Bundle Of Field Lines Research Articles

Magnetic field line separation by random ballistic decorrelation in transverse magnetic turbulence

ABSTRACT The statistics of the magnetic field line separation provide insight into how a bundle of field lines spreads out and the dispersion of non-thermal particles in a turbulent environment, which underlies various astrophysical phenomena. Its diffusive character depends on the distance along the field line, the initial separation, and the characteristics of the magnetic turbulence. This work considers the separation of two magnetic field lines in general transverse turbulence in terms of the magnetic power spectrum in three-dimensional wavenumber space. We apply non-perturbative methods using Corrsin’s hypothesis and assume random ballistic decorrelation to calculate the ensemble average field line separation for general transverse magnetic turbulence. For 2D + slab power spectra, our analytical formulae and computer simulations give similar results, especially at low slab fraction. Our analytical expression also demonstrates several features of field line separation that are verified by computer simulations.

Energy flow in light scattering by a small conducting sphere

Radiation energy scattered by a small particle can be expected to travel from the particle to a detector in the far field along the field lines of the Poynting vector. We consider the scattering off a small conducting sphere, for which only the induced electric and magnetic dipole moments contribute to the emitted radiation. Field lines of the energy flow due to interference between fields radiated by the electric and magnetic dipoles appear to form closed loops in the vicinity of the particle. Energy flows out of the particle at one side and then returns to the particle at the other side, and as such, this energy flow does not contribute to the radiated power. At larger distances, energy flows away from the particle at one side of the particle, but on the other side, radiation flows from infinity toward the particle. The energy for the scattered radiation is provided by the incident field. The energy flow is due to interference between the incident field and the scattered radiation, known as extinction. The flow pattern of this energy exhibits numerous singularities and vortices, and closed-loop flows near the particle. In the far field, energy flows along counter-oriented field line bundles, with only the net power flowing inward.

Transient small-scale brightenings in the quiet solar corona: A model for campfires observed with Solar Orbiter

Context. Recent observations by the Extreme Ultraviolet Imager (EUI) on board Solar Orbiter have characterized prevalent small-scale transient brightenings in the corona above the quiet Sun termed campfires. Aims. In this study we search for comparable brightenings in a numerical model and then investigate their relation to the magnetic field and the processes that drive these events. Methods. We used the MURaM code to solve the 3D radiation magnetohydrodynamic equations in a box that stretches from the upper convection zone to the corona. The model self-consistently produces a supergranular network of the magnetic field and a hot corona above this quiet Sun. For the comparison with the model, we synthesized the coronal emission as seen by EUI in its 174 Å channel, isolated the seven strongest transient brightenings, and investigated the changes of the magnetic field in and around these in detail. Results. The transients we isolated have a lifetime of about 2 min and are elongated loop-like features with lengths around 1 Mm to 4 Mm. They tend to occur at heights of about 2 Mm to 5 Mm above the photosphere, a bit offset from magnetic concentrations that mark the bright chromospheric network, and they reach temperatures of above 1 MK. As a result, they very much resemble the larger campfires found in observations. In our model most events are energized by component reconnection between bundles of field lines that interact at coronal heights. In one case, we find that untwisting a highly twisted flux rope initiates the heating. Conclusions. Based on our study, we propose that the majority of campfire events found by EUI are driven by component reconnection and our model suggests that this process significantly contributes to the heating of the corona above the quiet Sun.

Internal Structure of the 2019 April 2 CME

Abstract We present the first analysis of internal coronal mass ejection (CME) structure observed very close to the Sun by the Wide-field Imager for Solar PRobe (WISPR) instrument on board the Parker Solar Probe (PSP). The transient studied here is a CME observed during PSP’s second perihelion passage on 2019 April 2, when PSP was only 40 R ⊙ from the Sun. The CME was also well observed from 1 au by the STEREO-A spacecraft, which tracks the event all the way from the Sun to 1 au. However, PSP/WISPR observes internal structure not apparent in the images from 1 au. In particular, two linear features are observed, one bright and one dark. We model these features as two loops within the CME flux rope (FR) channel. The loops can be interpreted as bundles of field lines, with the brightness of the bright loop indicative of lots of mass being loaded into those field lines, and with the dark loop being devoid of such mass loading. It is possible that these loops are actually representative of two independent FR structures within the overall CME outline.

