Linear MHD Wave Propagation in Time-Dependent Flux Tube

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.     

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 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.     

Resonantly Damped Surface and Body MHD Waves in a Solar Coronal Slab with Oblique Propagation

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.     

Magneto‐seismology of the solar atmosphere

Magnetohydrodynamic (MHD) waves in solar coronal loops, which were previously only predicted by theory have actually been detected with space‐borne instruments. These observations have given an important and novel tool to measure fundamental parameters in the magnetically embedded solar corona. This paper will illustrate how information about the magnetic and density structure along coronal loops can be determined by measuring the frequency or amplitude profiles of standing fast kink mode oscillations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magneto-acoustic wave oscillations in solar spicules

Some observations suggest that solar spicules show small amplitude and high frequency oscillations of magneto-acoustic waves, which arise from photospheric granular forcing. We apply the method of MHD seismology to determine the period of kink waves. For this purposes, the oscillations of a magnetic cylinder embedded in a field-free environment is investigated. Finally, diagnostic diagrams displaying the oscillatory period in terms of some equilibrium parameters are provided to allow a comparison between theoretical results and those coming from observations.      

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density which travels at a relevant radial group speed C _g. The wave energy surface density and the wave angular momentum surface density are related to by = and = m respectively, where is the angular frequency in an inertial frame of reference and the integer m , proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discussed.     

Magnetohydrodynamic Waves in an Asymmetric Magnetic Slab

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.     

Nonlinear dynamics of Landau damped kinetic Alfvén waves

In the present paper we have studied the nonlinear dynamical equation of Landau damped kinetic Alfvén wave (KAW) to investigate the nonlinear evolution of KAW and the resulting turbulent spectra in solar wind plasmas. We have introduced a parameter g which governs the coupling between the amplitude of the pump KAW and the density perturbation. The numerical solution has been carried out to see the dependence on the parameter g in the nonlinear part of our equation. Our results reveal the formation of damped localized structures of KAW as well as steepening of the turbulent spectra by increasing g when damping is taken into account. The power spectra of magnetic field fluctuations indicate the redistribution of energy among the higher wave numbers. Each power spectrum with and without damping splits up into two different scaling ranges, Kolmogorov scaling followed by a steeper scaling. The steepening in the power spectra with Landau damping is more than without Landau damping case (for the same value of g). This type of steeper spectra has also been observed in the solar wind and is attributed to the Landau damping effects.     

Reflection Properties of Gravito-MHD Waves in an Inhomogeneous Horizontal Magnetic Field

We derive the dispersion equation for gravito-magnetohydrodynamical (MHD) waves in an isothermal, gravitationally stratified plasma with a horizontal inhomogeneous magnetic field. Sound and Alfvén speeds are constant. Under these conditions, it is possible to derive analytically the equations for gravito-MHD waves. The high values of the viscous and magnetic Reynolds numbers in the solar atmosphere imply that the dissipative terms in the MHD equations are negligible, except in layers around the positions where the frequency of the MHD wave equals the local Alfvén or slow wave frequency. Outside these layers the MHD waves are accurately described by the equations of ideal MHD. We consider waves that propagate energy upward in the atmosphere. For the plane boundary, z=0, between two isothermal plasma regions with horizontal but different magnetic fields, we discuss the boundary conditions and derive the equations for the reflection and transmission coefficients. In the simpler case of a gravitationally stratified plasma without magnetic field, these coefficients describe the reflection and transmission properties of gravito-acoustic waves.     

Numerical simulations of fast MHD waves in a coronal plasma

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.     

Effects of Random Flows on the Solar f Mode: I. Horizontal Flow

We examine the effect of random horizontal flows on the dispersion relation of high-degree solar f modes. We follow the approach of Murawski and Roberts (Astron. Astrophys. 272, 595, 1993), addressing some limitations of that paper, and extending the results to include damping and to apply for a general turbulent spectrum. We find a reduction in frequency below the classical result that is about three times that observed. For large wavenumber the damping rate is larger than the frequency correction by a factor of the order of the nondimensional wavenumber, which appears to be consistent with observation.     

