Behaviour of Magnetoacoustic Waves in the Neighbourhood of a Two-Dimensional Null Point: Initially Cylindrically Symmetric Perturbations

The propagation of magnetoacoustic waves in the neighbourhood of a 2D null point is investigated for both β=0 and β ≠ 0 plasmas. Previous work has shown that the Alfvén speed, here v _A ∝r, plays a vital role in such systems and so a natural choice is to switch to polar coordinates. For β=0 plasma, we derive an analytical solution for the behaviour of the fast magnetoacoustic wave in terms of the Klein–Gordon equation. We also solve the system with a semi-analytical WKB approximation which shows that the β=0 wave focuses on the null and contracts around it but, due to exponential decay, never reaches the null in a finite time. For the β ≠ 0 plasma, we solve the system numerically and find the behaviour to be similar to that of the β=0 system at large radii, but completely different close to the null. We show that for an initially cylindrically-symmetric fast magnetoacoustic wave perturbation, there is a decrease in wave speed along the separatrices and so the perturbation starts to take on a quasi-diamond shape; with the corners located along the separatrices. This is due to the growth in pressure gradients that reach a maximum along the separatrices, which in turn reduces the acceleration of the fast wave along the separatrices leading to a deformation of the wave morphology.     

Phase Mixing of Alfvén Waves Near a 2D Magnetic Null Point

The propagation of linear Alfvén wave pulses in an inhomogeneous plasma near a 2D coronal null point is investigated. When a uniform plasma density is considered, it is seen that an initially planar Alfvén wavefront remains planar, despite the varying equilibrium Alfvén speed, and that all the wave collects at the separatrices. Thus, in the non-ideal case, these Alfvénic disturbances preferentially dissipate their energy at these locations. For a non-uniform equilibrium density, it is found that the Alfvén wavefront is significantly distorted away from the initially planar geometry, inviting the possibility of dissipation due to phase mixing. Despite this however, we conclude that for the Alfvén wave, current density accumulation and preferential heating still primarily occur at the separatrices, even when an extremely non-uniform density profile is considered.     

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.     

Compound Effect of Alfvén Waves and Ion-Cyclotron Waves on Heating/Acceleration of Minor Ions via the Pickup Process

A scenario is proposed to explain the preferential heating of minor ions and differential-streaming velocity between minor ions and protons observed in the solar corona and in the solar wind. It is demonstrated by test-particle simulations that minor ions can be nearly fully picked up by intrinsic Alfvén-cyclotron waves observed in the solar wind based on the observed wave energy density. Both high-frequency ion-cyclotron waves and low-frequency Alfvén waves play crucial roles in the pickup process. A minor ion can first gain a high magnetic moment through the resonant wave–particle interaction with ion-cyclotron waves, and then this ion with a large magnetic moment can be trapped by magnetic mirror-like field structures in the presence of the low-frequency Alfvén waves. As a result, the ion is picked up by these Alfvén-cyclotron waves. However, minor ions can only be partially picked up in the corona because of the low wave energy density and low plasma β. During the pickup process, minor ions are stochastically heated and accelerated by Alfvén-cyclotron waves so that they are hotter and flow faster than protons. The compound effect of Alfvén waves and ion-cyclotron waves is important in the heating and acceleration of minor ions. The kinetic properties of minor ions from simulation results are generally consistent with in-situ and remote features observed in the solar wind and solar corona.     

Roles of Fast-Cyclotron and Alfvén-Cyclotron Waves for the Multi-Ion Solar Wind

Using linear Vlasov theory of plasma waves and quasi-linear theory of resonant wave–particle interaction, the dispersion relations and the electromagnetic field fluctuations of fast and Alfvén waves are studied for a low-beta multi-ion plasma in the inner corona. Their probable roles in heating and accelerating the solar wind via Landau and cyclotron resonances are quantified. In this paper, we assume that i) low-frequency Alfvén and fast waves, emanating from the solar surface, have the same spectral shape and the same amplitude of power spectral density (PSD); ii) these waves eventually reach ion cyclotron frequencies due to a turbulence cascade; iii) kinetic wave–particle interaction powers the solar wind. The existence of alpha particles in a dominant proton/electron plasma can trigger linear mode conversion between oblique fast-whistler and hybrid alpha–proton cyclotron waves. The fast-cyclotron waves undergo both alpha and proton cyclotron resonances. The alpha cyclotron resonance in fast-cyclotron waves is much stronger than that in Alfvén-cyclotron waves. For alpha cyclotron resonance, an oblique fast-cyclotron wave has a larger left-handed electric field fluctuation, a smaller wave number, a larger local wave amplitude, and a greater energization capability than a corresponding Alfvén-cyclotron wave at the same wave propagation angle θ, particularly at 80^°<θ<90^°. When Alfvén-cyclotron or fast-cyclotron waves are present, alpha particles are the chief energy recipient. The transition of preferential energization from alpha particles to protons may be self-modulated by a differential speed and a temperature anisotropy of alpha particles via the self-consistently evolving wave–particle interaction. Therefore, fast-cyclotron waves, as a result of linear mode coupling, constitute a potentially important mechanism for preferential energization of minor ions in the main acceleration region of the solar wind.     

