It is conjectured that energy sources of the gamma ray bursts are similar to energy sources which trigger solar and stellar transient activity phenomena like flares, plasma accelerated flows in the flux tubes and, dissipation of energy and acceleration of particles by the MHD waves. Phenomenologically we examine in detail the following energy sources which may trigger gamma ray bursts : (i) cosmic primordial flares which could be solar flare like phenomena in the region of inter galactic or inter galactic cluster regions, (ii) primordial magnetic flux tubes that might have been formed from the convective collapse of the primordial magnetic flux (iii) nonlinear interaction and dissipation of MHD waves that are produced from the perturbations of large-scale inter galactic or inter cluster magnetic field of primordial origin. We examine in detail each of the afore mentioned phenomena keeping in mind that whether such processes are responsible for energy sources of the gamma ray bursts.
By considering the similarity of observations and prevailing physical conditions in the cosmic environment, the following study suggests that most likely and a promising energy source for creation of the gamma ray bursts may be due to primordial flares.
Magnetic flux tubes reaching from the solar convective zone into the chromosphere have to pass through the relatively cool, and therefore non-ideal (i.e. resistive) photospheric region enclosed between the highly ideal sub-photospheric and chromospheric plasma. It is shown that stationary MHD equilibria of magnetic flux tubes which pass through this region require an inflow of photospheric material into the flux tube and a deviation from iso-rotation along the tube axis. This means that there is a difference in angular velocity of the plasma flow inside the tube below and above the non-ideal r…
The structure and dynamics of small vertical photospheric magnetic flux concentrations has been often treated in the framework of an approximation based upon a low-order truncation of the Taylor expansions of all quantities in the horizontal direction, together with the assumption of instantaneous total pressure balance at the boundary to the non-magnetic external medium. Formally, such an approximation is justified if the diameter of the structure (a flux tube or a flux sheet) is small compared to all other relevant length scales (scale height, radius of curvature, wavelength, etc.). The adve…
Magnetohydrodynamic (MHD) waves are often reported in the solar atmosphere and usually classified as slow, fast, or Alfvén. The possibility that these waves have mixed properties is often ignored. The goal of this work is to study and determine the nature of MHD kink waves. This is done by calculating the frequency, the damping rate and the eigenfunctions of MHD kink waves for three widely different MHD waves cases: a compressible pressure-less plasma, an incompressible plasma and a compressible plasma with non-zero plasma pressure which allows for MHD radiation. In all three cases the frequen…
Magnetohydrodynamic (MHD) waves are ubiquitously observed in the solar atmosphere. Kink waves are a type of transverse MHD waves in magnetic flux tubes that are damped due to resonant absorption. The theoretical study of kink MHD waves in solar flux tubes is usually based on the simplification that the transverse variation of density is confined to a nonuniform layer much thinner than the radius of the tube, i.e., the so-called thin boundary approximation. Here, we develop a general analytic method to compute the dispersion relation and the eigenfunctions of ideal MHD waves in pressureless flu…
The potential field approximation has been providing a fast, and computationally inexpensive estimation for the solar corona's global magnetic field geometry for several decades. In contrast, more physics-based global magnetohydrodynamic (MHD) models have been used for a similar purpose, while being much more computationally expensive. Here, we investigate the difference in the field geometry between a global MHD model and the potential field source surface model (PFSSM) by tracing individual magnetic field lines in the MHD model from the Alfven surface (AS), through the source surface (SS), a…
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 more or equal 1. The axial magnetic field strength inside and outside the tube will be allowed to vary,…
Magnetohydrodynamic (MHD) kink waves have been observed frequently in solar coronal flux tubes, which makes them a great tool for seismology of the solar corona. Here, the effect of viscosity is studied on the evolution of kink waves. To this aim, we solve the initial value problem for the incompressible linearized viscous MHD equations in a radially inhomogeneous flux tube in the limit of long wavelengths. Using a modal expansion technique the spatio-temporal behavior of the perturbations is obtained. We confirm that for large Reynolds numbers representative of the coronal plasma the decremen…
The aim of this paper is to model the propagation of slow magnetohydrodynamic (MHD) sausage waves in a thick expanding magnetic flux tube in the context of the quiescent (VAL C) solar atmosphere. The propagation of these waves is found to be described by the Klein-Gordon equation. Using the governing MHD equations and the VAL C atmosphere model we study the variation of the cut-off frequency along and across the magnetic tube guiding the waves. Due to the radial variation of the cut-off frequency the flux tubes act as low frequency filters for waves.
