1,108 research outputs found
Nonlinear theory of resonant slow MHD waves in twisted magnetic flux tubes
The nonlinear dynamics of resonant slow MHD waves in weakly dissipative plasmas is investigated in cylindrical geometry with a twisted equilibrium magnetic field. Linear theory has shown that the wave motion is governed by conservation laws and jump conditions across the resonant surface considered as a singularity – first derived in linear ideal MHD theory by Sakurai, Goossens and Hollweg [Solar Phys. 133, 227 (1991)]. By means of the simplified method of matched asymptotic expansions, we obtain the generalized connection formulae for the variables across the dissipative layer, and we derive a non-homogeneous nonlinear partial differential equation for the wave dynamics in the dissipative layer
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
Torsional Alfvén waves: magneto-seismology in static and dynamic coronal plasmas
Aims: We study the properties of torsional Alfvén waves in coronal loops so that they may be exploited for coronal seismological applications.
Methods: The governing equation is obtained for standing torsional Alfvén waves of a dynamic, gravitationally stratified plasma. The footpoints are assumed to obey line-tying conditions necessary for standing oscillations. Solutions are found in a number of different but typical scenarios to demonstrate the possibilities for both temporal and spatial magneto-seismology exploitation of waveguides with the standing torsional Alfvén oscillations.
Results: It is found that the frequency of the standing Alfvén oscillation increases as the stratification of the plasma increases. The ratio of the periods of the fundamental modeand the first overtone is also found to change as the stratification of the plasma increases. Further, the eigenfunctions of the higher overtones of the standing oscillations are found to experience a shift of their anti-nodes. The influence of a dynamic plasma on the amplitudes of the mode is also investigated. The amplitude of the torsional Alfvén mode is found to increase as the plasma within the coronal loop experiences cooling
Slow surface wave damping in plasmas with anisotropic viscosity and thermal conductivity
This paper studies the damping of slow surface MHD waves propagating along the equilibrium magnetic field on a finite-thickness magnetic interface. The plasma is assumed to be strongly magnetised, and the full Braginskii's expressions for viscosity and the heat flux are used. The primary focus of the paper is on the competition between resonant absorption in the thin dissipative layer embracing the ideal resonant position and the bulk wave damping due to viscosity and thermal conductivity as damping mechanisms for surface MHD waves. The dependence of the wave damping decrement on the wave length and the dissipative coefficients is studied. Application of the obtained results to the surface MHD wave damping in the solar chromosphere is discussed
Magneto-seismology of solar atmospheric loops by means of longitudinal oscillations
There is increasingly strong observational evidence that slow magnetoacoustic
modes arise in the solar atmosphere. Solar magneto-seismology is a novel tool
to derive otherwise directly un-measurable properties of the solar atmosphere
when magnetohydrodynamic (MHD) wave theory is compared to wave observations.
Here, MHD wave theory is further developed illustrating how information about
the magnetic and density structure along coronal loops can be determined by
measuring the frequencies of the slow MHD oscillations. The application to
observations of slow magnetoacoustic waves in coronal loops is discused.Comment: 4 pages, 2 figures, to appear in Proceedings of IAU Symp 286,
Comparative Magnetic Minima, C. H. Mandrini, ed
The effect of twisted magnetic field on the resonant absorption of MHD waves in coronal loops
The standing quasi modes in a cylindrical incompressible flux tube with
magnetic twist that undergoes a radial density structuring is considered in
ideal magnetohydrodynamics (MHD). The radial structuring is assumed to be a
linearly varying density profile. Using the relevant connection formulae, the
dispersion relation for the MHD waves is derived and solved numerically to
obtain both the frequencies and damping rates of the fundamental and
first-overtone modes of both the kink (m=1) and fluting (m=2,3) waves. It was
found that a magnetic twist will increase the frequencies, damping rates and
the ratio of the oscillation frequency to the damping rate of these modes. The
period ratio P_1/P_2 of the fundamental and its first-overtone surface waves
for kink (m=1) and fluting (m=2,3) modes is lower than 2 (the value for an
untwisted loop) in the presence of twisted magnetic field. For the kink modes,
particularly, the magnetic twists B_{\phi}/B_z=0.0065 and 0.0255 can achieve
deviations from 2 of the same order of magnitude as in the observations.
Furthermore, for the fundamental kink body waves, the frequency bandwidth
increases with increasing the magnetic twist.Comment: 18 pages, 9 figure
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
Heating of ions by low-frequency Alfv\'{e}n waves in partially ionized plasmas
In the solar atmosphere, the chromospheric and coronal plasmas are much
hotter than the visible photosphere. The heating of the solar atmosphere,
including the partially ionized chromosphere and corona, remains largely
unknown. In this paper we demonstrate that the ions can be substantially heated
by Alfv\'{e}n waves with very low frequencies in partially ionized low beta
plasmas. This differs from other Alfv\'{e}n wave related heating mechanisms
such as ion-neutral collisional damping of Alfv\'{e}n waves and heating
described by previous work on resonant Alfv\'{e}n wave heating. In this paper,
we find that the non-resonant Alfv\'{e}n wave heating is less efficient in
partially ionized plasmas than when there are no ion-neutral collisions, and
the heating efficiency depends on the ratio of the ion-neutral collision
frequency to the ion gyrofrequency.Comment: Published as Letter
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