MHD waves in coronal magnetic arcades

We analyze the eigenmodes of the solar coronal magnetic arcade that describes the magnetic field of a bipolar active region using the eikonal method for ideal magnetohydrodynamic equations. We write out the eikonal equations for Alfvèn and magnetoacoustic waves and derive the equations for the amplitudes of the zeroth approximation. We construct the wave fields for Alfvèn and fast magnetoacoustic modes and derive the expressions for the eigenfrequencies. We show that Alfvèn modes of a given frequency are near a number of magnetic surfaces, while fast magnetoacoustic eigenmodes are near nonmagnetic surfaces. A discrete set of eigenfrequencies that continuously change from one surface to another corresponds to each such surface.     

Three-Dimensional MHD Wave Propagation and Conversion to Alfvén Waves near the Solar Surface. I. Direct Numerical Solution

The efficacy of fast?–?slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfvén and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfvén wave may couple to the magnetoacoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical “scattering experiment,” placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvénic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfvén waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfvén fluxes are produced when the field is inclined 30°?–?40° from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60°?–?80°.     

Resonant Absorption of Fast Magnetoacoustic Waves due to Coupling into the Slow and Alfvén Continua in the Solar Atmosphere

Resonant absorption of fast magnetoacoustic (FMA) waves in an inhomogeneous, weakly dissipative, one-dimensional planar, strongly anisotropic and dispersive plasma is investigated. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localised slow or Alfvén waves present in the inhomogeneous layer and are partly reflected, dissipated and transmitted by this region. The presented research aims to find the coefficient of wave energy absorption under solar chromospheric and coronal conditions. Numerical results are analysed to find the coefficient of wave energy absorption at both the slow and Alfvén resonance positions. The mathematical derivations are based on the two simplifying assumptions that i) nonlinearity is weak, and ii) the thickness of the inhomogeneous layer is small in comparison to the wavelength of the wave, i.e. we employ the so-called long wavelength approximation. Slow resonance is found to be described by the nonlinear theory, while the dynamics at the Alvén resonance can be described within the linear framework. We introduce a new concept of coupled resonances, which occurs when two different resonances are in close proximity to each other, causing the incoming wave to act as though it has been influenced by the two resonances simultaneously. Our results show that the wave energy absorption is heavily dependent on the angle of the incident wave in combination with the inclination angle of the equilibrium magnetic field. In addition, it is found that FMA waves are very efficiently absorbed at the Alvén resonance under coronal conditions. Under chromospheric conditions the FMA waves are far less efficiently absorbed, despite an increase in efficiency due to the coupled resonances.     

Phase mixing of standing Alfvén waves with shear flows in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of such waves due to phase mixing at the presence of shear flow and field in the stratified atmosphere of solar spicules. The initial flow is assumed to be directed along spicule axis and to vary linearly in the x direction and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that the shear flow and field can fasten the damping of standing Alfvén waves. In spite of propagating Alfvén waves, standing Alfvén waves in Solar spicules dissipate in a few periods. As height increases, the perturbed velocity amplitude does increase in contrast to the behavior of perturbed magnetic field. Moreover, it should be emphasized that the stratification due to gravity, shear flow and field are the facts that should be considered in MHD models in spicules.     

Time-Distance Seismology and the Solar Transition Region

Time-Distance ‘travel time’ perturbations (as inferred from wave phase) are calculated relative to the quiet-Sun as a function of wave orientation and field inclination in a uniform inclined magnetic field. Modelling indicates that the chromosphere-corona Transition Region (TR) profoundly alters travel times at inclinations from the vertical θ for which the ramp-reduced acoustic cutoff frequency ω _c cosθ is similar to the wave frequency ω. At smaller inclinations phase shifts are much smaller as the waves are largely reflected before reaching the TR. At larger inclinations, the shifts resume their quiet-Sun values, although with some resonant oscillatory behaviour. Changing the height of the TR in the model atmosphere has some effect, but the thickness and temperature jump do not change the results substantially. There is a strong correspondence between travel-time shifts and the Alfvén flux that emerges at the top of the modelled region as a result of fast/Alfvén mode conversion. We confirm that the TR transmission coefficient for Alfvén waves generated by mode conversion in the chromosphere is far larger (typically 30 % or more) than for Alfvén waves injected from the photosphere.     

