Magnetic Tension Force Research Articles

Small‐Scale Flux Transfer Events Formed in the Reconnection Exhaust Region Between Two X Lines

AbstractWe report MMS observations of the ion‐scale flux transfer events (FTEs) that may involve two main X lines and tearing instability between the two X lines. The four spacecraft detected multiple isolated regions with enhanced magnetic field strength and bipolar Bn signatures normal to the nominal magnetopause, indicating FTEs. The currents within the FTEs flow mostly parallel to B, and the magnetic tension force is balanced by the total pressure gradient force. During these events, the plasma bulk flow velocity was directed southward. Detailed analysis of the magnetic and electric field and plasma moments variations suggests that the FTEs were initially embedded within the exhaust region north of an X line but were later located southward/downstream of a subsequent X line. The cross sections of the individual FTEs are in the range of ~2.5–6.8 ion inertial lengths. The observations suggest the formation of multiple secondary FTEs. The presence of an X line in the exhaust region southward of a second X line results from the southward drift of an old X line and the reformation of a new X line. The current layer between the two X lines is unstable to the tearing instability, generating multiple ion‐scale flux‐rope‐type secondary islands.

Consequences of Treating the Solar Magnetic Field as a Dipole on the Global Structure of the Heliosphere and Heliosheath

We investigate the effect of including the heliospheric current sheet on global modeling of the heliosphere. Due to inherent numerical dissipation in the current handling of the heliospheric current sheet, models have chosen to remove it to avoid numerical problems. We compare a model where the polarity of the Parker spiral is the same in both hemispheres (unipolar) to a dipole description of the solar magnetic field, with the magnetic and rotational axes aligned forming a flat heliospheric current sheet. The flat current sheet is pulled into the northern hemisphere, which reduces the magnetic field strength at the Voyager 1 trajectory over the last 22% of the heliosheath. The decrease in magnetic field intensity is transferred into the thermal energy of the plasma causing the dipole model to predict an entirely thermally dominated heliosheath; this is a stark contrast to the magnetically dominated region ahead of the heliopause in the unipole model. We find that the two-lobe structure of the solar wind magnetic field persists within the dipole model, with the flat current sheet not able to fully erode the magnetic tension force. However, there is a large amount of magnetic dissipation in the tail between the lobes, which affects the structure of the plasma in the region. Furthermore, the draped interstellar magnetic field in the dipole model is strongly affected by reconnection at the nose of the heliosphere, yielding a distinctly different draping pattern than that observed at Voyager 1.

Suppression of AGN-driven Turbulence by Magnetic Fields in a Magnetohydrodynamic Model of the Intracluster Medium

Abstract We investigate the role of active galactic nucleus (AGN) feedback in turbulent heating of galaxy clusters. Specifically, we analyze the production of turbulence by g-modes generated by the supersonic expansion and buoyant rise of AGN-driven bubbles. Previous work that neglects magnetic fields has shown that this process is inefficient, with less than 1% of the injected energy ending up in turbulence. This inefficiency primarily arises because the bubbles are shredded apart by hydrodynamic instabilities before they can excite sufficiently strong g-modes. Using a plane-parallel model of the intracluster medium (ICM) and 3D ideal magnetohydrodynamics (MHD) simulations, we examine the role of a large-scale magnetic field that is able to drape around these rising bubbles, preserving them from hydrodynamic instabilities. We find that while magnetic draping appears better able to preserve AGN-driven bubbles, the driving of g-modes and the resulting production of turbulence is still inefficient. The magnetic tension force prevents g-modes from transitioning into the nonlinear regime, suppressing turbulence in our model ICM. Our work highlights the ways in which ideal MHD is an insufficient description for the cluster feedback process, and we discuss future work such as the inclusion of anisotropic viscosity as a means of simulating high β plasma kinetic effects. These results suggest the hypothesis that other mechanisms of heating the ICM plasma such as sound waves or cosmic rays may be responsible for the observed feedback in galaxy clusters.