Localized Reconnection Heating Inferred from the Three-dimensional Locations of Bright Active Region Coronal Loops

Abstract Coronal loops observed in soft X-rays and extreme ultraviolet imaging data offer direct evidence that coronal plasma is heated by some mechanism. That mechanism appears to energize a particular bundle of field lines somehow selected from the magnetized coronal volume. Magnetic reconnection localized to a patch within a coronal current sheet is one mechanism that would select a flux bundle at the same time it energized it. Since magnetic reconnection occurs preferentially at topological boundaries, we would expect to find coronal loops concentrated there if it were at work. We explore this hypothesis using a data set, previously compiled by McCarthy et al., consisting of 301 coronal loops interconnecting a pair of active regions over a 48 hr period. That work computed the three-dimensional geometries and magnetic field strengths for most of the loops. This revealed many bright loops lying at the periphery of the interconnecting flux domain, possibly created and energized by the reconnection that created the interconnecting flux. There were, however, many loops well inside the domain which would be difficult to attribute to that mode of reconnection. Here we use detailed magnetic models of the interconnecting domain to show that these internal loops tend to occur along internal boundaries: separatrices. This offers a novel form of evidence that coronal loops are the products of patchy reconnection even under quiescent conditions.

Definition of the Spatial Propagator and Implications for Magnetic Field Properties

We present a theoretical framework to analyze the 3D coronal vector magnetic-field structure. We assume that the vector magnetic field exists and is a priori smooth. We introduce a generalized connectivity phase space associated with the vector magnetic field in which the basic elements are the field line and its linearized variation: the Spatial Propagator. We provide a direct formulation of these elements in terms of the vector magnetic field and its spatial derivatives, constructed with respect to general curvilinear coordinates and the equivalence class of general affine parameterizations. The Spatial Propagator describes the geometric organization of the local bundle of field lines, equivalent to the kinematic deformation of a propagated volume tied to the bundle. The Spatial Propagator’s geometric properties are characterized by dilation, anisotropic stretch, and rotation. Extreme singular values of the Spatial Propagator describe quasi-separatrix layers (QSLs), while true separatrix surfaces and separator lines are identified by the vanishing of one and two singular values, respectively. Finally, we show that, among other possible applications, the squashing factor [Q] is easily constructed from an analysis of particular sub-matrices of the Spatial Propagator.

AN INTERPRETATION OF FLARE-INDUCED AND DECAYLESS CORONAL-LOOP OSCILLATIONS AS INTERFERENCE PATTERNS

We present an alternative model of coronal-loop oscillations which considers that the waves are trapped in a 2D waveguide formed by the entire arcade of field lines. This differs from the standard 1D model which treats the waves as the resonant oscillations of just the visible bundle of field lines. Within the framework of our 2D model, the two types of oscillations that have been observationally identified, flare-induced waves and "decayless" oscillations, can both be attributed to MHD fast waves. The two components of the signal differ only because of the duration and spatial extent of the source that creates them. The flare-induced waves are generated by strong localized sources of short duration, while the decayless background can be excited by a continuous, stochastic source. Further, the oscillatory signal arising from a localized, short-duration source can be interpreted as a pattern of interference fringes produced by waves that have traveled diverse routes of various pathlengths through the waveguide. The resulting amplitude of the fringes slowly decays in time with an inverse square root dependence. The details of the interference pattern depend on the shape of the arcade and the spatial variation of the Alfv\'en speed. The rapid decay of this wave component, which has previously been attributed to physical damping mechanisms that remove energy from resonant oscillations, occurs as a natural consequence of the interference process without the need for local dissipation.