Magnetohydrodynamic simulation of the coronal transient associated with the solar limb flare of 1980, June 29, 18∶21 UT

Soft X-ray data from the XRP experiment on SMM are used to generate the temperature and density in the flaring region of the 1980, June 29 (18∶21 UT) solar flare. The temporal data (T _max ～- 20 × 10⁶ K and n _max ～- 4 × 10¹¹ cm^?3), together with an assumed velocity, are used to simulate mass injection as the input pulse for the MHD model of Wu et al. (1982a, 1983a). The spatial and temporal coronal response is compared with the ground-based, Mark III K-coronameter observations of the subsequent coronal transient. The simulation produces a spatially-wide, large amplitude, temporarily-steepened MHD wave for either of the two ‘canonical’ magnetic topologies (closed and open), but no shock wave. This result appears to be confirmed by the fact that a type II radio event was observed late in the event for only a few minutes, thereby indicating that a steepening wave with temporary, marginal shock formation, was indeed present. The density enhancements produced by the simulation move away from the Sun at the same velocity observed by the K-coronameter. However, the observation of the coronal transient included a rarefaction that does not appear in the simulation. A probable explanation for this discrepancy is the likelihood that the magnitude and temporal profile of the density of the soft X-ray emitting plasma should not have been used as part of the mass injection pulse. We believe that the temperature profile alone, as suggested by earlier simulations, might have been a necessary and sufficient condition to produce both the compression and rarefaction of the ambient corona as indicated by the K-coronameter data. Hence, the dense plasma observed by XRP was probably confined, for the most part, close to the Sun during the ～ 17 min duration of the observations.     

MESSENGER Observations of Magnetohydrodynamic Waves in the Solar Corona from Faraday Rotation

During the declining phase of the longest solar minimum in a century, the arrival of the MESSENGER spacecraft at superior conjunction allowed the measurement of magnetohydrodynamic (MHD) waves in the solar corona with its 8 GHz radio frequency signal. MHD waves crossing the line of sight were measured via Faraday rotation fluctuations (FRFs) in the plane of polarization (PP) of MESSENGER’s signal. FRFs in previous observations of the solar corona (at greater offset distances) consisted of a turbulent spectrum that decreased in power with increasing frequency and distance from the Sun. Occasionally a spectral line, a distinct peak in the power spectral density spectrum around 4 to 8 mHz, was also observed in these early data sets at offset distances of about 5 to 10 solar radii. The MESSENGER FRF data set shows a spectral line at an offset distance between 1.55 to 1.85 solar radii with a frequency of 0.6±0.2 mHz. Other possible spectral lines may be at 1.2, 1.7, and 4.5 mHz; MHD waves with these same frequencies have been observed in X-ray data traveling along closed coronal loops at lower offset distances. An initial analysis of the MESSENGER spectral line(s) shows behavior similar to turbulent spectra: decreasing power with increasing frequency and distance from the Sun. Here we detail the steps taken to process the MESSENGER change in PP data set for the MHD wave investigation.     

Nonlinearly selected frequencies in coronal loops

A nonlinear process for the resonant generation of low-frequency fast magnetosonic kink waves in coronal loops is discussed. The efficiency of the process is strongly enhanced due to the existence of a nonlinearly selected frequency produced by a constant frequency difference in the dispersion curves in the short wavelength limit. The kink wave with the selected frequency interacts with high-frequency kink and sausage waves. The efficiency of such interaction does not require coherence in the interactive waves. In a loop of width 2 × 10³ km, field strength 50 G and number density 5 × 10¹⁵ m^–3, the nonlinearly selected frequency is of order 46 mHz (period 21.8 s), but this may range through 11 mHz to 184 mHz (periods 86.5 s to 5.4 s) for typical coronal conditions.     

On Ponderomotive Effects Induced by Alfvén Waves in Inhomogeneous 2.5D MHD Plasmas

Where spatial gradients in the amplitude of an Alfvén wave are non-zero, a nonlinear magnetic-pressure gradient acts upon the medium (commonly referred to as the ponderomotive force). We investigate the nature of such a force in inhomogeneous 2.5D MHD plasmas by analysing source terms in the nonlinear wave equations for the general case of inhomogeneous B and ρ, and consider supporting nonlinear numerical simulations. Our equations indicate that there are two distinct classes of ponderomotive effect induced by Alfvén waves in general 2.5D MHD, each with both a longitudinal and transverse manifestation. i) Geometric effects: Gradients in the pulse geometry relative to the background magnetic field cause the wave to sustain cospatial disturbances, the longitudinal and transverse daughter disturbances – where we report on the transverse disturbance for the first time. ii) ?(c _A) effects: Where a pulse propagates through an inhomogeneous region (where the gradients in the Alfvén-speed profile c _A are non-zero), the nonlinear magnetic-pressure gradient acts to accelerate the plasma. Transverse gradients (phase mixing regions) excite independently propagating fast magnetoacoustic waves (generalising the result of Nakariakov, Roberts, and Murawski (Solar Phys. 175, 93, 1997)) and longitudinal gradients (longitudinally dispersive regions) perturb along the field (thus creating static disturbances in β=0, and slow waves in β≠0). We additionally demonstrate that mode conversion due the nonlinear Lorentz force is a one-way process, and does not act as a mechanism to nonlinearly generate Alfvén waves due to propagating magnetoacoustic waves. We conclude that these ponderomotive effects are induced by an Alfvén wave propagating in any MHD medium, and have the potential to have significant consequences on the dynamics of energy transport and aspects of dissipation provided the system is sufficiently nonlinear and inhomogeneous.     