Three-dimensional MHD Simulations of Solar Prominence Oscillations in a Magnetic Flux Rope

Abstract Solar prominences are subject to all kinds of perturbations during their lifetime, and frequently demonstrate oscillations. The study of prominence oscillations provides an alternative way to investigate their internal magnetic and thermal structures because the characteristics of the oscillations depend on their interplay with the solar corona. Prominence oscillations can be classified into longitudinal and transverse types. We perform three-dimensional ideal magnetohydrodynamic simulations of prominence oscillations along a magnetic flux rope, with the aim of comparing the oscillation periods with those predicted by various simplified models and examining the restoring force. We find that the longitudinal oscillation has a period of about 49 minutes, which is in accordance with the pendulum model where the field-aligned component of gravity serves as the restoring force. In contrast, the horizontal transverse oscillation has a period of about 10 minutes and the vertical transverse oscillation has a period of about 14 minutes, and both of them can be nicely fitted with a two-dimensional slab model. We also find that the magnetic tension force dominates most of the time in transverse oscillations, except for the first minute when magnetic pressure overwhelms it.

Understanding the Role of Mass-Unloading in a Filament Eruption

We describe a partial filament eruption on 11 December 2011 that demonstrates that the inclusion of mass is an important next step for understanding solar eruptions. Observations from the Solar Terrestrial Relations Observatory-Behind (STEREO-B) and the Solar Dynamics Observatory (SDO) spacecraft were used to remove line-of-sight projection effects in filament motion and correlate the effect of plasma dynamics with the evolution of the filament height. Flux cancellation and nearby flux emergence are shown to have played a role in increasing the height of the filament prior to eruption. The two viewpoints allow the quantitative estimation of a large mass-unloading, the subsequent radial expansion, and the eruption of the filament to be investigated. A 1.8 to 4.1 lower-limit ratio between gravitational and magnetic-tension forces was found. We therefore conclude that following the loss-of-equilibrium of the flux-rope, the radial expansion of the flux-rope was restrained by the filamentary material until 70% of the mass had evacuated the structure through mass-unloading.

Эксцентриситет ротора синхронных машин с постоянными магнитами

The article presents the results from studying the eccentricity in permanent magnet synchronous machines having different numbers of slots per pole and phase (q). The advantages and drawbacks of using winding arrangements with different values of qareshown. An expression describing the physical processes of interaction between spatial induction harmonic components in the air gap under eccentricity conditionsisanalyticallyobtained. The electromagnetic torque pulsations arising with different kinds of eccentricity—static, dynamic, and mixed—are determined with the aid of field models and using the Maxwell magnetic tension forces. Differences between the obtained characteristics are pointed out. Aprocedurefor calculating the electromagnetic torque pulsations in the no-load and on-load operation modes using the Femm finite-element computer program is presented. Recommendations on selecting the qvalue for reducing the negative effect of different eccentricity kinds aregiven.

Homologous Circular-ribbon Flares Driven by Twisted Flux Emergence

Abstract In this paper, we report two homologous circular-ribbon flares associated with two filament eruptions. They were well observed by the New Vacuum Solar Telescope and the Solar Dynamics Observatory on 2014 March 5. Prior to the flare, two small-scale filaments enclosed by a circular pre-flare brightening lie along the circular polarity inversion line around the parasitic polarity, which has shown a continuous rotation since its first appearance. Two filaments eventually erupt in sequence associated with two homologous circular-ribbon flares and display an apparent writhing signature. Supplemented by the nonlinear force-free field extrapolation and the magnetic field squashing factor investigation, the following are revealed. (1) This event involves the emergence of magnetic flux ropes into a pre-existing polarity area, which yields the formation of a 3D null-point topology in the corona. (2) Continuous input of the free energy in the form of a flux rope from beneath the photosphere may drive a breakout-type reconnection occurring high in the corona, supported by the pre-flare brightening. (3) This initiation reconnection could release the constraint on the flux rope and trigger the MHD instability to first make filament F1 lose equilibrium. The subsequent more violent magnetic reconnection with the overlying flux is driven during the filament rising. In return, the eruption of filament F2 is further facilitated by the reduction of the magnetic tension force above. These two processes form a positive feedback to each other to cause the energetic mass eruption and flare.

The Effect of a Twisted Magnetic Field on the Nature of Kink MHD Waves

We consider a pressureless plasma in a thin magnetic-flux tube with a twisted magnetic field. We study the effect of twisted magnetic field on the nature of propagating kink waves. To do this, the restoring forces of oscillations in the linear ideal magnetohydrodynamics (MHD) were obtained. In the presence of a twisted magnetic field, the ratio of the magnetic-tension force to the gradient of the magnetic pressure increases for the mode with negative azimuthal wave number, but it decreases for the mode with positive azimuthal wave number. For the kink mode with positive azimuthal mode number, the ratio of the forces is more affected by the twisted magnetic field in dense loops. For the kink mode with negative azimuthal mode number, the perturbed magnetic pressure is negligible under some conditions. The magnetic twist increases (diminishes) the damping of the kink waves with positive (negative) azimuthal mode number due to resonant absorption. Our conclusion is that introducing a twisted magnetic field breaks the symmetry between the nature of the kink waves with positive and negative azimuthal wave number, and the wave can be a purely Alfvenic wave in the entire loop.