We report and analyze the observational evidence of global kink oscillations in a solar filament as observed in H alpha by National Solar Observatory (NSO)/Global Oscillation Network Group (GONG) instrument. An M1.1-class flare in active region 11692 on 2013 March 15 induced a global kink mode in the filament lying in the south-west of AR11692.We find periods of about 61 - 67 minutes and damping times of 92 - 117 minutes at three vertical slice positions chosen in and around the filament apex. We find that the waves are damped. From the observed global kink mode period and damping time scale u…
Magnetohydrodynamic (MHD) kink waves are ubiquitously observed in the solar atmosphere. The propagation and damping of these waves may play relevant roles for the transport and dissipation of energy in the solar atmospheric medium. However, in the atmospheric plasma dissipation of transverse MHD wave energy by viscosity or resistivity needs very small spatial scales to be efficient. Here, we theoretically investigate the generation of small scales in nonuniform solar magnetic flux tubes due to phase mixing of MHD kink waves. We go beyond the usual approach based on the existence of a global qu…
In this study we explore the possibility of simplifying the modeling of magnetohydrodynamic (MHD) slow body modes observed in photospheric magnetic structure such as the umbrae of sunspots and pores. The simplifying approach assumes that the variation of the eigenvalues of slow body waves can be derived by imposing that the longitudinal component of velocity with respect to the tube axis is zero at the boundary of the magnetic flux tube, which is in a good agreement with observations. To justify our approach we compare the results of our simplified model for slow body modes in cylindrical flux…
Magnetohydrodynamic (MHD) instabilities allow energy to be released from stressed magnetic fields, commonly modelled in cylindrical flux tubes linking parallel planes, but, more recently, also in curved arcades containing flux tubes with both footpoints in the same photospheric plane. Uncurved cylindrical flux tubes containing multiple individual threads have been shown to be capable of sustaining an MHD avalanche, whereby a single unstable thread can destabilise many. We examine the properties of multi-threaded coronal loops, wherein each thread is created by photospheric driving in a realist…
We describe a 3D finite-difference spherical anelastic MHD (FSAM) code for modeling the subsonic dynamic processes in the solar convective envelope. A comparison of this code with the widely used global spectral anlastic MHD code, ASH (Anelastic Spherical Harmonics), shows that FSAM produces convective flows with statistical properties and mean flows similar to the ASH results. Using FSAM, we first simulate the rotating solar convection in a partial spherical shell domain and obtain a statistically steady, giant-cell convective flow with a solar-like differential rotation. We then insert buoya…
In this paper, we study kink and sausage oscillations in the presence of longitudinal background flow. We study resonant absorption of the kink and sausage modes in the slow continuum under magnetic pore conditions in the presence of flow. we determine the dispersion relation then solve it numerically, and find the frequencies and damping rates of the slow kink and sausage surface modes. We also, obtain analytical solution for the damping rate of the slow surface mode in the long wavelength limit. We show that in the presence of plasma flow, resonance absorption can result in strong damping fo…
In this study, the properties of wavefunctions of the MHD oscillations for a single and a system of straight flux tubes are investigated. Magnetic flux tubes with a straight magnetic field and longitudinal density stratification were considered in zero-βapproximation. A single three-dimensional wave equation (eigen value problem) is solved for longitudinal component of the perturbed magnetic field using the finite element method (FEM). Wavefunctions (eigenfunction of wave equation) of the MHD oscillations are categorized into sausage, kink, helical kink and fluting modes. Concerning the amplit…
We have performed a three-dimensional magnetohydrodynamic simulation to study the emergence of a twisted magnetic flux tube from -20,000 km of the solar convection zone to the corona through the photosphere and the chromosphere. The middle part of the initial tube is endowed with a density deficit to instigate a buoyant emergence. As the tube approaches the surface, it extends horizontally and makes a flat magnetic structure due to the photosphere ahead of the tube. Further emergence to the corona breaks out via the interchange-mode instability of the photospheric fields, and eventually severa…
We perform MHD modeling of a single bright coronal loop to include the interaction with a non-uniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube, in the solar atmosphere extending from the high-beta chromosphere to the low-beta corona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The ma…
