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1.
The oscillatory modes of a magnetically twisted compressible flux tube embedded in a compressible magnetic environment are investigated in cylindrical geometry. Solutions to the governing equations to linear wave perturbations are derived in terms of Whittaker’s functions. A general dispersion equation is obtained in terms of Kummer’s functions for the approximation of weak and uniform internal twist, which is a good initial working model for flux tubes in solar applications. The sausage, kink and fluting modes are examined by means of the derived exact dispersion equation. The solutions of this general dispersion equation are found numerically under plasma conditions representative of the solar photosphere and corona. Solutions for the phase speed of the allowed eigenmodes are obtained for a range of wavenumbers and varying magnetic twist. Our results generalise previous classical and widely applied studies of MHD waves and oscillations in magnetic loops without a magnetic twist. Potential applications to solar magneto-seismology are discussed. 相似文献
2.
Twisted magnetic flux tubes are of considerable interest because of their natural occurrence from the Sun’s interior, throughout
the solar atmosphere and interplanetary space up to a wide range of applicabilities to astrophysical plasmas. The aim of the
present work is to obtain analytically a dispersion equation of linear wave propagation in twisted incompressible cylindrical
magnetic waveguides and find appropriate solutions for surface, body and pseudobody sausage modes (i.e. m = 0) of a twisted magnetic flux tube embedded in an incompressible but also magnetically twisted plasma. Asymptotic solutions
are derived in long- and short-wavelength approximations. General solutions of the dispersion equation for intermediate wavelengths
are obtained numerically. We found, that in case of a constant, but non-zero azimuthal component of the equilibrium magnetic
field outside the flux tube the index ν of Bessel functions in the dispersion relation is not integer any more in general.
This gives rise to a rich mode-structure of degenerated magneto-acoustic waves in solar flux tubes. In a particular case of
a uniform magnetic twist the total pressure is found to be constant across the boundary of the flux tube. Finally, the effect
of magnetic twist on oscillation periods is estimated under solar atmospheric conditions. It was found that a magnetic twist
will increase, in general, the periods of waves approximately by a few percent when compared to their untwisted counterparts. 相似文献
3.
The solar corona, modeled by a low-, resistive plasma slab, sustains MHD wave propagations due to footpoint motions in the photosphere. Simple test cases are undertaken to verify the code. Uniform, smooth and steep density, magnetic profile and driver are considered. The numerical simulations presented here focus on the evolution and properties of the Alfvén, fast and slow waves in coronal loops. The plasma responds to the footpoint motion by kink or sausage waves depending on the amount of shear in the magnetic field. The larger twist in the magnetic field of the loop introduces more fast-wave trapping and destroys initially developed sausage-like wave modes. The transition from sausage to kink waves does not depend much on the steep or smooth profile. The slow waves develop more complex fine structures, thus accounting for several local extrema in the perturbed velocity profiles in the loop. Appearance of the remnants of the ideal singularities characteristic of ideal plasma is the prominent feature of this study. The Alfvén wave which produces remnants of the ideal x
–1 singularity, reminiscent of Alfvén resonance at the loop edges, becomes less pronounced for larger twist. Larger shear in the magnetic field makes the development of pseudo-singularity less prominent in case of a steep profile than that in case of a smooth profile. The twist also causes heating at the edges, associated with the resonance and the phase mixing of the Alfvén and slow waves, to slowly shift to layers inside the slab corresponding to peaks in the magnetic field strength. In addition, increasing the twist leads to a higher heating rate of the loop. Remnants of the ideal log ¦x¦ singularity are observed for fast waves for larger twist. For slow waves they are absent when the plasma experiences large twist in a short time. The steep profiles do not favour the creation of pseudo-singularities as easily as in the smooth case. 相似文献
4.
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 two (the value for an untwisted loop) in the presence of twisted magnetic field. For the kink modes, particularly, the magnetic twists B φ /B z =0.0065 and 0.0255 can achieve deviations from two of the same order of magnitude as in the observations. Furthermore, for the fundamental kink body waves, the frequency band width increases with increasing magnetic twist. 相似文献
5.
The theory of magnetohydrodynamic (MHD) waves in solar coronal slabs in a zero-β configuration and for parallel propagation of waves does not allow the existence of surface waves. When oblique propagation
of perturbations is considered, both surface and body waves are able to propagate. When the perpendicular wavenumber is larger
than a certain value, the body kink mode becomes a surface wave. In addition, a sausage surface mode is found below the internal
cutoff frequency. When nonuniformity in the equilibrium is included, surface and body modes are damped by resonant absorption.