On the nature of fast sausage waves in coronal loops

The effect of the parameters of coronal loops on the nature of fast sausage waves are investigated. To do this three models of the coronal loop considered, a simple loop model, a current-carrying loop model and a model with radially structured density called “Inner μ” profile. For all the models the Magnetohydrodynamic (MHD) equations solved analytically in the linear approximation and the restoring forces of oscillations obtained. The ratio of the magnetic tension force to the pressure gradient force obtained as a function of the distance from the axis of the loop. In the simple loop model for all values of the loop parameters the fast sausages wave have a mixed nature of Alfvénic and fast MHD waves, in the current-carrying loop model with thick annulus and low density contrast the fast sausage waves can be considered as purely Alfvénic wave in the core region of the loop, and in the “Inner μ” profile for each set of the parameters of the loop the wave can be considered as a purely Alfvénic wave in some regions of the loop.

Coronal Jet Collimation by Nonlinear Induced Flows

Abstract 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.

Simulating the Dynamics of Coronal Plasma Condensations

AbstractWe present numerical MHD simulations of the dynamics of cool plasma condensations in a coronal loop. We address 2 mechanisms for how coronal rain leads to the excitation of coronal loop oscillations. We find that the combined effect of pressure gradients in the coronal loop plasma and magnetic tension force resulting from changes in magnetic field geometry explains observed sub-ballistic motion of coronal rain and longitudinal oscillations of the individual condensations. We also find that the condensations can excite sustained, small amplitude, vertically polarised transverse loop oscillations.

Dynamics of plasma condensations in a gravitationally stratified coronal loop

Context Coronal rain composed of cool plasma condensations falling from coronal heights is a phenomenon occurring in footpoint-heated coronal loops as a result of thermal instability. High-resolution coronal rain observations suggest that condensations move with less than free-fall speed and can sometimes undergo longitudinal oscillations. Aims We investigate the evolution and dynamics of plasma condensations in a gravitationally stratified coronal loop. Methods We carried out 2.5 dimensional magnetohydrodynamic simulations of a cool plasma condensation in a gravitationally stratified coronal loop and analysed its evolution, kinematics, and the evolution of the forces acting on the condensation. We further propose a one-dimensional analytical model of the condensation dynamics. Results The motion of plasma condensations is found to be strongly affected by the pressure of the coronal loop plasma. Maximum downward velocities are in agreement with recent coronal rain observations. A high coronal magnetic field or low condensation mass can lead to damped oscillatory motion of the condensations that are caused by the pressure gradient force and magnetic tension force that results from bending of the magnetic field in the lower part of the coronal loop. Period and damping scaling time of the oscillatory motion seen in the simulations are consistent with values predicted by the model. Conclusions The combined effect of pressure gradients in the coronal loop plasma and magnetic tension force that results from changes in magnetic field geometry can explain observed sub-ballistic motion and longitudinal oscillations of coronal rain

Enhancement of Feedback Efficiency by Active Galactic Nucleus Outflows via the Magnetic Tension Force in the Inhomogeneous Interstellar Medium

Abstract By performing three-dimensional magnetohydrodynamics simulations of subrelativistic jets and disk winds propagating into the magnetized inhomogeneous interstellar medium (ISM), we investigate the magnetic effects on the active galactic nucleus feedback. Our simulations reveal that the magnetic tension force promotes the acceleration of the dense gas clouds, since the magnetic field lines, which are initially straight, bend around the gas clouds. In the jet models, the velocity dispersion of the clouds increases with an increase in the initial magnetic fields. The increment of the kinetic energy of the clouds is proportional to the initial magnetic fields, implying that the magnetic tension force increases the energy conversion efficiency from the jet to the gas clouds. Through simulations of the mildly collimated disk wind and the funnel-shaped disk wind, we confirm that such an enhancement of the energy conversion efficiency via the magnetic fields appears even if the energy is injected via the disk winds. The enhancement of the acceleration of the dense part of the magnetized ISM via the magnetic tension force will occur wherever the magnetized inhomogeneous matter is blown away.