Aims. We investigate the transfer of energy between a standing kink mode and azimuthal Alfven waves within an expanding flux tube. We consider the process of resonant absorption in a loop with a non-uniform Alfven frequency profile but in the absence of a radial density gradient. Methods. Using the MHD code, Lare3d, we model an oscillating magnetic flux tube that expands radially with height. An initially straight loop structure with a magnetic field enhancement is relaxed towards a force-free state before a standing kink mode is introduced. Results. We demonstrate that the transverse gradient…
Current sheets are ubiquitous in the solar wind.They are a major source of the solar wind MHD turbulence intermittency. They may result from non-linear interactions of the solar wind MHD turbulence or are the boundaries of flux tubes that originate from the solar surface. Some current sheets appear in pairs and are the boundaries of transient structures such as magnetic holes and reconnection exhausts, or the edges of pulsed Alfvén waves. For an individual current sheet, discerning whether it is a flux tube boundary or due to non-linear interactions, or the boundary of a transient structure is…
We study the conditions under which high mode magnetohydrodynamic (MHD) waves propagating on a rotating jet emerging from the filament eruption on 2013 April 10--11 can became unstable against the Kelvin--Helmholtz instability (KHI). The evolution of jet indicates the blob like structure at its boundary which could be one of the observable features of the KHI development. We model the jet as a twisted rotating axially moving magnetic flux tube and explore the propagation characteristics of the running MHD modes on the basis of dispersion relations derived in the framework of the ideal magnetoh…
There are observational evidences for the existence of twisted magnetic field in the solar corona. Here, we have investigated resonant damping of the magnetohydrodynamic (MHD) kink waves in magnetic flux tubes. A realistic model of the tube with continuous magnetic twist and radially inhomogeneous density profile has been considered. We have obtained the dispersion relation of the kink wave using the solution to the linear MHD equations outside the density inhomogeneity and the appropriate connection formula to the solutions across the thin transitional boundary layer. The dependence of the os…
Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. Alfven waves and magneto-sonic waves are particular classes of MHD waves. These wave modes are clearly different and have pure properties in uniform plasmas of infinite extent only. Due to plasma non-uniformity MHD waves have mixed properties and cannot be classified as pure Alfven or magneto-sonic waves. However, vorticity is a quantity unequivocally related to Alfven waves as compression is for magneto-sonic waves. Here, we investigate MHD waves superimposed on a one-dimensional non-uniform straight cylinder with constan…
The astropause (heliopause for the Sun) is the tangential discontinuity separating the stellar wind from the interstellar plasma. The global shape of the heliopause is a matter of debates. Two types of the shape are under discussion: comet-like and tube-like. In the second type the two-jets oriented toward the stellar rotation axis are formed by the action of azimuthal component of the stellar magnetic field. We explore a simplified global astrosphere in which: (1) the surrounding and moving with respect to the star circumstellar medium is fully ionized, (2) the interstellar magnetic field is …
Transverse oscillations of coronal loops are often observed and have been theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical simulations by Terradas et al. (2008, ApJ 687, L115) suggest that shear flows generated at the loop boundary during kink oscillations could give rise to a Kelvin-Helmholtz instability (KHI). Here, we investigate the linear stage of the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear motions. We consider the basic, linearized MHD equations in the beta = 0 approximation, and apply them to a straight and homogeneous cylin…
Observations show that waves are ubiquitous in the solar atmosphere and may play an important role for plasma heating. The study of waves in the solar corona is usually based on linear ideal magnetohydrodynamics (MHD) for a fully ionized plasma. However, the plasma in the photosphere and the chromosphere is only partially ionized. Here we investigate theoretically the impact of partial ionization on MHD wave propagation in cylindrical flux tubes in the two-fluid model. We derive the general dispersion relation that takes into account the effects of neutral-ion collisions and the neutral gas pr…
Waves and oscillations can provide vital information about the internal structure of waveguides they propagate in. Here, we analytically investigate the effects of density and magnetic stratification on linear longitudinal magnetohydrodynamic (MHD) waves. The focus of this paper is to study the eigenmodes of these oscillations. It is our specific aim is to understand what happens to these MHD waves generated in flux tubes with non-constant (e.g., expanding or magnetic bottle) cross-sectional area and density variations. The governing equation of the longitudinal mode is derived and solved anal…