Radiation of magnetoacoustic waves in the interstellar medium by physical variable stars

Radially pulsating stars are shown to radiate fast and slow magnetoacoustic waves into the interstellar gas. No Alfvén waves are excited, because the oscillations are radially symmetric. Calculations were performed for the following two limiting cases: hot, weakly magnetized interstellar plasma and cold plasma with a strong magnetic field. In these limiting cases, pulsating stars excite mostly fast magnetoacoustic waves, while the excitation of slow magnetoacoustic waves is weak. Magnetogasdynamic fields of density, velocity, and magnetic-field perturbations in the interstellar medium were found. Relations were derived to calculate the radiated power and its estimates are given for various conditions in the medium. It is shown that radially stratified wave structures with wavelengths from 1 AU to several tenths of a parsec must exist in the vicinity of pulsating stars.     

Hydromagnetic waves in structured magnetic fields

Although the inhomogeneous nature of solar magnetic fields is now well established, most theoretical analyses of hydromagnetic wave propagation assume infinite homogeneous fields. Here we reformulate the hydromagnetic wave problem for magnetic fields which vary in one direction perpendicular to the field. The permitted modes of small amplitude hydromagnetic oscillations are considered, first in the case of a single interface between semi-infinite magnetic and non-magnetic compressible regions, and secondly for a magnetic flux sheath of given thickness imbedded in a nonmagnetic region. It is shown that, for small values of R (the ratio of the Alfvén to the sound speed), an acoustic or p-mode wave front passes through the flux sheath with only minor deformation. However, for large R, the transmitted acoustic wave is attenuated and, depending upon the thickness of the flux sheath and the angle of incidence, a hydromagnetic wave may be effectively trapped and guided along the flux sheath. It is also shown that, for the symmetric vibration of the flux sheath in the absence of incident acoustic waves, only slow mode type waves are permitted. Thus, in compressible regions for which R > 1 the Alfvénic-type fast mode is not a permitted mode of free vibration of a flux sheath.     

Slip-Running Reconnection in Quasi-Separatrix Layers

Using time dependent MHD simulations, we study the nature of three-dimensional magnetic reconnection in thin quasi-separatrix layers (QSLs), in the absence of null points. This process is believed to take place in the solar atmosphere, in many solar flares and possibly in coronal heating. We consider magnetic field configurations which have previously been weakly stressed by asymmetric line-tied twisting motions and whose potential fields already possessed thin QSLs. When the line-tied driving is suppressed, magnetic reconnection is solely due to the self-pinching and dissipation of narrow current layers previously formed along the QSLs. A generic property of this reconnection process is the continuous slippage of magnetic field lines along each other, while they pass through the current layers. This is contrary to standard null point reconnection, in which field lines clearly reconnect by pair and abruptly exchange their connectivities. For sufficiently thin QSLs and high resistivities, the field line footpoints slip-run at super-Alfvénic speeds along the intersection of the QSLs with the line-tied boundary, even though the plasma velocity and resistivity are there fixed to zero. The slip-running velocities of a given footpoint have a well-defined maximum when the field line crosses the thinnest regions of the QSLs. QSLs can then physically behave as true separatrices on MHD time scales, since magnetic field lines can change their connections on time scales far shorter than the travel-time of Alfvén waves along them. Since particles accelerated in the diffusive regions travel along the field much faster than the Alfvén speed, slip-running reconnection may also naturally account for the fast motion of hard X-ray sources along chromospheric ribbons, as observed during solar flares. Electronic Supplementary Material Supplementary material is available for this article at     

The problem of phase mixed shear Alfvén waves in the solar corona revisited

The problem of phase mixing of shear Alfvén waves is revisited taking into account dissipative phenomena specific for the solar corona. In regions of space plasmas where the dynamics is controlled by the magnetic field, transport coefficients become anisotropic with transport mechanism having different behavior and magnitude depending on the orientation with respect to the ambient magnetic field. Taking into account realistic values for dissipative coefficients we obtain that the previous results derived in context of torsional Alfvén wave phase mixing are actually heavily underestimated so phase mixing cannot be used to explain the damping of torsional Alfvén waves and heating of open coronal structures. The presented results indicate that in order for phase mixing to still be a viable mechanism to explain heating or wave damping unrealistic assumptions have to be made. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fast Magnetoacoustic Waves in a Fan Structure Above a Coronal Magnetic Null Point

We analyze the 26 November 2005 solar radio event observed interferometrically at frequencies of 244 and 611 MHz by the Giant Metrewave Radio Telescope (GMRT) in Pune, India. These observations are used to make interferometric maps of the event at both frequencies with the time cadence of 1 s from 06:50 to 07:12 UT. These maps reveal several radio sources. The light curves of these sources show that only two sources at 244 MHz and 611 MHz are well correlated in time. The EUV flare is more localized with flare loops located rather away from the radio sources. Using SoHO/MDI observations and potential magnetic field extrapolation we demonstrate that both the correlated sources are located in the fan structure of magnetic field lines starting from a coronal magnetic null point. Wavelet analysis of the light curves of the radio sources detects tadpoles with periods in the range P=10?–?83 s. These wavelet tadpoles indicate the presence of fast magnetoacoustic waves that propagate in the fan structure of the coronal magnetic null point. We estimate the plasma parameters in the studied radio sources and find them consistent with the presented scenario involving the coronal magnetic null point.     

