Characterized by cyclic axisymmetric perturbations to both the magnetic and fluid parameters, magnetohydrodynamic fast sausage modes (FSMs) have proven useful for solar coronal seismology given their ...strong dispersion. This review starts by summarizing the dispersive properties of the FSMs in the canonical configuration where the equilibrium quantities are transversely structured in a step fashion. With this preparation we then review the recent theoretical studies on coronal FSMs, showing that the canonical dispersion features have been better understood physically, and further exploited seismologically. In addition, we show that departures from the canonical equilibrium configuration have led to qualitatively different dispersion features, thereby substantially broadening the range of observations that FSMs can be invoked to account for. We also summarize the advances in forward modeling studies, emphasizing the intricacies in interpreting observed oscillatory signals in terms of FSMs. All these advances notwithstanding, we offer a list of aspects that remain to be better addressed, with the physical connection of coronal FSMs to the quasi-periodic pulsations in solar flares particularly noteworthy.
Kink Oscillations of Coronal Loops Nakariakov, V. M.; Anfinogentov, S. A.; Antolin, P. ...
Space science reviews,
09/2021, Letnik:
217, Številka:
6
Journal Article
Recenzirano
Odprti dostop
Kink oscillations of coronal loops, i.e., standing kink waves, is one of the most studied dynamic phenomena in the solar corona. The oscillations are excited by impulsive energy releases, such as low ...coronal eruptions. Typical periods of the oscillations are from a few to several minutes, and are found to increase linearly with the increase in the major radius of the oscillating loops. It clearly demonstrates that kink oscillations are natural modes of the loops, and can be described as standing fast magnetoacoustic waves with the wavelength determined by the length of the loop. Kink oscillations are observed in two different regimes. In the rapidly decaying regime, the apparent displacement amplitude reaches several minor radii of the loop. The damping time which is about several oscillation periods decreases with the increase in the oscillation amplitude, suggesting a nonlinear nature of the damping. In the decayless regime, the amplitudes are smaller than a minor radius, and the driver is still debated. The review summarises major findings obtained during the last decade, and covers both observational and theoretical results. Observational results include creation and analysis of comprehensive catalogues of the oscillation events, and detection of kink oscillations with imaging and spectral instruments in the EUV and microwave bands. Theoretical results include various approaches to modelling in terms of the magnetohydrodynamic wave theory. Properties of kink oscillations are found to depend on parameters of the oscillating loop, such as the magnetic twist, stratification, steady flows, temperature variations and so on, which make kink oscillations a natural probe of these parameters by the method of magnetohydrodynamic seismology.
ABSTRACT
The aim is to state the properties of ion acoustic solitary waves in course of collision and extract characteristics of the daughter wave in a magnetized electron–ion plasma. The magnetized ...plasma medium that is a constituent of white dwarfs and astrophysical plasmas that possesses relativistically degenerate electrons and thermal ions in the presence of a constant background magnetic field. The model is based on the extended Poincaré–Lighthill–Kuo (ePLK) method where a set of Korteweg–de Vries equations is obtained to show the phase shifts of colliding waves together with the amplitude and width of the born daughter solitary waves. The numerical results and presented figures regarding the amplitude and width of solitons provide a description of the influence of plasma parameters on soliton interactions, namely ion to electron temperature ratio (σi), ion cyclotron frequency (ωci), and angle between magnetic field and collision line (θ) together with their interplay in shaping the character of solitary waves. It is concluded that only rarefactive electrostatic non-linear waves are able to propagate in such plasma media. The daughter wave amplitude possesses a scaling behaviour regarding the impact angle. Interplay of the parameters on the phase shifts is presented. Ratio of amplitude and width of the daughter wave is directly proportional to the background field, the impact angle controls its maximum. It is observed that the magnetic field elevates ratio of the solitary wave amplitude to width leading it to a shorter life and hence interaction range with neighbouring sites.
