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We study kink oscillations of the system of two parallel magnetic tubes in the presence of plasma cooling. We assume that the characteristic cooling time is much larger than the characteristic time of kink oscillations. Using the ratio of two characteristic times as a small parameter, we derive the expression for the adiabatic invariant, which is a quantity that remains constant during the cooling process. Then, we study in detail a particular case where the plasma densities in the two tubes are the same, the plasma temperature outside of the tube does not change, and the plasma temperature inside the tubes decreases exponentially. We found that cooling causes the increase of the oscillation frequencies and amplitudes. These results are the generalization of similar results previously obtained for a single magnetic tube. We compared the efficiency of amplification of kink oscillations caused by cooling in counteracting the damping of oscillations due to resonant absorption in two models of coronal magnetic loops: monolithic and consisting of two parallel filaments. [ABSTRACT FROM AUTHOR]

We study oscillations of two parallel interacting magnetic tubes in the presence of plasma flow along the tubes. Using the cold plasma and thin tube approximations we derive the system of two equations describing these oscillations. This system of equations is valid for equilibria where the plasma density and flow velocity can vary along the tube axes and in time. This system of equations is used to study the effect of flow in the tubes on the frequency of standing waves. There are two modes of oscillations, fast and slow. We calculated the dependence of frequencies of fast and slow modes of the Alfvén Mach number. We found that the effect of flow in coronal loops on the oscillation frequency is fairly weak for typical flow velocities observed in coronal loops. However it can be substantial in the case of prominence threads. We discuss the implication of the obtained results on coronal seismology. [ABSTRACT FROM AUTHOR]

We study kink oscillations of a straight magnetic tube with a transitional region at its boundary. The tube is homogeneous in the axial direction. The plasma density monotonically decreases in the transitional region from its value inside the tube to that in the surrounding plasma. The plasma motion is described by the linear magnetohydrodynamic equations in the cold plasma approximation. We use the ideal equations inside the tube and in the surrounding plasma, but take viscosity into account in the transitional region. We also use the thin tube and thin transitional or boundary layer (TTTB) approximation. Kink oscillations are assumed to be driven by a driver at the tube footpoint. We derive the equation describing the displacement in the fundamental mode and overtones. We use this equation to study kink oscillations in both the case of harmonic and random driving. In the case of random driving, we assume that the driver is described by a stationary random function. The displacements in the fundamental mode and overtones are also described by stationary random functions. We derive the relation between the power spectra of the fundamental mode and all overtones and the power spectrum of the driver. We suggest a new method of obtaining information on the internal structure of coronal magnetic loops based on the shape of graphs of the power spectrum of the fundamental mode. [ABSTRACT FROM AUTHOR]

We study the propagation and stability of kink waves in a twisted magnetic tube with the flow. The flow velocity is assumed to be parallel to the magnetic field, and the magnetic field lines are straight outside the tube. The density is constant inside and outside of the tube, and it monotonically decreases from its value inside the tube to that outside in the transitional or boundary layer. The flow speed and magnetic twist monotonically decrease in the transitional layer from their values inside the tube to zero outside. Using the thin tube and thin boundary layer (TTTB) approximation, we derived the dispersion equation determining the dependence of the wave frequency and decrement/increment on the wavenumber. When the kink wave frequency coincides with the local Alfvén frequency at a resonant surface inside the transitional layer, the kink wave is subjected to either resonant damping or resonant instability. We study the properties of kink waves in a particular unperturbed state where there is no flow and magnetic twist in the transitional layer. It is shown that in a tube with flow, the kink waves can propagate without damping for particular values of the flow speed. Kink waves propagating in the flow direction either damp or propagate without damping. Waves propagating in the opposite direction can either propagate without damping, or damp, or become unstable. The theoretical results are applied to the problem of excitation of kink waves in spicules and filaments in the solar atmosphere. [ABSTRACT FROM AUTHOR]

We study the resonant damping of kink oscillations of thin expanding magnetic flux tubes. The tube consists of a core region and a thin transitional region at the tube boundary. The resonance occurs in this transitional layer where the oscillation frequency coincides with the local Alfvén frequency. Our investigation is based on the system of equations that we previously derived. This system is not closed because it contains the jumps of the magnetic pressure perturbation and plasma displacement across the transitional layer. We calculate these jumps and thus close the system. We then use it to determine the decrements of oscillation eigenmodes. We introduce the notion of homogeneous stratification. In accordance with this condition the ratio of densities in the tube core and outside the tube does not vary along the tube, while the density in the transitional layer can be factorised and written as a product of two function, one depending on the variable along the tube and the other on the magnetic flux function. Our main result is that, under the condition of homogeneous stratification, the ratio of the decrement to the oscillation frequency is independent of a particular form of the density variation along the tube. This ratio is also the same for all oscillation eigenmodes. [ABSTRACT FROM AUTHOR]