Transmission of Alfvén waves through the rotational discontinuity at magnetopause

The reflection and refraction of MHD waves through an “open” magnetopause (rotational discontinuity) is studied. It is found that most of the incident wave energy can be transmitted through the open magnetopause. A transverse Alfvén wave (or a compressional magnetosonic wave) from the solar wind incident upon the open magnetopause would generally lead to the generation of both the transverse Alfvén and compressional magnetosonic waves in the magnetosphere. Transmission of Alfvén waves in the coplanar rotational discontinuity is studied in detail. The integral power of the Alfvén-wave transfer is found to be proportional to the open magnetic flux of the magnetosphere and is typically ～ 1% of the power of the total electromagnetic energy transfer through the open magnetopause. The transmitted wave power may contribute significantly to the geomagnetic pulsations observed on the ground, especially in the open-field-line region.     

On the role of transition region on the Alfvén wave phase mixing in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of standing Alfvén waves due to phase mixing at the presence of steady flow and sheared magnetic field in the stratified atmosphere of solar spicules. The transition region between chromosphere and corona has also been considered. The initial flow is assumed to be directed along spicule axis, and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that in contrast to propagating Alfvén waves, standing Alfvén waves dissipate in time rather than in space. Density gradients and sheared magnetic fields can enhance damping due to phase mixing. Damping times deduced from our numerical calculations are in good agreement with spicule lifetimes. Since spicules are short living and transient structures, such a fast dissipation mechanism is needed to transport their energy to the corona.     

Interchange Reconnection Alfvén Wave Generation

Given recent observational results of interchange reconnection processes in the solar corona and the theoretical development of the S-Web model for the slow solar wind, we extend the analysis of the 3D MHD simulation of interchange reconnection by Edmondson et al. (Astrophys. J. 707, 1427, 2009). Specifically, we analyze the consequences of the dynamic streamer-belt jump that corresponds to flux opening by interchange reconnection. Information about the magnetic field restructuring by interchange reconnection is carried throughout the system by Alfvén waves propagating away from the reconnection region, distributing the shear and twist imparted by the driving flows, including shedding the injected stress-energy and accumulated magnetic helicity along newly open fieldlines. We quantify the properties of the reconnection-generated wave activity in the simulation. There is a localized high-frequency component associated with the current sheet/reconnection site and an extended low-frequency component associated with the large-scale torsional Alfvén wave generated from the interchange reconnection field restructuring. The characteristic wavelengths of the torsional Alfvén wave reflect the spatial size of the energized bipolar flux region. Lastly, we discuss avenues of future research by modeling these interchange reconnection-driven waves and investigating their observational signatures.     

Ion acceleration and Alfvén wave generation at the Earth’s bow shock

The processes of ion acceleration and Alfvén wave generation by accelerated particles at the Earth’s bow shock are studied within a quasi-linear approach. Steady-state ion and wave spectra are shown to be established in a time of 0.3–4 h, depending on the background level of Alfvénic turbulence in the solar wind. The Alfvén waves produced by accelerated ions are confined within the frequency range 10^?2–1 Hz and their spectral peak with a wave amplitude βB ～ B comparable to the interplanetary magnetic field strength B corresponds to the frequency v = (2–3) × 10^?2 Hz. The high-frequency part of the wave spectrum (v > 0.2 Hz) undergoes damping by thermal ions. The calculated spectra of the accelerated ions and the Alfvén waves generated by them reproduce the main features observed in experiments.     

Influence of the Conversion Layer on the Dispersion Relation of Waves in the Solar Atmosphere

Observations carried out with the Magneto-Optical Filter at Two Heights (MOTH) experiment show upward-traveling wave packets in magnetic regions with frequencies below the acoustic cut-off. We demonstrate that the frequency dependence of the observed travel times, i.e. the dispersion relation, shows significant differences in magnetic and non-magnetic regions. More importantly, at and above the layer where the Alfvén speed equals the sound speed we do not see the dispersion relation of the slow acoustic mode with a lowered cut-off frequency. Our comparisons with theoretical dispersion relations suggest that this is not the slow acoustic wave type for the upward low-frequency wave. From this we speculate that partial mode conversion from the fast acoustic to the fast magnetic wave might take place.