Parameterisation of coronal heating: spatial distribution and observable consequences

We investigate the difference in the spatial distribution of the energy input for parametrizations of different mechanisms to heat the corona of the Sun and possible impacts on the coronal emission. We use a 3D MHD model of a solar active region as a reference and compare the Ohmic-type heating in this model to parametrizations for alternating current (AC) and direct current (DC) heating models, in particular, we use Alfven wave and MHD turbulence heating. We extract the quantities needed for these two parametrizations from the reference model and investigate the spatial distribution of the heat input in all three cases, globally and along individual field lines. To study differences in the resulting coronal emission we employ 1D loop models with a prescribed heat input based on the heating rate we extracted along a bundle of field lines. On average, all heating implementations show a roughly drop of the heating rate with height. This also holds for individual field lines. While all mechanism show a concentration of the energy input towards the low parts of the atmosphere, for individual field lines the concentration towards the footpoints is much stronger for the DC mechanisms than for the Alfven wave AC case. In contrast, the AC model gives a stronger concentration of the emission towards the footpoints. This is because the more homogeneous distribution of the energy input leads to higher coronal temperatures and a more extended transition region. The significant difference in the concentration of the heat input towards the foot points for the AC and DC mechanisms, and the pointed difference in the spatial distribution of the coronal emission for these cases shows that the two mechanisms should be discriminable by observations. Before drawing final conclusions, these parametrizations should be implemented in new 3D models in a more self-consistent way.

Dynamics of the foreshock compressional boundary and its connection to foreshock cavities

AbstractWe use several global hybrid (kinetic ions, fluid electrons) simulation runs for steady and time‐varying interplanetary magnetic field (IMF) conditions to examine the dynamics of the foreshock compressional boundary (FCB) and its connection to foreshock cavities. The results demonstrate that for steady IMF conditions, the FCB forms and evolves over a long period of time due to the dynamics of the bow shock and ion foreshock. Formation of the FCB is tied to the generation and nonlinear evolution of ULF waves associated with large‐amplitude fluctuations in magnetic field and density within the foreshock. As a result, even during steady IMF conditions, the transitions in the magnetic field strength and direction across an FCB evolve. Although the FCB itself is associated with increases in the magnetic field strength and density, these quantities are reduced on the turbulent side of the FCB as compared to the pristine solar wind. Hybrid simulations with time‐varying IMF have been performed to examine the relationship between the FCB and foreshock cavities generated under two possible scenarios. In the first scenario, a bundle of field lines connects to an otherwise quasi‐perpendicular bow shock and results in the formation of a finite‐sized foreshock region that travels with this bundle of field lines as it connects to different parts of the bow shock surface. Two FCBs bound the traveling foreshock region. In the second scenario, solar wind discontinuities cause the IMF cone angle (angle between the IMF and the solar wind flow direction) to vary and thereby modify the foreshock geometry and the position of the FCB. We demonstrate that structures similar to foreshock cavities bounded by FCBs form in both scenarios. We show that the two scenarios cannot be distinguished based on convecting or nonconvecting FCBs. We also demonstrate that depending on spacecraft location and the nature of the solar wind discontinuities, foreshock cavities may be bounded by an FCB on one side and a foreshock bubble on the other.

THREE-DIMENSIONAL RECONNECTION INVOLVING MAGNETIC FLUX ROPES

Two and three magnetic flux ropes are created and studied in a well-diagnosed laboratory experiment. The twisted helical bundles of field lines rotate and collide with each other over time. In the two rope case, reverse current layers indicative of reconnection are observed. Using a high spatial and temporal resolution three-dimensional volume data set in both cases, quasi-separatrix layers (QSLs) are identified in the magnetic field. Originally developed in the context of solar magnetic reconnection, QSLs are thought to be preferred sites for reconnection. This is verified in these studies. In the case of three flux ropes there are multiple QSLs, which come and go in time. The divergence of the field lines within the QSLs and the field line motion is presented. In all cases, it is observed that the reconnection is patchy in space and bursty in time. Although it occurs at localized positions it is the result of the nonlocal behavior of the flux ropes.