We investigate the conditions under which the magnetohydrodynamic (MHD) modes in a cylindrical magnetic flux tube moving along its axis become unstable against the Kelvin--Helmholtz (KH) instability. We \textbf{use} the dispersion relations of MHD modes \textbf{obtained} from the linearized Hall MHD equations for cool (zero beta) plasma \textbf{by assuming} real wave numbers and complex angular wave frequencies\textbf{/complex wave phase velocities}. The dispersion equations are solved numerically at fixed input parameters and varying values of the ratio $l_\mathrm{Hall}/a$, where $l_\mathrm{H…
It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere and therefore, the study of resonant absorption for these modes have become a pressing issue as it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is base…
We model an imaged Kelvin-Helmholtz (KH) instability on a coronal mass ejecta (CME) in the lower corona by investigating conditions under which kink ($m = 1$) and $m = -3$ magnetohydrodynamic (MHD) modes in an uniformly twisted flux tube moving along its axis become unstable. We employ the dispersion relations of MHD modes derived from the linearised magnetohydrodynamic equations. We assume real wave numbers and complex angular wave frequencies, namely complex wave phase velocities. The dispersion relations are solved numerically at fixed input parameters (taken from observational data) and va…
Magnetic twist is thought to play an important role in coronal loops. The effects of magnetic twist on stable magnetohydrodynamic (MHD) waves is poorly understood because they are seldom studied for relevant cases. The goal of this work is to study the fingerprints of magnetic twist on stable transverse kink oscillations. We numerically calculated the eigenmodes of propagating and standing MHD waves for a model of a loop with magnetic twist. The azimuthal component of the magnetic field was assumed to be small in comparison to the longitudinal component. We did not consider resonantly damped m…
High-resolution observations of the solar photosphere have identified a wide variety of spiralling motions in the solar plasma. These spirals vary in properties, but are observed to be abundant at the solar surface. In this work these spirals are studied for their potential as magnetohydrodynamic (MHD) wave generation mechanisms. The inter-granular lanes, where these spirals are commonly observed, are also regions where the magnetic field strength is higher than average. This combination of magnetic field and spiralling plasma is a recipe for the generation of Alfvén waves and other MHD waves.…
In the context of the solar atmosphere, we re-examine the role of of neutral and ionized species in dissipating the ordered energy of intermediate-mode MHD waves into heat. We solve conservation equations for the hydrodynamics and for hydrogen and helium ionization stages, along closed tubes of magnetic field. First, we examine the evolution of coronal plasma under conditions where coronal heating has abruptly ceased. We find that cool ($< 10^5$K) structures are formed lasting for several hours. MHD waves of modest amplitude can heat the plasma through ion-neutral collisions with sufficient en…
The standing quasi-modes of the ideal MHD in a zero-$β$ cylindrical magnetic flux tube that undergoes a longitudinal density stratification and radial density structuring is considered. The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae of the resonant absorption, the dispersion relation for the fast MHD body waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone, $k=1,2$ modes of both the kink ($m=1$), and fluting ($m=2$) waves. Where $k$ and $m$ are the long…
The aim of this work is to study the energy transport by means of MHD waves propagating in quiet Sun magnetic topology from layers below the surface to the corona. Upward propagating waves find obstacles, such as the equipartition layer with plasma b=1 and the transition region, and get converted, reflected and refracted. Understanding the mechanisms by which MHD waves can reach the corona can give us information about the solar atmosphere and the magnetic structures. We carry out two-dimensional numerical simulations of wave propagation in a magnetic field structure that consists of two verti…
In this paper, we apply the Rayleigh-Ritz Variational Scheme for studying the transverse oscillations of a magnetic flux tube. The flux tube is considered in low-$β$ solar coronal condition. The perturbations decomposed into irrotational and solenoidal components and MHD equations are reduced as a matrix eigenvalue problem. In the case of longitudinally stratified thin flux tube, the fundamental and higher order kink frequencies are computed. The results are in good agreements with previous studies.