Harmonics of low-amplitude anisotropic wave trains in cosmic rays

The purpose of this work is to investigate the first three harmonics of low-amplitude anisotropic wave trains (LAEs) of cosmic ray intensity and their association with solar and heliospheric parameters. The significant behaviour of these events is that the amplitude remains low for the first harmonic and high for the second/third harmonics, whereas direction of the anisotropy shift is towards earlier hours for the first harmonic and towards later hours for the second/third harmonic compared to annual average anisotropy. The first two harmonics are found to correlate well with the solar activity cycle during these LAEs. The amplitude and the direction of the first two harmonics do not show any significant association with the polarity change of the Bx/By component of the interplanetary magnetic field during LAEs. However, the third harmonic (amplitude and phase) shows some positive correlation with the Bx and negative correlation with the By component. The occurrence of LAEs is dominant for the positive polarity of Bx and the negative polarity of By. The occurrence of LAEs is dominant during the period of average solar wind velocity but their occurrence during high-speed solar wind streams cannot be overlooked. The frequency of occurrence of these LAEs is more during co-rotating streams.The amplitude of first and second harmonic shows deviations for different values of geomagnetic activity index Ap. However, the amplitude of second harmonic and direction of all the three harmonics do not show any significant association with the Ap-index. The Ap-index consistently remains in the range 14?Kp?31 during these events.The amplitude of first and third harmonic and the direction of first harmonic show deviations for different values of proton density. However, the amplitude of the second harmonic and the direction of the second and third harmonics do not show any significant association with proton density. The occurrence of LAEs is dominant when proton density remains ?20. The cosmic ray intensity during LAEs has good anti-correlation with interplanetary magnetic field strength (B) and its Bx component, whereas it shows a good correlation with its By component. However, it shows significant anti-correlation with sunspot number, the product (R×V) and (R×B).     

Observation of kink waves and their reconnection-like origin in solar spicules

We analyze the time series of Ca?ii H-line obtained from Hinode/SOT on the solar limb. We follow three cases of upwardly propagating kink waves along a spicule and inverted Y-shaped structures at the cusp of it. The time-distance analysis shows that the axis of spicule undergos quasi-periodic transverse displacement at different heights from the photosphere. The mean period of transverse displacement is ～175 s and the mean amplitude is 1 arc?sec. The oscillation periods are increasing linearly with height which may be counted as the signature that the spicule is working as a low pass filter and allows only the low frequencies to propagate towards higher heights. The oscillations amplitude is increasing with height due to decrease in density. The phase speeds are increasing until some heights and then decreasing which may be related to the small scale reconnection at the spicule basis. We conclude that transversal displacement of spicules axis can be related to the propagation of kink waves along them. Moreover, we observe signatures of small-scale magnetic reconnection at the cusp of spicules which may excite kink waves.     

Non-linear damping of visco-resistive Alfvén waves in solar spicules

Interaction of Alfvén waves with plasma inhomogeneities generates phase mixing which can lead to dissipate Alfvén waves and to heat the solar plasma. Here we study the dissipation of Alfvén waves by phase mixing due to viscosity and resistivity variations with height. We also consider nonlinear magnetohydrodynamic (MHD) equations in our theoretical model. Non-linear terms of MHD equations include perturbed velocity, magnetic field, and density. To investigate the damping of Alfvén waves in a stratified atmosphere of solar spicules, we solve the non-linear MHD equations in the x–z plane. Our simulations show that the damping is enhanced due to viscosity and resistivity gradients. Moreover, energy variations is influenced due to nonlinear terms in MHD equations.     

Mhd Study of Coronal Waves: A Numerical Approach

The solar corona, modelled by a low β, resistive plasma slab sustains MHD wave propagations due to footpoint motions in the photosphere. The density, magnetic profile and driver are considered to be neither very smooth nor very steep. The numerical simulation presents the evolution of MHD waves and the formation of current sheet. Steep gradients in slow wave at the slab edges which are signature of resonance layer where dissipation takes place are observed. Singularity is removed by the inclusion of finite resistivity. Dissipation takes place around the resonance layer where the perturbation develops large gradients. The width of the resonance layer is calculated. The thickness of the Alfvén resonance layer is more than that of the slow wave resonance layer. Attempt is made to distinguish between slow and Alfvén wave resonance layers. Fast waves develop into kink modes. As plasma evolves the current sheets which provide the heating at the edges gets distorted and fragment into two current sheets at each edge which in turn come closer when the twist is enhanced. This revised version was published online in July 2006 with corrections to the Cover Date.