UNTWISTING MAGNETOSPHERES OF NEUTRON STARS

Magnetospheres of neutron stars are anchored in the rigid crust and can be twisted by sudden crustal motions (starquakes). The twisted magnetosphere does not remain static and gradually untwists, dissipating magnetic energy and producing radiation. The equation describing this evolution is derived, and its solutions are presented. Two distinct regions coexist in untwisting magnetospheres: a potential region where curl(B)=0 (cavity) and a current-carrying bundle of field lines (j-bundle). The cavity has a sharp boundary, which expands with time and eventually erases all of the twist. In this process, the electric current of the j-bundle is sucked into the star. Observational appearance of the untwisting process is discussed. A hot spot forms at the footprints of the j-bundle. The spot shrinks with time toward the magnetic dipole axis, and its luminosity and temperature gradually decrease. As the j-bundle shrinks, the amplitude of its twist can grow to the maximum possible value ~ 1. The strong twist near the dipole axis increases the spindown rate of the star and can generate a broad beam of radio emission. The model explains the puzzling behavior of magnetar XTE J1810-197 -- a canonical example of magnetospheric evolution following a starquake. We also discuss implications for other magnetars. The untwisting theory suggests that the nonthermal radiation of magnetars is preferentially generated on a bundle of extended closed field lines near the dipole axis.

Magnetopause mapping to the ionosphere for northward IMF

Abstract. We study the topological structure of the magnetosphere for northward IMF. Using a magnetospheric magnetic field model we study the high-latitude response to prolonged periods of northward IMF. For forced solar wind conditions we investigate the location of the polar cap region, the polar cap potential drop, and the field-aligned acceleration potentials, depending on the solar wind pressure and IMF By and Bx changes. The open field line bundles, which connect the Earth's polar ionosphere with interplanetary space, are calculated. The locations of the magnetospheric plasma domains relative to the polar ionosphere are studied. The specific features of the open field line regions arising when IMF is northward are demonstrated. The coefficients of attenuation of the solar wind magnetic and electric fields which penetrate into the magnetosphere are determined.

Implications of rapid planetary rotation for the Dungey magnetotail of Saturn

Employing our current understanding of the structure and dynamics of Saturn's magnetosphere, we present a time‐dependent model of the kronian Dungey cycle magnetotail, which is based upon a modification of a similar model developed for Earth's magnetotail (Milan, 2004a). The major difference arises due to the rapid rotation of Saturn and the partial corotation that this imposes on the open field lines threading the polar cap. This results in twisted tail lobes, with the form of concentric cylinders of oldest to newest open flux from the inside out. The oldest, and hence longest, open field lines form the backbone of a highly extended magnetotail. Surrounding this are bundles of field lines disconnected by tail reconnection, propagating down‐tail at the solar wind speed. Owing to the twisted nature of the tail, these bundles remain entangled with the lobe cores to form “exterior flux ropes.” In the limit that the addition and removal of open flux from the magnetosphere by magnetic reconnection can be treated as a last‐in‐first‐out system, we formulate a description of the flux transport within the tail and drive this with estimated dayside reconnection voltages deduced from Cassini observations of the IMF made upstream of Saturn (Jackman et al., 2004).

The Magnetohydrodynamic Kelvin‐Helmholtz Instability: A Three‐dimensional Study of Nonlinear Evolution

We investigate through high-resolution three-dimensional simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. As in our earlier work, we have considered periodic sections of flows that contain a thin, transonic shear layer but are otherwise uniform. The initially uniform magnetic field is parallel to the shear plane but oblique to the flow itself. We confirm in three-dimensional flows the conclusion from our two-dimensional work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in three dimensions by this work because it shows how field-line bundles can be stretched and twisted in three dimensions as the quasi-two-dimensional Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of 2 over the two-dimensional effect. If, by these developments, the Alfvén Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest that magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memory of the original shear. For our flow configurations, the regime in three dimensions for such reorganization is 4 ≲ MAx ≲ 50, expressed in terms of the Alfvén Mach number of the original velocity transition and the initial Alfvén speed projected to the flow plan. When the initial field is stronger than this, the flow either is linearly stable (if MAx ≲ 2) or becomes stabilized by enhanced magnetic tension as a result of the corrugated field along the shear layer before the Cat's Eye forms (if MAx ≳ 2). For weaker fields the instability remains essentially hydrodynamic in early stages, and the Cat's Eye is destroyed by the hydrodynamic secondary instabilities of a three-dimensional nature. Then, the flows evolve into chaotic structures that approach decaying isotropic turbulence. In this stage, there is considerable enhancement to the magnetic energy due to stretching, twisting, and turbulent amplification, which is retained long afterward. The magnetic energy eventually catches up to the kinetic energy, and the nature of flows becomes magnetohydrodynamic. Decay of the magnetohydrodynamic turbulence is enhanced by dissipation accompanying magnetic reconnection. Hence, in three dimensions as in two dimensions, very weak fields do not modify substantially the character of the flow evolution but do increase global dissipation rates.