Observations show that transverse magnetohydrodynamic (MHD) waves and flows are often simultaneously present in magnetic loops of the solar corona. The waves are resonantly damped in the Alfvén continuum because of plasma and/or magnetic field nonuniformity across the loop. The resonant damping is relevant in the context of coronal heating, since it provides a mechanism to cascade energy down to the dissipative scales. It has been theoretically shown that the presence of flow affects the waves propagation and damping, but most of the studies rely on the unjustified assumption that the transver…
We study the physical properties and behavior of the solar atmosphere during the GOES X1.6 solar flare on 2014 September 10. The steady plasma flows and the fast sausage MHD waves were analysed with the wavelet separation method. The magnetically coupled atmosphere and the forced magnetic field reconnection were studied with the help of the Vertical-Current Approximation Non-linear Force-Free Field code. We studied a mechanism of MHD wave transfer from the photosphere without dissipation or reflection before reaching the corona and a mechanism of the wave energy distribution over the solar cor…
We present the results of three-dimensional numerical simulations to investigate the excitation of waves in the magnetic network of the Sun due to footpoint motions of a magnetic flux tube. We consider motions that typically mimic granular buffeting and vortex flows and implement them as driving motions at the base of the flux tube. The driving motions generates various MHD modes within the flux tube and acoustic waves in the ambient medium. The response of the upper atmosphere to the underlying photospheric motion and the role of the flux tube in channeling the waves is investigated. We compu…
The equilibrium of current-carrying magnetic fields (e.g. flux tubes) embedded in a large-scale background field is developed and discussed in the astrophysical context. Embedded non-force-free current-carrying fields require a minimum surrounding atmosphere, which by direct pressure balance has a gas pressure everywhere proportional to the background magnetic pressure. Formally, the MHD equations, with flows and gravity as part of a wide class of physical processes, separate into independent local and global relations representing an equilibrium solution for embedded current-carrying fields. …
I present results from a set of 3D spherical-shell MHD simulations of the buoyant rise of active region flux tubes in the solar interior which put new constraints on the initial twist of the subsurface tubes in order for them to emerge with tilt angles consistent with the observed Joy's law for the mean tilt of solar active regions. Due to the asymmetric stretching of the $Ω$-shaped tube by the Coriolis force, a field strength asymmetry develops with the leading side having a greater field strength and thus being more cohesive compared to the following side. Furthermore, the magnetic flux in t…
We investigate the conditions under which the fluting ($m = 2$), $m = 3$, and $m = 12$ magnetohydrodynamic (MHD) modes in a uniformly twisted flux tube moving along its axis become unstable in order to model the Kelvin--Helmholtz (KH) instability in a twisting solar coronal hole jet near the northern pole of the Sun. Using a twisting jet of 2010 August 21 by \emph{SDO}/AIA and other observations of coronal jets we set the parameters of our theoretical model and have obtained that in a twisted magnetic flux tube of radius of $9.8$~Mm, at a density contrast of $0.474$ and fixed Alfvén Mach numbe…
Alfvénic Motions in a Stratified Open Flux Tube: Transition from Propagating to Locally Standing Motions and Implications for the Kelvin-Helmholtz Instability
Institute of Frontier and Interdisciplinary Science, Shandong University（山东大学前沿交叉科学研究院）；Shandong Key Laboratory of Space Environment and Exploration Technology, Institute of Space Sciences, Shandong University（山东大学空间科学学院山东省空间环境与探测技术重点实验室）；School of Earth and Space Sciences, Peking University（北京大学地球与空间科学学院）；Centre for mathematical Plasma Astrophysics (CmPA), Department of Mathematics, KU Leuven（荷语鲁汶大学数学系数学等离子体天体物理中心）
Magnetic flux emergence from the solar interior to the atmosphere is believed to be a key process of formation of solar active regions and driving solar eruptions. Due to the limited capability of observation, the flux emergence process is commonly studied using numerical simulations. In this paper, we developed a numerical model to simulate the emergence of a twisted magnetic flux tube from the convection zone to the corona using the AMR--CESE--MHD code, which is based on the conservation-element solution-element method with adaptive mesh refinement. The result of our simulation agrees with t…