Magnetohydrodynamic Modeling of Solar Coronal Dynamics with an Initial Non-force-free Magnetic Field

Abstract The magnetic fields in the solar corona are generally neither force-free nor axisymmetric and have complex dynamics that are difficult to characterize. Here we simulate the topological evolution of solar coronal magnetic field lines (MFLs) using a magnetohydrodynamic model. The simulation is initialized with a non-axisymmetric non-force-free magnetic field that best correlates with the observed vector magnetograms of solar active regions (ARs). To focus on these ideas, simulations are performed for the flaring AR 11283 noted for its complexity and well-documented dynamics. The simulated dynamics develops as the initial Lorentz force pushes the plasma and facilitates successive magnetic reconnections at the two X-type null lines present in the initial field. Importantly, the simulation allows for the spontaneous development of mass flow, unique among contemporary works, that preferentially reconnects field lines at one of the X-type null lines. Consequently, a flux rope consisting of low-lying twisted MFLs, which approximately traces the major polarity inversion line, undergoes an asymmetric monotonic rise. The rise is attributed to a reduction in the magnetic tension force at the region overlying the rope, resulting from the reconnection. A monotonic rise of the rope is in conformity with the standard scenario of flares. Importantly, the simulated dynamics leads to bifurcations of the flux rope, which, being akin to the observed filament bifurcation in AR 11283, establishes the appropriateness of the initial field in describing ARs.

Penumbral thermal structure below the visible surface

$Context$. The thermal structure of the penumbra below its visible surface (i.e., $\tau_5 \ge 1$) has important implications for our present understanding of sunspots and their penumbrae: their brightness and energy transport, mode conversion of magneto-acoustic waves, sunspot seismology, and so forth. $Aims$. We aim at determining the thermal stratification in the layers immediately beneath the visible surface of the penumbra: $\tau_5 \in [1,3]$ ($\approx 70-80$ km below the visible continuum-forming layer). $Methods$. We analyzed spectropolarimetric data (i.e., Stokes profiles) in three Fe \textsc{i} lines located at 1565 nm observed with the GRIS instrument attached to the 1.5-meter solar telescope GREGOR. The data are corrected for the smearing effects of wide-angle scattered light and then subjected to an inversion code for the radiative transfer equation in order to retrieve, among others, the temperature as a function of optical depth $T(\tau_5)$. $Results$. We find that the temperature gradient below the visible surface of the penumbra is smaller than in the quiet Sun. This implies that in the region $\tau_5 \ge 1$ the penumbral temperature diverges from that of the quiet Sun. The same result is obtained when focusing only on the thermal structure below the surface of bright penumbral filaments. We interpret these results as evidence of a thick penumbra, whereby the magnetopause is not located near its visible surface. In addition, we find that the temperature gradient in bright penumbral filaments is lower than in granules. This can be explained in terms of the limited expansion of a hot upflow inside a penumbral filament relative to a granular upflow, as magnetic pressure and tension forces from the surrounding penumbral magnetic field hinder an expansion like this.

Shock–Cloud Interaction in the Solar Corona

Abstract Flare-associated coronal shock waves sometimes interact with solar prominences, leading to large-amplitude prominence oscillations (LAPOs). Such prominence activation gives us a unique opportunity to track the time evolution of shock–cloud interaction in cosmic plasmas. Although the dynamics of interstellar shock–cloud interaction has been extensively studied, coronal shock–solar prominence interaction is rarely studied in the context of shock–cloud interaction. Associated with the X5.4 class solar flare that occurred on 2012 March 7, a globally propagated coronal shock wave interacted with a polar prominence, leading to LAPO. In this paper, we studied bulk acceleration and excitation of the internal flow of the shocked prominence using three-dimensional magnetohydrodynamic (MHD) simulations. We studied eight MHD simulation runs, each with different mass density structure of the prominence, and one hydrodynamic simulation run, and we compared the result. In order to compare the observed motion of activated prominence with the corresponding simulation, we also studied prominence activation by injection of a triangular-shaped coronal shock. We found that the prominence is first accelerated mainly by magnetic tension force as well as direct transmission of the shock, and later decelerated mainly by magnetic tension force. The internal flow, on the other hand, is excited during the shock front sweeps through the prominence and damps almost exponentially. We construct a phenomenological model of bulk momentum transfer from the shock to the prominence, which agreed quantitatively with all the simulation results. Based on the phenomenological prominence activation model, we diagnosed physical parameters of the coronal shock wave. The estimated energy of the coronal shock is several percent of the total energy released during the X5.4 flare.