A new view of the solar outer atmosphere by the transition region and Coronal Explorer

The Transition Region and Coronal Explorer (TRACE) – described in the companion paper by Handy et al. (1999) – provides an unprecedented view of the solar outer atmosphere. In this overview, we discuss the initial impressions gained from, and interpretations of, the first million images taken with TRACE. We address, among other topics, the fine structure of the corona, the larger-scale thermal trends, the evolution of the corona over quiet and active regions, the high incidence of chromospheric material dynamically embedded in the coronal environment, the dynamics and structure of the conductively dominated transition region between chromosphere and corona, loop oscillations and flows, and sunspot coronal loops. With TRACE we observe a corona that is extremely dynamic and full of flows and wave phenomena, in which loops evolve rapidly in temperature, with associated changes in density. This dynamic nature points to a high degree of spatio-temporal variability even under conditions that traditionally have been referred to as quiescent. This variability requires that coronal heating can turn on and off on a time scale of minutes or less along field-line bundles with cross sections at or below the instrumental resolution of 700 km. Loops seen at 171 A (∼1 MK) appear to meander through the coronal volume, but it is unclear whether this is caused by the evolution of the field or by the weaving of the heating through the coronal volume, shifting around for periods of up to a few tens of minutes and lighting up subsequent field lines. We discuss evidence that the heating occurs predominantly within the first 10 to 20 Mm from the loop footpoints. This causes the inner parts of active-region coronae to have a higher average temperature than the outer domains.

Models for X‐Ray Emission from Isolated Pulsars

A model is proposed for the observed combination of power-law and thermal X-rays from rotationally powered pulsars. For gamma-ray pulsars with accelerators very many stellar radii above the neutron star surface, 100 MeV curvature gamma-rays from e(-) or e(+) flowing starward out of such accelerators are converted to e1 pairs on closed field lines all around the star. These pairs strongly affect X-ray emission from near the star in two ways. (1) The pairs are a source of synchrotron emission immediately following their creation in regions where B approx. 10(exp 10) G. This emission, in the photon energy range 0.1 keV less than E(sub X) less than 5 MeV, has a power-law spectrum with energy index 0.5 and X-ray luminosity that depends on the back-flow current, and is typically approx. 10(exp 33) ergs/ s. (2) The pairs ultimately a cyclotron resonance surrounding the star except for two holes along the open field line bundles which pass through it. In such a blanket the gravitational pull on e(+,-) pairs toward the star is balanced by the hugely amplified push of outflowing surface emitted X-rays wherever cyclotron resonance occurs. Because of it the neutron star is surrounded by a leaky hohlraum of hot blackbody radiation with two small holes, which prevents direct X-ray observation of a heated polar cap of a gamma-ray pulsar. Weakly spin modulated radiation from the blanket together with more strongly spin-modulated radiation from the holes through it would then dominate observed low energy (0.1-10 keV) emission. For non-y-ray pulsars, in which no such accelerators with their accompanying extreme relativistic back-flow toward the star are expected, optically thick e1 resonance blankets should not form (except in special cases very close to the open field line bundle). From such pulsars blackbody radiation from both the warm stellar surface and the heated polar caps should be directly observable. In these pulsars, details of the surface magnetic field evolution, especially of polar cap areas, become relevant to observations. The models are compared to X-ray data from Geminga, PSR 1055-52, PSR 0656+14, PSR 1929+10, and PSR 0950+08.