There is ample evidence of twisted magnetic structures in the solar corona. This motivates us to consider the magnetic twist as the cause of Alfven frequency continuum in the coronal loops, which can support the resonant absorption as a rapid damping mechanism for the observed coronal kink magnetohydrodynamic (MHD) oscillations. We model a coronal loop with a straight cylindrical magnetic flux tube which has constant but different densities in the interior and exterior regions. The magnetic field is assumed to be constant and aligned with the cylinder axis everywhere except a thin layer near t…
Recent observations by Hinode/SOT show that MHD waves and mass flows are simultaneously present in the fine structure of solar prominences. We investigate standing kink magnetohydrodynamic (MHD) waves in flowing prominence threads from a theoretical point of view. We model a prominence fine structure as a cylindrical magnetic tube embedded in the solar corona with its ends line-tied in the photosphere. The magnetic cylinder is composed of a region with dense prominence plasma, which is flowing along the magnetic tube, whereas the rest of the flux tube is occupied by coronal plasma. We use the …
The nonaxisymmetric magnetohydrodynamic (MHD) modes in a zero-beta cylindrical compressible thin magnetic flux tube modelled as a twisted core surrounded by a magnetically twisted annulus, both embedded in a straight ambient external field is considered. The dispersion relation is derived and solved analytically and numerically to obtain the frequencies of the nonaxisymmetric MHD waves. The main result is that the twisted magnetic annulus does affect the period ratio P_1/P_2 of the kink modes. For the kink modes, the magnetic twist in the annulus region can achieve deviations from P_1/P_2 = 2 …
The separation of a filament and sigmoid is observed during an X1.4 flare on July 12, 2012 in solar active region 11520, but the corresponding magnetic field change is not clear. We construct a data-constrained magnetohydrodynamic simulation of the filament-sigmoid system with the flux rope insertion method and magnetic flux eruption code, which produces the magnetic field evolution that may explain the separation of the low-lying filament and high-lying hot channel (sigmoid). The initial state of the magnetic model contains a magnetic flux rope with a hyperbolic flux tube, a null point struct…
We discuss some aspects of magnetic reconnection which could help in understanding many aspects of magnetic plasma interactions. We will show that the helical structure often observed in polar jets is a natural consequence of magnetic helicity conservation in 3D reconnection driven by a collision of two parts of an emerging flux tube within the single emerged loop. We perform 3D simulations by solving the time-dependent, ideal MHD equations with a uniform initial twist. We deduce that the emergence of highly twisted magnetic flux introduces several null points, which in turn causes reconnectio…
In this paper we study the dynamics of toroidal flux tubes emerging from the solar interior, through the photosphere and into the corona. Many previous theoretical studies of flux emergence use a twisted cylindrical tube in the solar interior as the initial condition. Important insights can be gained from this model, however, it does have shortcomings. The axis of the tube never fully emerges as dense plasma becomes trapped in magnetic dips and restrains its ascent. Also, since the entire tube is buoyant, the main photospheric footpoints (sunspots) continually drift apart. These problems make …
Magneto-hydrodynamic (MHD) simulations of the emergence of twisted magnetic flux tubes from the solar interior into the corona are discussed to illustrate how twisted and sheared coronal magnetic structures (with free magnetic energy), capable of driving filament eruptions, can form in the corona in emerging active regions. Several basic mechanisms that can disrupt the quasi-equilibrium coronal structures and trigger the release of the stored free magnetic energy are discussed. These include both ideal processes such as the onset of the helical kink instability and the torus instability of a t…