We study damping of phase-mixed Alfvén waves propagating in non-reflective axisymmetric magnetic plasma configurations. We derive the general equation describing the attenuation of the Alfvén wave amplitude. Then we applied the general theory to a particular case with the exponentially divergent magnetic field lines. The condition that the configuration is nonreflective determines the variation of the plasma density along the magnetic field lines. The density profiles exponentially decreasing with the height are not among non-reflective density profiles. However, we managed to find non-reflective profiles that fairly well approximate exponentially decreasing density.We calculate the variation of the total wave energy flux with the height for various values of shear viscosity. We found that to have a substantial amount of wave energy dissipated at the lower corona, one needs to increase shear viscosity by seven orders of magnitude in comparison with the value given by the classical plasma theory. An important result that we obtained is that the efficiency of the wave damping strongly depends on the density variation with the height. The stronger the density decrease, the weaker the wave damping is. On the basis of this result, we suggested a physical explanation of the phenomenon of the enhanced wave damping in equilibrium configurations with exponentially diverging magnetic field lines. [ABSTRACT FROM AUTHOR]

We study kink waves and oscillations in a thin expanding magnetic tube in the presence of flow. The tube consists of a core region and a thin transitional region at the tube boundary. In this region the plasma density monotonically decreases from its value in the core region to the value outside the tube. Both the plasma density and velocity of background flow vary along the tube and in time. Using the multiscale expansions we derive the system of two equations describing the kink oscillations. When there is no transitional layer the oscillations are described by the first of these two equations. We use this equation to study the effect of plasma density variation with time on kink oscillations of an expanding tube with a sharp boundary. We assume that the characteristic time of the density variation is much greater than the characteristic time of kink oscillations. Then we use the Wentzel-Kramer-Brillouin (WKB) method to derive the expression for the adiabatic invariant, which is the quantity that is conserved when the plasma density varies. The general theoretical results are applied to the kink oscillations of coronal magnetic loops. We consider an expanding loop with the half-circle shape and assume that the plasma temperature inside a loop decays exponentially with time. We numerically calculated the dependences of the fundamental mode frequency, the ratio of frequencies of the first overtone and fundamental mode, and the oscillation amplitude on time. We obtained that the oscillation frequency and amplitude increase and the frequency ratio decreases due to cooling. The amplitude increase is stronger for loops with a greater expansion factor. This effect is also more pronounced for higher loops. However, it is fairly moderate even for loops that are quite high. [ABSTRACT FROM AUTHOR]

In this article we study standing kink waves in twisted magnetic tubes. We use the cold plasma and thin tube approximation. We assume that the plasma density is constant inside and outside the tube. We also assume that the magnetic twist is weak and take the ratio of the azimuthal and axial component of the magnetic field to be of the order of ratio of the tube radius and tube length. The azimuthal component of the magnetic field is proportional to the distance from the tube axis inside the tube, and inversely proportional to this distance outside the tube. Using the method of asymptotic expansions we derived the governing integral equation that determines the eigenfrequencies and eigenmodes of the tube kink oscillations. In the approximation of a very weak twist, we calculated analytically the corrections to the frequencies of the fundamental mode and first overtone of a straight magnetic tube related to the presence of twist. The analytical results are compared with the numerical results obtained using the full set of linear ideal magnetohydrodynamic equations. We also calculated the ratio of frequencies of the fist overtone and fundamental mode. We found that the magnetic twist enhances this ratio for moderate values of the density ratio, and reduces this ratio for large values of the density ratio. In general, the deviation of the frequency ratio from 2 caused by the magnetic twist is comparable to that found in simultaneous observations of the fundamental mode and first overtone of the coronal loop kink oscillations. Finally, we studied the eigenmode polarization. We found that, in a particular case of linear polarization, the polarization direction rotates along the tube. [ABSTRACT FROM AUTHOR]

