Evolution Of Magnetic Flux Ropes Research Articles

Solar magnetic flux rope identification with GUITAR: GUI for Tracking and Analysing flux Ropes

Modelling the early evolution of magnetic flux ropes (MFRs) in the solar atmosphere is crucial for understanding their destabilization and eruption mechanism. Identifying the relevant magnetic field lines in simulation data, however, is not straightforward. In previous work an extraction and tracking method was developed to facilitate this task. Here, we present the corresponding graphical user interface (GUI), called GUITAR (GUI for Tracking and Analysing flux Ropes), with the aim to offer a variety of tools to the community for identifying and tracking MFRs. The starting point is a map of a selected proxy parameter for MFRs, e.g., a map of the twist-parameter Tw, current density, etc. We showcase how the GUITAR tools can be used to disentangle a multi-MFR system and facilitate in-depth analysis of their properties and evolution by applying them on a time-dependent data-driven magnetofrictional model (TMFM) simulation of solar active region AR12473. We show the MFR extraction using Tw maps, together with targeted use of mathematical morphology algorithms and discuss the evolution of the system.

Evolution of a Magnetic Flux Rope toward Eruption

Abstract It is well accepted that a magnetic flux rope (MFR) is a critical component of many coronal mass ejections (CMEs), yet how it evolves toward eruption remains unclear. Here we investigate the continuous evolution of a pre-existing MFR, which is rooted in strong photospheric magnetic fields and electric currents. The evolution of the MFR is observed by the Solar Terrestrial Relations Observatory (STEREO) and the Solar Dynamics Observatory (SDO) from multiple viewpoints. From STEREO’s perspective, the MFR starts to rise slowly above the limb five hours before it erupts as a halo CME on 2012 June 14. In SDO observations, conjugate dimmings develop on the disk, simultaneously with the gradual expansion of the MFR, suggesting that the dimmings map the MFR’s feet. The evolution comprises a two-stage gradual expansion followed by another stage of rapid acceleration/eruption. Quantitative measurements indicate that magnetic twist of the MFR increases from 1.0 ± 0.5 to 2.0 ± 0.5 turns during the five-hour expansion, and further increases to about 4.0 turns per astronomical unit (au) when detected as a magnetic cloud at 1 au two days later. In addition, each stage is preceded by flare(s), implying reconnection is actively involved in the evolution and eruption of the MFR. The implications of these measurements on the CME initiation mechanisms are discussed.

Toward Understanding the 3D Structure and Evolution of Magnetic Flux Ropes in an Extremely Long Duration Eruptive Flare

Abstract In this work, we analyze the initial eruptive process of an extremely long duration C7.7-class flare that occurred on 2011 June 21. The flare had a 2 hr long rise time in soft X-ray emission, which is much longer than the rise time of most solar flares, including both impulsive and gradual ones. Combining the facts that the flare occurred near the disk center as seen by the Solar Dynamic Observatory (SDO) but near the limb as seen by two Solar Terrestrial Relations Observatory (STEREO) spacecraft, we are able to track the evolution of the eruption in 3D in a rare slow-motion manner. The time sequence of the observed large-scale EUV hot channel structure in the Atmospheric Imaging Assembly (AIA) high-temperature passbands of 94 and 131 Å clearly shows the process of how the sigmoid structure prior to the eruption was transformed into a near-potential post-eruption loop arcade. We believe that the observed sigmoid represents the structure of a twisted magnetic flux rope (MFR), which has reached a height of about 60 Mm at the onset of the eruption. We argue that the onset of the flare precursor phase is likely triggered by the loss of the magnetohydrodynamic equilibrium of a preexisting MFR, which leads to the slow rise of the flux rope. The rising motion of the flux rope leads to the formation of a vertical current sheet underneath, triggering the fast magnetic reconnection that in turn leads to the main phase of the flare and fast acceleration of the flux rope.

A comparison of the formation and evolution of magnetic flux ropes in solar coronal mass ejections and magnetotail plasmoids

Solar coronal mass ejections and their interplanetary counterparts often show evidence of a twisted flux rope structure that is nearly identical, though of vastly different spatial scale, to plasmoids observed in the Earth's magnetotail. This paper reviews the current understanding of flux rope formation, morphology, and evolution in coronal mass ejections and magnetotail plasmoids. It highlights the idea that flux rope formation is a common space physics phenomenon and that the physical mechanisms responsible for flux rope formation occur over a wide range of plasma conditions wherever current sheets exist.