In this paper, first, a normal-mode analysis is performed and the period, the damping rate, and the spatial structure of the
eigenfunctions are obtained. Then, the time-dependent problem is solved, and the conditions under which one or the other type
of mode is excited are investigated. 相似文献
6.
The propagation of magnetohydrodynamic (MHD) waves is an area that has been thoroughly studied for idealised static and steady state magnetised plasma systems applied to numerous solar structures. By applying the generalisation of a temporally varying background density to an open magnetic flux tube, mimicking the observed slow evolution of such waveguides in the solar atmosphere, further investigations into the propagation of both fast and slow MHD waves can take place. The assumption of a zero-beta plasma (no gas pressure) was applied in Williamson and Erdélyi (Solar Phys. 2013, doi: 10.1007/s11207-013-0366-9 , Paper I) is now relaxed for further analysis here. Firstly, the introduction of a finite thermal pressure to the magnetic flux tube equilibrium modifies the existence of fast MHD waves which are directly comparable to their counterparts found in Paper I. Further, as a direct consequence of the non-zero kinetic plasma pressure, a slow MHD wave now exists, and is investigated. Analysis of the slow wave shows that, similar to the fast MHD wave, wave amplitude amplification takes place in time and height. The evolution of the wave amplitude is determined here analytically. We conclude that for a temporally slowly decreasing background density both propagating magnetosonic wave modes are amplified for over-dense magnetic flux tubes. This information can be very practical and useful for future solar magneto-seismology applications in the study of the amplitude and frequency properties of MHD waveguides, e.g. for diagnostic purposes, present in the solar atmosphere. 相似文献
7.
Yu. G. Kopylova A. V. Melnikov A. V. Stepanov Yu. T. Tsap T. B. Goldvarg 《Astronomy Letters》2007,33(10):706-713
The dispersion properties of the sausage eigenmodes of oscillations in a thin magnetic flux tube are numerically analyzed in terms of ideal magnetohydrodynamics (MHD). The period of the modes accompanied by the emission of MHD waves into the surrounding medium, which leads to acoustic damping of oscillations, is determined by the radius of the tube, not by its length. The dissipation of the sausage oscillations in comparatively high (?0.7R ⊙) and tenuous (?6 × 108 cm?3) coronal loops is considered. Their Q factor has bound found to be determined by the acoustic damping mechanism. The ratio of the plasma densities outside and inside the loop and the characteristic height of the emission source have been estimated by assuming the quasi-periodic pulsations of meter-wavelength radio emission to be related to the sausage oscillations. 相似文献
8.
The effects of both density stratification and magnetic field expansion on torsional Alfvén waves in magnetic flux tubes are
studied. The frequencies, the period ratio P
1/P
2 of the fundamental and its first-overtone, and eigenfunctions of torsional Alfvén modes are obtained. Our numerical results
show that the density stratification and magnetic field expansion have opposite effects on the oscillating properties of torsional
Alfvén waves. 相似文献
9.
Analytical models of solar atmospheric magnetic structures have been crucial for our understanding of magnetohydrodynamic (MHD) wave behaviour and in the development of the field of solar magneto-seismology. Here, an analytical approach is used to derive the dispersion relation for MHD waves in a magnetic slab of homogeneous plasma enclosed on its two sides by non-magnetic, semi-infinite plasma with different densities and temperatures. This generalises the classic magnetic slab model, which is symmetric about the slab. The dispersion relation, unlike that governing a symmetric slab, cannot be decoupled into the well-known sausage and kink modes, i.e. the modes have mixed properties. The eigenmodes of an asymmetric magnetic slab are better labelled as quasi-sausage and quasi-kink modes. Given that the solar atmosphere is highly inhomogeneous, this has implications for MHD mode identification in a range of solar structures. A parametric analysis of how the mode properties (in particular the phase speed, eigenfrequencies, and amplitudes) vary in terms of the introduced asymmetry is conducted. In particular, avoided crossings occur between quasi-sausage and quasi-kink surface modes, allowing modes to adopt different properties for different parameters in the external region. 相似文献
10.
