Incompressible magnetohydrodynamic modes in the thin magnetically twisted flux tube

Context. Observations have shown that twisted magnetic fields naturally occur, and indeed are omnipresent in the Sun’s atmosphere. It is therefore of great theoretical interest in solar atmospheric waves research to investigate the types of magnetohydrodynamic (MHD) wave modes that can propagate along twisted magnetic flux tubes. Aims. Within the framework of ideal MHD, the main aim of this work is to investigate small amplitude incompressible wave modes of twisted magnetic flux tubes with m ≥ 1. The axial magnetic field strength inside and outside the tube will be allowed to vary, to ensure the results will not be restricted to only cold plasma equilibria conditions. Methods. The dispersion equation for these incompressible linear MHD wave modes was derived analytically by implementing the long wavelength approximation. Results. It is shown, in the long wavelength limit, that both the frequency and radial velocity profile of the m = 1 kink mode are completely unaffected by the choice of internal background magnetic twist. However, fluting modes with m ≥ 2 are sensitive to the particular radial profile of magnetic twist chosen. Furthermore, due to background twist, a low frequency cut-off is introduced for fluting modes that is not present for kink modes. From an observational point of view, although magnetic twist does not affect the propagation of long wavelength kink modes, for fluting modes it will either work for or against the propagation, depending on the direction of wave travel relative to the sign of the background twist

MHD waves in the plasma system with dipole magnetic field configuration

The eigenmode spectrum of the ultra low frequency (ULF) waves in the Earth magnetosphere is discrete and consists of Alfvén and slow magnetosonic modes. Their interaction depends on ionospheric conductivity and the magnetic field curvature. We present the physical conditions of resonant ULF waves realization obtained for different wave polarization types. ULF waves with poloidal polarization are strongly coupled to slow magnetohydrodynamic (MHD) waves. The magnetic field pressure oscillates with 180° phase shift with respect to the plasma pressure. Thus, for such coupled waves the partial pressure compensation is observed. The crucial influence of the background magnetic field shear on the poloidal modes is shown. The toroidal field line resonant ULF waves do not have magnetic pressure and plasma pressure perturbations. Results presented in this paper are common for the ULF waves in the Earth's magnetosphere and include different scale disturbations. The verification of the obtained conditions with parameters of waves collected in the Earth's magnetosphere ULF is carried out by use of AMPTE/CCE and Equator-S data. The good agreement is obtained

Corrugation instability of a coronal arcade

AbstractWe analyse the behaviour of linear magnetohydrodynamic perturbations of a coronal arcade modelled by a half-cylinder with an azimuthal magnetic field and non-uniform radial profiles of the plasma pressure, temperature, and the field. Attention is paid to the perturbations with short longitudinal (in the direction along the arcade) wavelengths. The radial structure of the perturbations, either oscillatory or evanescent, is prescribed by the radial profiles of the equilibrium quantities. Conditions for the corrugation instability of the arcade are determined. It is established that the instability growth rate increases with decreases in the longitudinal wavelength and the radial wave number. In the unstable mode, the radial perturbations of the magnetic field are stronger than the longitudinal perturbations, creating an almost circularly corrugated rippling of the arcade in the longitudinal direction. For coronal conditions, the growth time of the instability is shorter than one minute, decreasing with an increase in the temperature. Implications of the developed theory for the dynamics of coronal active regions are discussed

Atmospheric waves disturbances from the solar terminator according to the VLF radio stations data

The perturbations from the solar terminator in the range of acoustic-gravity waves (AGWs) periods from 5 minutes to 1 hour were analysed with the use of measurements of VLF radio signals amplitudes on the European radio path GQD--A118 (Great Britain--France). These observations provide information on the propagation of waves at altitudes near the mesopause ($\sim$ 90 km), where VLF radio waves are reflected. On the considered radio path a systematic increase in fluctuations in the amplitudes of radio waves was observed within a few hours after the passage of the evening terminator. For April, June, October 2020 and February 2021 events, the distribution of the number of wave perturbations with large amplitudes over AGWs time periods has been studied. Our results show that the evening terminator for different seasons is dominated by waves in the range of periods of 15--20 minutes. The amplitudes of the AGWs from the terminator at the heights of the mesosphere (fluctuations in the concentration of neutral particles, velocity components and vertical displacement of the volume element) are approximately determined by the fluctuations of the amplitudes of the VLF radio signals. The amplitudes of the AGWs on the terminator are 12--14\% in relative concentration fluctuations, which correspond to the vertical displacement of the atmospheric gas volume of 1.1--1.3 km. Based on the analysis of the AGW energy balance equation, it was concluded that the waves predominantly propagate in a quasi-horizontal direction at the terminator. The possibility of studying the long-term changes in the mesosphere parameters using fluctuations in the amplitudes of VLF radio waves at the terminator is shown

On the stability of incompressible MHD modes in magnetic cylinder with twisted magnetic field and flow

In this work, we studied MHD modes in a magnetically twisted flux tube with a twisted flow that is embedded in the uniform magnetic field. We consider when the azimuthal magnetic field and velocity are linear functions of radius (case i) and also more generally when they are arbitrary functions of radius (case ii). Under these assumptions, we obtain the dispersion equation in the incompressible limit. This solution can also be used to describe the MHD perturbations in plasma pinches and vortices. The dispersion equation is simplified by implementing the thin flux tube approximation. It is shown that sausage modes (m = 0) become unstable for large enough azimuthal flow speeds. Also, we obtained the unstable modes for m > 0. It is shown that the stability criterion of the m = 1 mode (for case i) is independent of the background azimuthal components of the plasma velocity and magnetic field. These criteria fully coincide with the result that was previously obtained by Syrovatskiy for a plane interface. Moreover, this result even remains valid when the azimuthal magnetic field and velocity have an arbitrary dependence on radius (case ii). A criterion for the stability of the m ≥ 2 modes is also obtained. It was found that instability of these modes is determined by both longitudinal and azimuthal flows. It is shown that if there is sufficient azimuthal background flow, then all modes with m ≥ 2 will become unstable

Generation of low-frequency kinetic waves at the footpoints of pre-flare coronal loops

In this study we discuss the excitation of low-frequency plasma waves in the lower-middle chromosphere region of loop footpoints for the case when the plasma can be considered to be in a pre-flare state. It is shown that among the well-known semi-empirical models of the solar atmosphere, only the VAL (F) model together with a particular set of basic plasma parameters and amplitudes of the electric and magnetic fields supports generation of low-frequency wave instability. Our results show that it is possible to predict the onset of the flare process in the active region by using the interaction of kinetic Alfvén and kinetic ion-acoustic waves, which are solutions of the derived dispersion equation. The VAL (F) model allows situations when the main source of the aforementioned instability can be a sub-Dreicer electric field and drift plasma movements due to presence of spatial inhomogeneities. We also show that the generation of kinetic Alfvén and kinetic ion-acoustic waves can occur both, in plasma with a purely Coulomb conductivity and in the presence of small-scale Bernstein turbulence. The excitation of the small amplitude kinetic waves due to the development of low threshold instability in plasma with relatively low values of the magnetic field strength is also discussed