ABSTRACT
The aim of this study is to shed light on the effects connected with thermal misbalance due to non-equal cooling and heating rates induced by density and temperature perturbations in solar ...active regions hosting either propagating torsional or shear Alfvén waves. A description for the non-linear forces connected with Alfvén waves in non-ideal conditions is provided, based on the second-order thin flux tube approximation. This provides insight into the effects of Alfvén-induced motions on the boundary of thin magnetic structures in thermally active plasmas. The equations describing the process of generating longitudinal velocity perturbations, together with density perturbations by non-linear torsional Alfvén waves, are obtained and solved analytically. It is shown that the phase shift (compared with the ideal case) and the amplitude of the induced longitudinal plasma motions against the period of the mother Alfvén wave are greater for shear Alfvén waves compared with torsional Alfvén waves, although following the same pattern. The difference in the influence of thermal misbalance on the induced velocity perturbations is governed by the plasma-β although its effect is stronger for shear waves. It is deduced that for a harmonic Alfvén driver the induced density perturbations are left uninfluenced by the thermal misbalance.
Abstract
The aim of this study is to model the nature of nonlinear torsional magnetohydrodynamic waves propagating in solar jets as they are elevated to the outer solar atmosphere. The contribution ...of sequential processes to the transfer of energy is taken under consideration: the nonlinear cascade and shock formation. Thus a straight magnetic cylinder embedded in a plasma with an initial magnetic field and parallel flow to the cylinder axis is implemented. To resemble a jet where the oscillation wavelength highly exceeds the radius, the second-order thin flux tube approximation proves adequate. A Cohen–Kulsrud type equation is presented, and its solution highly depends on the parameter presented in this study, which itself is constituted of various environmental and equilibrium conditions that affect the perturbations of the variables as well as the nonlinear forces connected to Alfvén wave propagation. The shock formation time of torsional waves is inversely proportional to the density contrast of the jet, while the efficiency of energy transfer to shorter scales is directly proportional to the density contrast. While the parallel flow with a shear at the boundary expedites shock formation, its efficiency regarding energy transfer is dramatically enhanced by the plasma-
β
, significantly contributing to coronal heating. The observational and seismological aspect of the present study is that faster jets are less probable for observations at higher altitudes, as they experience energy transfer mostly at the base of the corona, while slow speed jets may be observed at higher altitudes contributing to solar wind acceleration.
We model fast magnetohydrodynamic sausage and kink wave characteristics propagating in solar slab-like plasma structures. By implementing Cartesian coordinates, explicit expressions are provided ...governing the dependence of the frequency, damping, damping time, phase, and group speeds of fast sausage and kink waves on the wavenumber and density contrasts of solar slab-like plasmas. Explicit expressions are presented through equilibrium conditions and physical parameters controlling the plasma structure. Solutions of the explicit expressions are compared with numerical results. The overlap of curves proves adequate for the robustness of the explicit expressions. Kink modes possess higher frequencies compared to sausage modes in the leaky regime, while the sausage mode phase speed increases more rapidly compared to the kink speed. This explains the higher group speeds of sausage waves compared to kink waves around the cutoff. Sausage waves damp quicker compared with kink waves. The damping is inversely proportional to the mode number. As the damping time is directly proportional with the wavenumber, the damping time is much higher around the cutoff frequency compared to the long wavelength limit. The presented expressions prove adequate for coronal seismology, where, as the magnetoacoustic oscillations damp and disappear, the local and neighboring physical parameters and conditions could be estimated. As leaky kink modes live longer than sausage modes, they have a higher chance of being observed while transporting energy to a broader region. Sausage modes penetrate less due to fast damping providing higher heating rates in shorter ranges. Both modes contribute to coronal heating in various scales.
ABSTRACT
The aim here is to model torsional waves in homogeneous and expanding twisted flux tubes of solar coronal magnetic plasma structures. For the sake of simplicity, a force-free condition ...applicable to solar magnetic structures is presented to determine the existing three-dimensional equilibrium magnetic fields. The determined magnetic field is implemented to study the effects of the magnetic twist parameter on the eigenvalues and eigenfunctions of torsional waves. Solenoidal and force-free conditions are applied to find the three-dimensional components of the magnetic field with respect to the numerical flux function. The obtained differential equation is linear where the technique of the separation of variables is implemented in order to solve it. The equilibrium magnetic field components and appropriate vector potential are extracted. Using the provided components in the magnetohydrodynamic theory, a differential equation that governs the frequency dependence of the torsional wave is obtained, whereby the differential transform method is solved. Both eigenvalues and eigenfunctions of torsional waves are calculated numerically. The obtained values for the frequency of the fundamental mode and its first harmonic, together with appropriate functions, exhibit a fine consistency with observations, with regards to the ratio of ω2/ω1, which is estimated to be around 2. At a fixed distance from the tube axis, the ratio increases with the increase of the twist parameter. The higher the applied twist parameter, the more variations of the ω2/ω1 ratio are observed. We cannot find significant variations of the eigenfunctions of torsional waves due to the twist parameter. The consistency between analytical results and observations proves adequate for implementing a force-free equilibrium magnetic field subject to conditions in solar plasma structures regarding torsional wave propagation.