Examination of thermal plasma data obtained by low-altitude satellite measurements indicates that the intersection of the cusp in the dayside magnetosphere with the topside ionosphere creates a distinct plasma geometry at low altitudes. This region consists of one or two plasma discontinuities with steep boundaries. As a result of the plasma structuring in the cusp which commonly takes place in the winter hemisphere, the propagation of compressional surface MHD waves is supported. This point is illustrated by an analysis of the polarization state of compressional surface MHD waves propagating along a plasma layer with thickness a and ambient magnetic field B0 parallel to the interfaces. The results obtained are applicable to the case of a single interface, which is derived in the limit a → ∞. In the general case the polarization of the compressional surface MHD waves in the plane transverse to the magnetic field B0 is elliptical. This feature of the polarization state of the compressional surface modes does not follow from the former analysis by Edwin and Roberts (1982, Solar Phys. 76, 239) for a magnetic slab, because the disturbance components parallel to the interfaces and perpendicular to the magnetic field B0 have not been examined. Although the absence of these components does not prove to be essential for deriving the exact dispersion equation for arbitrary wave directions of the surface modes, they must be included when considering polarization states. The surface mode polarization in the plasma layer changes its sense three times: at interfaces X = 0 and X = a and in the middle plane X = a/2. For the symmetrical (sausage) mode the wave disturbance component bn transverse (normal) to the interfaces becomes zero in the middle plane; for the asymmetrical (kink) mode, the component bt parallel to the interfaces and transverse to the ambient magnetic field is zeroed in the same plane. For a moving observer such as a satellite the polarization patterns which might be recorded change, depending on the velocity of the observer and the angles at which the layered cusp is traversed. An essential feature in the polarization of the compressional surface MHD modes is the presence of jumps in the magnetic disturbance component bt at the interfaces. These jumps disappear only for propagation along the ambient magnetic field. In this particular case the component bt vanishes and then the surface modes are undistinguishable from the body modes. 相似文献
11.
Three-dimensional numerical simulations have been used to study the scattering of a surface-gravity wave packet by vertical
magnetic-flux tubes, with radii from 200 km to 3 Mm, embedded in stratified polytropic atmosphere. The scattered wave has
been found to consist primarily of m=0 (axisymmetric) and m=1 modes. The ratio of the amplitude of these two modes was found to be strongly dependent on the radius of the flux tube.
The kink mode is the dominant mode excited in tubes with a small radius, while the sausage mode is dominant for large tubes.
Simulations of this type provide a simple, efficient, and robust way to start to understand the seismic signature of flux
tubes, which have recently begun to be observed. 相似文献
12.
The temporal evolution of ducted waves under coronal conditions is studied in the framework of linearized low MHD by means of numerical simulations. Coronal loops are represented by smoothed slabs of enhanced gas density embedded within a uniform magnetic field. The simulations show that for a smoothed density profile there is an energy leakage from the slab, associated with the propagation of sausage and kink waves. Wave energy leakage in the kink wave is generally small, whereas the wave energy in sausage waves leaks more strongly for long wavelengths and smoother slabs. 相似文献
13.
The propagation of linear and non-linear magnetohydrodynamic (MHD) waves in a straight homogeneous cylindrical magnetic flux tube embedded in a homogeneous magnetic environment is investigated. Both the tube and its environment are in steady state. Steady flows break the symmetry of forward (field-aligned) and backward (anti-parallel to magnetic field) propagating MHD wave modes because of the induced Doppler shifts. It is shown that strong enough flows change the sense of propagation of MHD waves. The flow also induces shifts in cut-off values and phase-speeds of the waves. Under photospheric conditions, if the flow is strong enough, the slow surface modes may disappear and the fast body modes may become present. The crossing of modes is also observed due to the presence of flows. The effect of steady-state background has to be considered particularly carefully when evaluating observation signatures of MHD waves for diagnostics in the solar atmosphere. 相似文献
14.
The magnetosonic modes of magnetic plasma structures in the solar atmosphere are considered taking into account steady flows of plasma in the internal and external media and using a slab geometry. The investigation brings nearer the theory of magnetosonic waveguides, in such structures as coronal loops and photospheric flux tubes, to realistic conditions of the solar atmosphere. The general dispersion relation for the magnetosonic modes of a magnetic slab in magnetic surroundings is derived, allowing for field-aligned steady flows in either region. It is shown that flows change both qualitatively and quantitatively the characteristics of magnetosonic modes. The flow may lead to the appearance of a new type of trapped mode, namelybackward waves. These waves are the usual slab modes propagating in the direction opposite to the internal flow, but advected with the flow. The disappearance of some modes due to the flow is also demonstrated.The results are applied to coronal and photospheric magnetic structures. In coronal loops, the appearance of backward slow body waves or the disappearance of slow body waves, depending upon the direction of propagation, is possible if the flow speed exceeds the internal sound speed ( 300 km s–1). In photospheric tubes, the disappearance of fast surface and slow body waves may be caused by an external downdraught of about 3 km s–1. 相似文献
15.
We investigated the propagation of kink waves in thin and isothermal expanding flux tubes in cylindrical geometry. By using the method of radial expansion for fluctuating variables we obtained a new kink wave equation. We show that including the radial component of the tube magnetic field leads to cutoff-free propagation of kink waves along thin flux tubes. 相似文献
16.