Self-similar evolution of the two-dimensional cylindrical magnetohydrodynamic flux rope

One of the important features of the one-dimensional cylindrical self-similar magnetohydrodynamic (MHD) model of magnetic rope is that it oscillates about a force-free solution [Osherovich et al., 1993. Nonlinear evolution of magnetic flux ropes. 1. Low-beta limit. Journal of Geophysical Research 98, 13225–13231; Osherovich et al., 1995. Nonlinear evolution of magnetic flux ropes. 2. Finite-beta plasma. Journal of Geophysical Research 100, 12307-12318.] due to the reduced dimensionality of the system, as in laboratory Z pinch plasmas [Felber, 1982. Self-similar oscillations of a Z pinch. Physics of Fluids 25, 643–645]. However, such oscillations have never been confirmed by observations. Following the approach of Low [1982a. Self-similar magnetohydrodynamics. I. The γ = 4 / 3 Polytrope and the Coronal transient. Astrophysical Journal 254, 796–805; 1982b. Self-similar magnetohydrodynamics. II. The expansion of a Stella envelope into a surrounding vacuum. Astrophysical Journal 261, 351–369], a two-dimensional self-similar MHD model under radial expansion is analyzed in cylindrical geometry with translational symmetry in the z-axis. Non-oscillatory solutions are established with polytropic index γ = 1 and 2. For γ = 2 , the system is linear, and the plasma pressure is balanced by the longitudinal magnetic pressure. As for γ = 1 , the plasma pressure is balanced by the transverse magnetic pressure, and it is also the driving force of non-linearity that stresses the system. Due to the two-dimensional structure of the magnetic field and plasma, this model allows the possibility of an energetic magnetic cloud with a southward component impinging on Earth without raising expected magnetic storms.

Geometric considerations of the evolution of magnetic flux ropes.

We use flux conservation and magnetohydrodynamics (MHD) theory to discuss essential differences in the nature of the evolution of two analytical solutions describing magnetic flux tubes evolving in time. The first of these maintains the elongation of the tube, while the second maintains a constant angular extension with respect to a possible pointlike source. In the first case, free expansion of the plasma (density N) occurs only in a direction perpendicular to the flux-tube x axis. In the second case, isotropic evolution is considered. In both cases it is assumed that at initial time t(0) the flux-tube B field is the force-free magnetostatic Lundquist solution, which energetically corresponds to the most stable state for any flux-tube structure. We show that for each case conservation of magnetic flux is enough to establish the scaling with time of the B field. While both expansions may correspond to the evolution of observed flux tubes in the heliosphere, the isotropic expansion appears to capture consistently essential features associated with the actual observations of expanding coronal mass ejections within 30 solar radii. For isotropic expansion of the plasma the force-free nature of the B field is preserved for all time. As an example the MHD solutions are applied to an interplanetary magnetic cloud observed with the spacecraft Wind, which passed Earth's vicinity on June 2, 1998.

Evolution of magnetic flux rope in the active region NOAA 9077 on 14 July 2000

The finite energy force-free magnetic fields of the active region NOAA 9077 on 14 July 2000 above the photosphere were reconstructed. We study the evolution of the 3D magnetic field structures in AR 9077 and compare the reconstructed field lines with TRACE EUV 171 A flare loops during the flare maximum, which confirms the process that flaring loops extended from lower sheared level to higher arcades. We also demonstrate the 3D magnetic field evolution before the 3B/X5.7 flare on 14 July and the magnetic structure after the flare on 15 July. This shows that the helical magnetic structures were significantly changed, suggesting that the flux rope was indeed erupted during the energetic flare at 10:24 UT on 14 July.

The evolution of magnetic flux ropes in sheared plasma flows

The evolution of magnetic flux ropes in a sheared plasma flow is investigated. When the magnetic field outside the flux rope lies parallel to the axis of the flux rope, a flux rope of circular cross-section, whose centre is located at the midpoint of the shear layer, has its shape distorted, but remains in the shear layer. Small displacements of the flux-rope centre above or below the midpoint of the shear layer lead to the flux-rope being expelled from the shear layer. This motion arises because small asymmetries in the plasma pressure around the flux-rope boundary leads to a force that forces the flux rope into a region of uniform flow. When the magnetic field outside the flux rope lies in a plane perpendicular to the flux-rope axis, the flux rope and external magnetic field reconnect with each other, leading to the destruction of the flux rope.