We studied the magnetic Rayleigh-Taylor (MRT) instability of a magnetohydrodynamic tangential discontinuity in an infinitely conducting incompressible plasma in the presence of flow. We assumed that the flow magnitude is small enough to guarantee that there is no Kelvin-Helmholtz (KH) instability. In addition, we assumed that there is the magnetic shear, that is, the magnetic field has different directions at the two side of the discontinuity. In this case, only perturbations whose wavelength is greater than the critical one are unstable. As a consequence, the perturbation growth rate is bounded, and the initial-value problem describing their evolution is well posed. We also studied the absolute and convective nature of the MRT instability using the Briggs method. We obtained the necessary and sufficient condition for a perturbation propagating in a given direction to be only convectively unstable but absolutely stable. We also obtained the condition for perturbations propagating in any direction to be only convectively unstable, but absolutely stable. The results of the general analysis were applied to the MRT instability of prominence threads and the heliopause. Similar to previous research, we assumed that the thread disappearance is related to the MRT instability and the thread lifetime is equal to the inverse instability increment. Using this assumption we estimated the angle between the magnetic field inside the thread and in the surrounding plasma and studied how this estimate depends on the magnitude of the flow inside the thread. We found that this dependence is very weak. To apply this to the heliopause stability, we carried out the local analysis and restricted it to the near flanks of the heliopause only where the plasma flow can be considered incompressible. We showed that, for values of the magnetic field magnitude observed by Voyager 1, there is no KH instability. We then studied the MRT instability that can occur when the heliosheath is accelerated in the antisolar direction due to the increase in the solar wind dynamic pressure. We showed that, for typical values of the plasma flow and magnetic field parameters, there are directions such that perturbations propagating in this directions are absolutely unstable. [ABSTRACT FROM AUTHOR]

In this paper, we study kink waves in twisted magnetic tubes. In the equilibrium state there is the electrical current with constant density inside the tube directed along the tube axis. This current creates the azimuthal magnetic field with the magnitude proportional to the distance from the tube axis inside the tube and inversely proportional to this distance outside the tube. We derive the dispersion equations for propagating waves and for unstable perturbations in the long wavelength approximation. We show that there are no solutions to the dispersion equation determining the frequencies of unstable perturbations, which implies that there are no unstable long kink modes. We study the dispersion equation for propagating waves both in the case when the plasma density is larger than that in the surrounding plasma as well as when it is smaller. In the first case we obtain that, depending on the wave number, the dispersion equation for propagating waves has either no solutions, or one solution, or two solutions. In the case when there is one solution, in the approximation of very weak twist, the wave mode propagates with the phase speed slightly larger than the kink speed. This wave mode is called the accelerated kink wave. In the case when there are two solutions to the dispersion equation, one of the two solutions gives the frequency of a quasi-mode that is subjected to the Alfvén resonance outside the tube. The other solution gives the frequency of a true eigenmode of linear ideal MHD. In the approximation of very weak twist its phase speed is smaller than the kink speed. This mode is called the decelerated kink wave. In the case of rarefied tube, depending on the wave number, the dispersion equation has either one or three solutions. When there is only one solution, the mode frequency is very close to the Alfvén frequency far from the tube, so the wave mode practically coincides with the Alfvén wave. When there are three solutions, the largest frequency practically coincides with the Alfvén frequency far from the tube. Two other solutions almost coincide. In all cases the wave modes existing in the case of rarefied tube are quasi-modes that are subjected to the Alfvén resonance. A possible application of the obtained results to the solar atmospheric seismology is discussed. [ABSTRACT FROM AUTHOR]

Aims. We investigate the spatial damping of propagating kink waves in an inhomogeneous plasma. In the limit of a thin tube surrounded by a thin transition layer, an analytical formulation for kink waves driven in from the bottom boundary of the corona is presented. Methods. The spatial form for the damping of the kink mode was investigated using various analytical approximations. When the density ratio between the internal density and the external density is not too large, a simple differential-integral equation was used. Approximate analytical solutions to this equation are presented. Results. For the first time, the form of the spatial damping of the kink mode is shown analytically to be Gaussian in nature near the driven boundary. For several wavelengths, the amplitude of the kink mode is proportional to (1+exp(-z2/L2g ))/2, where L2g = 16/ϵκ2k2. Although the actual value of 16 in Lg depends on the particular form of the driver, this form is very general and its dependence on the other parameters does not change. For large distances, the damping profile appears to be roughly linear exponential decay. This is shown analytically by a series expansion when the inhomogeneous layer width is small enough. [ABSTRACT FROM AUTHOR]