avalanche of discoveries of magnetohydrodynamic (MHD) waves by the Solar and Heliospheric Observatory and Transition Region and Coronal Explorer observatories. Both standing and propagating versions of fast magnetoacoustic and slow magnetoacoustic MHD waves have been detected. Information on the damping times and damping distances of these waves is less detailed and less accurate than that on periods and amplitudes. Nevertheless, observations show the damping times and damping lengths are often short. Also, different types of MHD waves in different types of magnetic structures likely require different damping mechanisms. The phenomenon of fast damping is well documented for the standing fast magnetosonic kink waves in coronal loops. This paper concentrates on standing fast magnetosonic waves. It reports on results on periods and damping times due to resonant absorption in one-dimensional and two-dimensional models of coronal loops. Special attention is given to multiple modes.

Evolution of nonlinear Alfvén waves propagating along the magnetic field in a collisionless plasma

1982 ◽  
Vol 28 (3) ◽  
pp. 459-468 ◽  
Author(s):  
M. Khanna ◽  
R. Rajaram
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Momentum Equation ◽  
Finite Amplitude ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Flr Effects ◽  
The Magnetic Field

It is shown that the asymptotic evolution of a finite-amplitude Alfvén wave propagating parallel to the uniform magnetic field in a warm homogeneous collisionless plasma is governed by the modified nonlinear Schrödinger equation. The dispersion is provided by the ion finite Larmor radius (FLR) effects in the momentum equation and the Hall current and electron pressure corrections to the generalized Ohm's law. In the cold plasma limit the equations reduce to those available in the literature. It is suggested that these calculations can have a bearing on the investigation of the structure of MHD waves in the solar wind.

scholarly journals A fluid description for Landau damping of dispersive MHD waves

2004 ◽  
Vol 11 (2) ◽  
pp. 245-258 ◽  
Author(s):  
T. Passot ◽  
P. L. Sulem
Keyword(s):  
Fluid Model ◽  
Collisionless Plasma ◽  
Alfven Waves ◽  
Landau Damping ◽  
Mhd Waves ◽  
Larmor Radius ◽  
Alfvén Waves ◽  
Weakly Nonlinear ◽  
Linear Character ◽  
Finite Larmor Radius

Abstract. The dynamics of long oblique MHD waves in a collisionless plasma permeated by a uniform magnetic field is addressed using a Landau-fluid model that includes Hall effect and electron-pressure gradient in a generalized Ohm's law and retains ion finite Larmor radius (FLR) corrections to the gyrotropic pressure (Phys. Plasmas 10, 3906, 2003). This one-fluid model, built to reproduce the weakly nonlinear dynamics of long dispersive Alfvén waves propagating along an ambient field, is shown to correctly capture the Landau damping of oblique magnetosonic waves predicted by a kinetic theory based on the Vlasov-Maxwell system. For oblique and kinetic Alfvén waves (for which second order FLR corrections are to be retained), the linear character of waves with small but finite amplitudes is established, and the dispersion relation reproduced in the regime of adiabatic protons and isothermal electrons, associated with the condition me/mp

scholarly journals Seismology of kink oscillations in coronal loops: Two decades of resonant damping

2007 ◽  
Vol 3 (S247) ◽  
pp. 228-242 ◽  
Author(s):  
Marcel Goossens
Keyword(s):  
Wave Theory ◽  
Resonant Absorption ◽  
Mhd Waves ◽  
Coronal Loops ◽  
Equilibrium Models ◽  
Kink Waves ◽  
The Common ◽  
Uniform Equilibrium ◽  
Transverse Oscillations ◽  
Alfven Velocity

AbstractThe detection of rapidly damped transverse oscillations in coronal loops by Aschwanden et al. (1999) and Nakariakov et al. (1999) gave a strong impetus to the study of MHD waves and their damping. The common interpretation of the observations of these oscillations is based on kink modes. This paper reviews how the observed period and damping time can be reproduced by MHD wave theory when non-uniform equilibrium models are considered that have a transversal variation of the local Alfven velocity. The key point here is that resonant absorption cannot be avoided and occurs as natural damping mechanism for kink waves in non-uniform equilibrium models. The present paper starts with work by Hollweg & Yang (1988) and discusses subsequent developments in theory and their applications to seismology of coronal loops. It addresses the consistent use of observations of periods and damping times as seismological tools within the framework of resonant absorption. It shows that within the framework of resonant absorption infinitely many equilibrium models can reproduce the observed values of periods and damping times.

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