The non-linear evolution of magnetic flux ropes: 3. effects of dissipation

Abstract. We study the evolution (expansion or oscillation) of cylindrically symmetric magnetic flux ropes when the energy dissipation is due to a drag force proportional to the product of the plasma density and the radial speed of expansion. The problem is reduced to a single, second-order, ordinary differential equation for a damped, non-linear oscillator. Motivated by recent work on the interplanetary medium and the solar corona, we consider polytropes whose index, γ, may be less than unity. Numerical analysis shows that, in contrast to the small-amplitude case, large-amplitude oscillations are quasi-periodic with frequencies substantially higher than those of undamped oscillators. The asymptotic behaviour described by the momentum equation is determined by a balance between the drag force and the gradient of the gas pressure, leading to a velocity of expansion of the flux rope which may be expressed as (1/2γ)r/t, where r is the radial coordinate and t is the time. In the absence of a drag force, we found in earlier work that the evolution depends both on the polytropic index and on a dimensionless parameter, κ. Parameter κ was found to have a critical value above which oscillations are impossible, and below which they can exist only for energies less than a certain energy threshold. In the presence of a drag force, the concept of a critical κ remains valid, and when κ is above critical, the oscillatory mode disappears altogether. Furthermore, critical κ remains dependent only on γ and is, in particular, independent of the normalized drag coefficient, ν*. Below critical κ, however, the energy required for the flux rope to escape to infinity depends not only on κ (as in the conservative force case) but also on ν*. This work indicates how under certain conditions a small change in the viscous drag coefficient or the initial energy may alter the evolution drastically. It is thus important to determine ν* and κ from observations.

The non-linear evolution of magnetic flux ropes: 3. effects of dissipation

The non-linear evolution of magnetic flux ropes: 3. effects of dissipation

A Global Magnetohydrodynamic Simulation of the Origin and Evolution of Magnetic Flux Ropes in the Magnetotail

We have used a three dimensional global magnetohydrodynamic simulation to model the response of the magnetosphere to an interplanetary magnetic field (IMF) with Bz < 0 and By ≠ 0 in order to study the origin and evolution of magnetic flux ropes in the magnetotail. The southward IMF leads to dayside magnetic reconnection followed by reconnection on closed plasma sheet field lines. When there initially was no IMF By in the plasma sheet, reconnection led to the formation of a plasmoid composed of a quasi-two dimensional closed magnetic loop structure. When IMF By reached the equatorial region the quasi-two dimensional plasmoid became a magnetic flux rope. For IMF By ≠ 0 initially in the plasma sheet the reconnection immediately led to the formation of a flux rope structure. The pitch of the flux rope field lines is determined by the amount of By. For the case with no initial By in the plasma sheet the pitch was relatively large while when By ≠ 0 initially the flux rope resembled a flux tube lying across the tail. Flux ropes in the magnetotail consist of closed, open and IMF field lines. The open and IMF field lines in the flux rope become attached to the IMF when closed field lines in the flux rope reconnect with IMF field lines at the flank magnetopause. Flux ropes can move tailward before all of the closed field lines have reconnected. This is primarily caused by the tension on IMF field lines which drape over the flux rope when lobe field lines reconnect. However the tailward velocity is less for flux ropes than for plasmoids because of the connection to the Earth. In the simulation closed flux rope field lines are found over 100RE down the tail.

Nonlinear evolution of magnetic flux ropes: 2. Finite beta plasma

In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a poly tropic relationship and reduce the set of ideal MHD equations to a single, second‐order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue—a one‐dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index γ and a dimensionless quantity κ the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and γ. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for γ&gt;1 and all values of κ, only oscillations are possible. For γ&lt;1, however, both oscillations and expansion are allowed. For γ&lt;1 and κ below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For γ&lt;1 and κ above critical, however, only expansion occurs. Thus by increasing κ while keeping γ fixed (&lt;1), a phase transition occurs at κ = κcritical and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self‐similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases critical conditions can occur for γ&gt;1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of κ and γ, collapse may be averted.

Evolution of magnetic flux ropes associated with flux transfer events and interplanetary magnetic clouds

Spacecraft observations suggest that flux transfer events and interplanetary magnetic clouds may be associated with magnetic flux ropes which are magnetic flux tubes containing helical magnetic field lines. In the magnetic flux ropes, the azimuthal magnetic field (Bθ) is superposed on the axial field (Bz). In this paper the time evolution of a localized magnetic flux rope is studied. A two‐dimensional compressible magnetohydrodynamic simulation code with a cylindrical symmetry is developed to study the wave modes associated with the evolution of flux ropes. It is found that in the initial phase both the fast magnetosonic wave and the Alfvén wave are developed in the flux rope. After this initial phase, the Alfvén wave becomes the dominant wave mode for the evolution of the magnetic flux rope and the radial expansion velocity of the flux rope is found to be negligible. Numerical results further show that even for a large initial azimuthal component of the magnetic field (Bθ ≃ 1–4 Bz) the propagation velocity along the axial direction of the flux rope remains to be the Alfvén velocity. Diagnoses show that after the initial phase the transverse kinetic energy equals the transverse magnetic energy, which is characteristic of the Alfvén mode. It is also found that the localized magnetic flux rope tends to evolve into two separate magnetic ropes propagating in opposite directions. The simulation results are used to study the evolution of magnetic flux ropes associated with flux transfer events observed at the Earth's dayside magnetopause and magnetic clouds in the interplanetary space.