Quasi-static and dynamic magnetic tension forces in arched, line-tied magnetic flux ropes

Solar eruptions are often driven by magnetohydrodynamic instabilities such as the torus and kink instabilities that act on line-tied magnetic flux ropes. Recent laboratory experiments designed to study these eruptive instabilities have demonstrated the key role of both dynamic (Myers et al 2015 Nature 528 526) and quasi-static (Myers et al 2016 Phys. Plasmas 23 112102) magnetic tension forces in contributing to the equilibrium and stability of line-tied magnetic flux ropes. In this paper, we synthesize these laboratory results and explore the relationship between the dynamic and quasi-static tension forces. While the quasi-static tension force is found to contribute to the flux rope equilibrium in a number of regimes, the dynamic tension force is substantial mostly in the so-called failed torus regime where magnetic self-organization events prevent the flux rope from erupting.

Forces driving fast flow channels, dipolarizations, and turbulence in the magnetotail

AbstractFast flow channels are a major contributor to earthward transport in the magnetotail. Fast flow channels originate at reconnection sites in the magnetotail and terminate with dipolarizations, earthward moving regions of enhanced magnetic field. We have used a global magnetohydrodynamic simulation of magnetotail dynamics during a substorm on 7 February 2009 to investigate the stresses in the plasma sheet. In particular, we present an analysis of forces in and around flow channels and dipolarizations. Earthward of the dipolarization magnetic and thermal pressure forces are nearly in equilibrium. Tailward of the dipolarization the pattern of stresses is complex, but several general features are evident. In the earthward flow channel the magnetic tension force dominates. In the dipolarization a tailward magnetic force is partially balanced by the earthward pressure force. The stresses in azimuth (y) are variable. In some places they cause the flow stream to meander, while in others they cause the stream to become wider or narrower. A major consequence of fast earthward flow channels is that they drive large‐scale vortices that initiate turbulence.

Generalized magnetotail equilibria: Effects of the dipole field, thin current sheets, and magnetic flux accumulation

AbstractGeneralizations of the class of quasi‐1‐D solutions of the 2‐D Grad‐Shafranov equation, first considered by Schindler in 1972, are investigated. It is shown that the effect of the dipole field, treated as a perturbation, can be included into the original 1972 class solution by modification of the boundary conditions. Some of the solutions imply the formation of singularly thin current sheets. Equilibrium solutions for such sheets resolving their singular current structure on the scales comparable to the thermal ion gyroradius can be obtained assuming anisotropic and nongyrotropic plasma distributions. It is shown that one class of such equilibria with the dipole‐like boundary perturbation describes bifurcation of the near‐Earth current sheet. Another class of weakly anisotropic equilibria with thin current sheets embedded into a thicker plasma sheet helps explain the formation of thin current sheets in a relatively distant tail, where such sheets can provide ion Landau dissipation for spontaneous magnetic reconnection. The free energy for spontaneous reconnection can be provided due to accumulation of the magnetic flux at the tailward end of the closed field line region. The corresponding hump in the normal magnetic field profile Bz(x,z = 0) creates a nonzero gradient along the tail. The resulting gradient of the equatorial magnetic field pressure is shown to be balanced by the pressure gradient and the magnetic tension force due to the higher‐order correction of the latter in the asymptotic expansion of the tail equilibrium in the ratio of the characteristic tail current sheet variations across and along the tail.

A comparative study of dipolarization fronts at MMS and Cluster.

We present a statistical study of dipolarization fronts (DFs), using magnetic field data from MMS and Cluster, at radial distances below 12 R E and 20 R E, respectively. Assuming that the DFs have a semicircular cross section and are propelled by the magnetic tension force, we used multispacecraft observations to determine the DF velocities. About three quarters of the DFs propagate earthward and about one quarter tailward. Generally, MMS is in a more dipolar magnetic field region and observes larger‐amplitude DFs than Cluster. The major findings obtained in this study are as follows: (1) At MMS ∼57 % of the DFs move faster than 150 km/s, while at Cluster only ∼35 %, indicating a variable flux transport rate inside the flow‐braking region. (2) Larger DF velocities correspond to higher B z values directly ahead of the DFs. We interpret this as a snow plow‐like phenomenon, resulting from a higher magnetic flux pileup ahead of DFs with higher velocities.