Ergodization of the magnetic field at the plasma edge by the dynamic ergodic divertor of TEXTOR 94

The structure of the resonant helical magnetic field of the dynamic ergodic divertor (DED) which is planned for TEXTOR is presented. The ergodic features are investigated by field line tracing calculations by the Gourdon code. The island widths and the related Chirikov parameters are determined by Poincaré plots. The deduced values are smaller than the ones predicted by the standard theory and a correction of the standard theory is presented. The onset of stochastization by the nonlinear interaction of neighboring island chains as well as remnant islands and barriers for field line diffusion at the maximum perturbation level, for which the Chirikov parameter is slightly above 1, are shown. The effect of hot spots sweeping over the limiter surface due to the rotation of the perturbation field is demonstrated. Local effects of the helical field and the divergence of a bundle of field lines are shortly worked out. Poincaré plots for lower mode operation are shown, which can penetrate deeper into the plasma to act at the q=2 surface. The accuracy of the numerical tool is demonstrated to be sufficient for these problems.

Magnetic reconnection at three-dimensional null points

The skeleton of an isolated null point in three dimensions consists of a ‘spine curve’ and a ‘fan surface’. Two isolated magnetic field lines approach (or recede from) the null point from both directions along the spine, and a continuum of field lines recedes from (or approaches) the null in the plane of the fan surface. Two bundles of field lines approach the null point around the spine (one from each direction) and spread out near the fan. The kinematics of steady reconnection at such a null point is considered, depending on the nature of the imposed boundary conditions on the surface that encloses the null, in particular on a cylindrical surface with its axis along the spine. Three kinds of reconnection are discovered. In ‘spine reconnection’ continuous footpoint motions are imposed on the curved cylindrical surface, crossing the fan and driving singular jetting flow along the spine. In ‘fan reconnection’ continuous footpoint motions are prescribed on the ends of the cylinder, crossing the spine and driving a singular swirling motion at the fan. An antireconnection theorem is proved, which states that steady MHD reconnection in three dimensions with plasma flow across the spine or fan is impossible in an inviscid plasma with a highly subAlfvenic flow and uniform magnetic diffusivity. One implication of this is that reconnection tends to be an inherently nonlinear phenomenon. A linear theory for slow steady reconnection is developed which demonstrates explicitly the nature of the spine singularity in spine reconnection. Finally, the properties of separator reconnection’ in complex configurations containing two null points are discussed by means of analytical examples.

Generation of the magnetic field at the magnetopauses of the rapidly rotating planets

This paper is a study of a possible mechanism of magnetic field amplification in the thin transition layer just outside the magnetopause of a quickly spinning planet. Here we present analysis of a new magnetospheric magnetic field source arising due to the rapid rotation. When the ionosphere and magnetopause conductivities of the rapidly roating planet are sufficiently high (but less than the field‐aligned conductivity) the circulation exists at the magnetopause in the open field line bundles. The toroidal magnetic field is generated there from the poloidal ambient magnetosheath magnetic field by differential rotation. The requirement of the α effect existence is satisfied due to the deviation from axial symmetry about the planet's rotation axis of the initial magnetosheath velocity and magnetic fields. The increasing poloidal magnetic field can be regenerated from the toroidal one by the α effect. This mechanism may act as a hydromagnetic dynamo. The generated magnetic field penetrates into the magnetosphere and adds to the magnetospheric magnetic field.

Turbulent relaxation of magnetic fields: 2. Self‐ organization and intermittency

The intermittent nature of the stochastic MHD reconnection model of magnetic fields presented by Tetreault (this issue) is developed. It is shown that the large‐scale magnetic field topology relaxes in spatially localized regions or “domains”. This occurs where the magnetic fluctuations, initially generated nonlinearly in the form of field line bundles, self‐organize into coherent structures. The self‐organization is driven by the tendency for parallel currents flowing along field lines within a bundle to attract each other. The self‐organized structures take the form of flux tubes or ropes which in cross section are localized, topologically closed, magnetic island structures. The emergence of the structures out of the underlying MHD turbulence is an intermittent, macroscopic signature of the reconnection process and of a phase transition in the magnetic field topology. The structures are derived from a coarse‐grained variational principle satisfying the dynamical invariants of MHD, and as such, their emergence can be expected to occur in a wide variety of magnetic field topologies. The model may have geophysical and astrophysical application, including reconnection and associated flux transfer events (FTEs) in the Earth's dayside magnetopause, as well as flux emergence and the occurrence of solar flares on the Sun. Quantitative comparison (spatial scales, speeds, time scales, thresholds, intermittency, and spatial distribution) with satellite data of magnetopause FTEs is favorable.