4,614 research outputs found
Linear and nonlinear resonant interaction of sound waves in dissipative layers
The theory of resonant nonlinear magnetohydrodynamic (MHD) waves in dissipative steady plasmas developed by Ballai and Erdélyi is used to study the effect of steady flows on nonlinear resonant heating of MHD waves in (a) linear, (b) weakly and (c) strongly nonlinear approximations. Nonlinear connection formulae for slow MHD waves are derived. This nonlinear theory of driven MHD waves is then used to study the interaction of sound waves with one-dimensional isotropic steady plasmas.
We find that a steady equilibrium flow can significantly influence the efficiency of resonant absorption in the considered limits. In the case of strong nonlinearity, the efficiency of the resonant coupling is found to be proportional to the counterpart obtained in linear theory. The factor of proportion is approximately of the order of unity, justifying the commonly applied linear approximations
Nonlinear theory of non-axisymmetric resonant slow waves in straight magnetic flux tubes
Nonlinear resonant slow magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotropic plasmas for a cylindrical equilibrium model. The equilibrium magnetic field lines are unidirectional and parallel with the z axis. The nonlinear governing equations for resonant slow magnetoacoustic (SMA) waves are derived. Using the method of matched asymptotic expansions inside and outside the narrow dissipative layer, we generalize the connection formulae for the Eulerian perturbation of the total pressure and for the normal component of the velocity.
These nonlinear connection formulae in dissipative cylindrical MHD are an important extention of the connection formulae obtained in linear ideal MHD [Sakurai et al., Solar Phys. 133, 227 (1991)], linear dissipative MHD [Goossens et al., Solar Phys. 175, 75 (1995); Erdélyi, Solar Phys. 171, 49 (1997)] and in nonlinear dissipative MHD derived in slab geometry [Ruderman et al., Phys. Plasmas4, 75 (1997)]. These generalized connection formulae enable us to connect the solutions at both sides of the dissipative layer without solving the MHD equations in the dissipative layer. We also show that the nonlinear interaction of harmonics in the dissipative layer is responsible for generating a parallel mean flow outside the dissipative layer
On the nature of kink MHD waves in magnetic flux tubes
Magnetohydrodynamic (MHD) waves are often reported in the solar atmosphere
and usually classified as slow, fast, or Alfv\'en. The possibility that these
waves have mixed properties is often ignored. The goal of this work is to study
and determine the nature of MHD kink waves. This is done by calculating the
frequency, the damping rate and the eigenfunctions of MHD kink waves for three
widely different MHD waves cases: a compressible pressure-less plasma, an
incompressible plasma and a compressible plasma with non-zero plasma pressure
which allows for MHD radiation. In all three cases the frequency and the
damping rate are for practical purposes the same as they differ at most by
terms proportional to . In the magnetic flux tube the kink waves are
in all three cases, to a high degree of accuracy incompressible waves with
negligible pressure perturbations and with mainly horizontal motions. The main
restoring force of kink waves in the magnetised flux tube is the magnetic
tension force. The total pressure gradient force cannot be neglected except
when the frequency of the kink wave is equal or slightly differs from the local
Alfv\'{e}n frequency, i.e. in the resonant layer. Kink waves are very robust
and do not care about the details of the MHD wave environment. The adjective
fast is not the correct adjective to characterise kink waves. If an adjective
is to be used it should be Alfv\'{e}nic. However, it is better to realize that
kink waves have mixed properties and cannot be put in one single box
Spectral mixture analysis to assess post-fire vegetation regeneration using Landsat Thematic Mapper imagery: accounting for soil brightness variation
The effect of longitudinal flow on resonantly damped kink oscillations
The most promising mechanism acting towards damping the kink oscillations of
coronal loops is resonant absorption. In this context most of previous studies
neglected the effect of the obvious equilibrium flow along magnetic field
lines. The flows are in general sub-Alfv\'enic and hence comparatively slow.
Here we investigate the effect of an equilibrium flow on the resonant
absorption of linear kink MHD waves in a cylindrical magnetic flux tube with
the aim of determining the changes in the frequency of the forward and backward
propagating waves and in the modification of the damping times due to the flow.
A loop model with both the density and the longitudinal flow changing in the
radial direction is considered. We use the thin tube thin boundary (TTTB)
approximation in order to calculate the damping rates. The full resistive
eigenvalue problem is also solved without assuming the TTTB approximation.
Using the small ratio of flow and Alfv\'en speeds we derive simple analytical
expressions to the damping rate. The analytical expressions are in good
agreement with the resistive eigenmode calculations. Under typical coronal
conditions the effect of the flow on the damped kink oscillations is small when
the characteristic scale of the density layer is similar or smaller than the
characteristic width of the velocity layer. However, in the opposite situation
the damping rates can be significantly altered, specially for the backward
propagating wave which is undamped while the forward wave is overdamped
On the validity of nonlinear Alfvén resonance in space plasmas
Aims. In the approximation of linear dissipative magnetohydrodynamics (MHD), it can be shown that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfvén (or slow) frequency of a magnetic surface. This behaviour is confined to a thin region, known as the dissipative layer, which embraces the resonant magnetic surface. Although driven MHD waves have small dimensionless amplitude far away from the resonant surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. Our aim is to study the nonlinear effects in Alfvén dissipative layer
Methods. In the present paper, the method of simplified matched asymptotic expansions developed for nonlinear slow resonant waves is used to describe nonlinear effects inside the Alfvén dissipative layer.
Results. The nonlinear corrections to resonant waves in the Alfvén dissipative layer are derived, and it is proved that at the Alfvén resonance (with isotropic/anisotropic dissipation) wave dynamics can be described by the linear theory with great accuracy
Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads
We analyse the oscillatory properties of resonantly damped transverse kink
oscillations in two-dimensional prominence threads. The fine structures are
modelled as cylindrically symmetric magnetic flux tubes with a dense central
part with prominence plasma properties and an evacuated part, both surrounded
by coronal plasma. The equilibrium density is allowed to vary non-uniformly in
both the transverse and the longitudinal directions.We examine the influence of
longitudinal density structuring on periods, damping times, and damping rates
for transverse kink modes computed by numerically solving the linear resistive
magnetohydrodynamic (MHD) equations. The relevant parameters are the length of
the thread and the density in the evacuated part of the tube, two quantities
that are difficult to directly estimate from observations. We find that both of
them strongly influence the oscillatory periods and damping times, and to a
lesser extent the damping ratios. The analysis of the spatial distribution of
perturbations and of the energy flux into the resonances allows us to explain
the obtained damping times. Implications for prominence seismology, the physics
of resonantly damped kink modes in two-dimensional magnetic flux tubes, and the
heating of prominence plasmas are discussed.Comment: 12 pages, 9 figures, A&A accepte
Nonlinear effects in resonant layers in solar and space plasmas
The present paper reviews recent advances in the theory of nonlinear driven
magnetohydrodynamic (MHD) waves in slow and Alfven resonant layers. Simple
estimations show that in the vicinity of resonant positions the amplitude of
variables can grow over the threshold where linear descriptions are valid.
Using the method of matched asymptotic expansions, governing equations of
dynamics inside the dissipative layer and jump conditions across the
dissipative layers are derived. These relations are essential when studying the
efficiency of resonant absorption. Nonlinearity in dissipative layers can
generate new effects, such as mean flows, which can have serious implications
on the stability and efficiency of the resonance
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