ABSTRACT
Torsional Alfvén waves in coronal plasma loops are usually considered to be non-collective, i.e. consist of cylindrical surfaces evolving independently, which significantly complicates their ...detection in observations. This non-collective nature, however, can get modified in the non-linear regime. To address this question, the propagation of non-linear torsional Alfvén waves in straight magnetic flux tubes has been investigated numerically using the astrophysical MHD code Athena++ and analytically, to support numerical results, using the perturbation theory up to the second order. Numerical results have revealed that there is radially uniform-induced density perturbation whose uniformity does not depend on the radial structure of the mother Alfvén wave. Our analysis showed that the ponderomotive force leads to the induction of the radial and axial velocity perturbations, while the mechanism for the density perturbation is provided by a non-equal elasticity of a magnetic flux tube in the radial and axial directions. The latter can be qualitatively understood by the interplay between the Alfvén wave perturbations, external medium, and the flux tube boundary conditions. The amplitude of these non-linearly induced density perturbations is found to be determined by the amplitude of the Alfvén driver squared and the plasma parameter β. The existence of the collective and radially uniform density perturbation accompanying non-linear torsional Alfvén waves could be considered as an additional observational signature of Alfvén waves in the upper layers of the solar atmosphere.
Our objective is to study the collimation of solar jets by nonlinear forces corresponding to torsional Alfvén waves together with external forces. We consider a straight, initially non-rotating, ...untwisted magnetic cylinder embedded in a plasma with a straight magnetic field, where a shear between the internal and external flows exists. By implementing magnetohydrodynamic theory and taking into account the second-order thin flux tube approximation, the balance between the internal nonlinear forces is visualized. The nonlinear differential equation containing the ponderomotive, magnetic tension, and centrifugal forces in the presence of the shear flow is obtained. The solution presents the scale of influence of the propagating torsional Alfvén wave on compressive perturbations. Explicit expressions for the compressive perturbations caused by the forces connected to the torsional Alfvén wave show that, in the presence of a shear flow, the magnetic tension and centrifugal forces do not cancel each other's effects as they did in its absence. This shear flow plays in favor of the magnetic tension force, resulting in a more efficient collimation. Regarding the ponderomotive force, the shear flow has no effect. The phase relations highlight the interplay of the shear flow and the plasma-β. As the shear flow and plasma-β increase, compressive perturbation amplitudes emerge. We conclude that the jet collimation due to the torsional Alfvén wave highly depends on the location of the jet. The shear flow tightens the collimation as the jet elevates up to the solar corona.
The dynamics of networks forming on Heider balance theory moves towards lower tension states. The condition derived from this theory enforces agents to reevaluate and modify their interactions to ...achieve equilibrium. These possible changes in network’s topology can be considered as various paths that guide systems to minimum energy states. Based on this theory the final destination of a system could reside on a local minimum energy, “jammed state”, or the global minimum energy, balanced states. The question we would like to address is whether jammed states just appear by chance? Or there exist some pseudo paths that bound a system towards a jammed state. We introduce an indicator to suspect the location of a jammed state based on the Inverse Participation Ratio method (IPR). We provide a margin before a local minimum where the number of possible paths dramatically drastically decreases. This is a condition that proves adequate for ending up on a jammed states.
•We show how the participation of individuals affects the evolution of communities.•We show that the minimum locals based on the Heider balance theory just do not pop up.•We introduce an indicator that suspects the minimum states.•The paths that bound the system to end up in a jammed state are flagged.
PDF