In the current study we present ab initio numerical computations of the generation and propagation of longitudinal waves in magnetic flux tubes embedded in the atmospheres of late-type stars. The interaction between convective turbulence and the magnetic structure is computed and the obtained longitudinal wave energy flux is used in a self-consistent manner to excite the small-scale magnetic flux tubes. In the current study we reduce the number of assumptions made in our previous studies by considering the full magnetic wave energy fluxes and spectra as well as time-dependent ionization (TDI) of hydrogen, employing multi-level Ca II atomic models, and taking into account departures from local thermodynamic equilibrium. Our models employ the recently confirmed value of the mixing-length parameter \(\alpha=1.8\). Regions with strong magnetic fields (magnetic filling factors of up to 50%) are also considered in the current study.The computed Ca II emission fluxes show a strong dependence on the magnetic filling factors, and the effect of time-dependent ionization (TDI) turns out to be very important in the atmospheres of late-type stars heated by acoustic and magnetic waves. The emitted Ca II fluxes with TDI included into the model are decreased by factors that range from 1.4 to 5.5 for G0V and M0V stars, respectively, compared to models that do not consider TDI.The results of our computations are compared with observations. Excellent agreement between the observed and predicted basal flux is obtained. The predicted trend of Ca II emission flux with magnetic filling factor and stellar surface temperature also agrees well with the observations but the calculated maximum fluxes for stars of different spectral types are about two times lower than observations. Though the longitudinal MHD waves considered here are important for chromosphere heating in high activity stars, additional heating mechanism(s) are apparently present. 相似文献
17.
The exact nonlinear cylindrical solution for incompressible Hall – magnetohydrodynamic (HMHD) waves, including dissipation,
essentially from electron – neutral collisions, is obtained in a uniformly rotating, weakly ionized plasma such as exists
in photospheric flux tubes. The ω – k relation of the waves, called here Hall – MHD waves, demonstrates the dispersive nature of the waves, introduced by the Hall
effect, at large axial and radial wavenumbers. The Hall – MHD waves are in general elliptically polarized. The partially ionized
plasma supports lower frequency modes, lowered by the factor δ≡ratio of the ion mass density to the neutral particle mass density, as compared to the fully ionized plasma (δ=1). The relation between the velocity and the magnetic field fluctuations departs significantly from the equipartition found
in Alfvén waves. These short-wavelength and arbitrarily large amplitude waves could contribute toward the heating of the solar
atmosphere. 相似文献
18.
We study the dispersion characteristics of fast MHD surface waves travelling on a plasma slab immersed in a complex magnetic field consisting of a large longitudinal B
0z
component and a small sheared B
0y
component. The analysis shows that for typical coronal conditions both the sausage and kink waves are generally pseudo-surface waves. The tangential magnetic field, B
0y
, modifies the dispersion curves, and for sufficiently large sheared fields there is a transition from pseudo-surface to pure-surface fast kink waves.On leave from Faculty of Physics, Sofia University, BG-1126 Sofia, Bulgaria. 相似文献
19.
The sunspot-associated sources at the frequency of 17 GHz give information on plasma parameters in the regions of magnetic
field about B=2000 G at the level of the chromosphere-corona transition region. The observations of short period (from one to ten minutes)
oscillations in sunspots reflect propagation of magnetohydrodynamic (MHD) waves in the magnetic flux tubes of the sunspots.
We investigate the oscillation parameters in active regions in connection with their flare activity. We confirm the existence
of a link between the oscillation spectrum and flare activity. We find differences in the oscillations between pre-flare and
post-flare phases. In particular, we demonstrate a case of powerful three-minute oscillations that start just before the burst.
This event is similar to the cases of the precursors investigated by Sych et al. (Astron. Astrophys.
505, 791, 2009). We also found well-defined eight-minute oscillations of microwave emission from sunspot. We interpret our observations
in terms of a relationship between MHD waves propagating from sunspots and flare processes. 相似文献
20.
Twisted magnetic flux tubes are often used to model the filed in coronal loops, and much attention has been given to analysing their stability. Previous astrophysical studies have concentrated on establishing the existence of an instability or determining stability bounds, and little information seems available on the associated eigenvalues, which give crucial information on the energy released. This paper develops methods of determining eigenvalues for infinitely long flux tubes. The most striking feature of the results is that the eigenvalues are always small-of order 10–2 (in dimensionless units) even for the fastest helical kink modes (m=1). The more localized higher-m modes have even smaller eigenvalues. A family of flux tubes with field line twist proportional tor
is investigated, and it appears that the most energetic instabilities occur in the Gold-Hoyle tube with uniform twist (=0). Implications of these results are discussed. 相似文献