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

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

Spatial magneto-seismology : effect of density stratification on the first harmonic amplitude profile of transversal coronal loop oscillations

Context. The new generation of extreme-ultraviolet (EUV) imagers onboard missions such as the Solar Dynamics Observatory (SDO)and Solar Orbiter (SO) will provide the most accurate spatial measurements of post-flare coronal loop oscillations yet. The amplitude profiles of these loop oscillations contain important information about plasma fine structure in the corona. Aims. We show that the position of the anti-nodes of the amplitude profile of the first harmonic of the standing fast kink wave of a coronal loop relate to the plasma density stratification of that loop. Methods. The MHD kink transversal waves of coronal loops are modelled both numerically and analytically. The numerical model implements the implicit finite element code pollux. Dispersion relations are derived and solved analytically. The results of the two methods are compared and verified. Results. Density stratification causes the anti-nodes of the first harmonic to shift towards the loop footpoints. The greater the density stratification, the larger the shift. The anti-node shift of the first harmonic of a semi-circular coronal loop with a density scale height H = 50 Mm and loop half length L = 100 Mm is approximately 5.6Mm. Shifts in the Mm range are measureable quantities providing valuable information about the subresolution structure of coronal loops. Conclusions. The measurement of the anti-node shift of the first harmonic of the standing fast kink wave of coronal loops is potentially a new tool in the field of solar magneto-seismology, providing a novel complementary method of probing plasma fine structure in the corona

Magnetohydrodynamic code for gravitationally-stratified media

Aims. We describe a newly-developed magnetohydrodynamic (MHD) code with the capacity to simulate the interaction of any arbitrary perturbation (i.e., not necessarily limited to the linearised limit) with a magnetohydrostatic equilibrium background. Methods. By rearranging the terms in the system of MHD equations and explicitly taking into account the magnetohydrostatic equilibrium condition, we define the equations governing the perturbations that describe the deviations from the background state of plasma for the density, internal energy and magnetic field. We found it was advantageous to use this modified form of the MHD equations for numerical simulations of physical processes taking place in a stable gravitationally-stratified plasma. The governing equations are implemented in a novel way in the code. Sub-grid diffusion and resistivity are applied to ensure numerical stability of the computed solution of the MHD equations. We apply a fourth-order central difference scheme to calculate the spatial derivatives, and implement an arbitrary Runge-Kutta scheme to advance the solution in time. Results. We have built the proposed method, suitable for strongly-stratified magnetised plasma, on the base of the well-documented Versatile Advection Code (VAC) and performed a number of one- and multi-dimensional hydrodynamic and MHD tests to demonstrate the feasibility and robustness of the code for applications to astrophysical plasmas