Topology Of Magnetic Field Lines Research Articles

Zooming in on the circumgalactic medium with GIBLE

We used a cosmological zoom-in simulation of a Milky Way-like galaxy to study and quantify the topology of magnetic field lines around cold gas clouds in the circumgalactic medium (CGM). This simulation is a new addition to Project GIBLE, a suite of cosmological magnetohydrodynamic simulations of galaxy formation with preferential super-Lagrangian refinement in the CGM, reaching an unprecedented CGM gas mass resolution of ∼225 M⊙. To maximize statistics and resolution, we focused on a sample of ∼200 clouds with masses of ∼106 M⊙. The topology of magnetic field lines around clouds is diverse, from threading to draping, and there is large variation in the magnetic curvature (κ) within cloud-background interfaces. We typically find little variation of κ between upstream and downstream cloud faces, implying that strongly draped configurations are rare. In addition, κ correlates strongly with multiple properties of the interface and the ambient background, including cloud overdensity and relative velocity, suggesting that cloud properties impact the topology of interface magnetic fields.

The Effect of Magnetic Field Line Topology on ICME-related GCR Modulation

The large-scale magnetic structure of interplanetary coronal mass ejections (ICMEs) has been shown to affect the galactic cosmic-ray (GCR) flux measured in situ by spacecraft, causing temporary decreases known as Forbush decreases (FDs). In some ICMEs, the magnetic ejecta exhibits a magnetic flux rope (FR) structure; the strong magnetic field strength and closed field line geometry of such ICME FRs have been proposed to act as a shield to GCR transport. In this study, we identify four ICMEs near Earth that drove FDs with similar mean magnetic field strengths (20–25 nT), two ICMEs with more typical mean speeds (∼400 km s−1), and two fast (∼750 km s−1) ICMEs. Within each speed pairing, we identify an ICME that exhibited an open magnetic field line topology and compare its effect on the GCR flux to that which exhibited a mostly closed topology. We investigate the different mechanisms that contribute to the resulting ICME-related FDs and their recovery and determine which properties, if any, play a more important role than others in driving FDs. We find that much of the GCR response to the ICME events in this study is independent of the open or closed magnetic field line topology of the FR and that features such as the fluctuations in speed, magnetic field structure, and expansion within the FR may play more of a role in determining the smaller-scale structure of the FD profile.

Topology of turbulence within collisionless plasma reconnection

In near-collisionless plasmas, which are ubiquitous in astrophysics, entropy production relies on fully-nonlinear processes such as turbulence and reconnection, which lead to particle acceleration. Mechanisms for turbulent reconnection include multiple magnetic flux ropes interacting to generate thin current sheets which undergo reconnection, leading to mixing and magnetic merging and growth of coherent structures, unstable reconnection current layers that fragment and turbulent reconnection outflows. All of these processes act across, and encompass, multiple reconnection sites. We use Magnetospheric Multi Scale four-point satellite observations to characterize the magnetic field line topology within a single reconnection current layer. We examine magnetopause reconnection where the spacecraft encounter the Electron Diffusion Region (EDR). We find fluctuating magnetic field with topology identical to that found for dynamically evolving vortices in hydrodynamic turbulence. The turbulence is supported by an electron-magnetohydrodynamic (EMHD) flow in which the magnetic field is effectively frozen into the electron fluid. Accelerated electrons are found in the EDR edge where we identify a departure from this turbulent topology, towards two-dimensional sheet-like structures. This is consistent with a scenario in which sub-ion scale turbulence can suppress electron acceleration within the EDR which would otherwise be possible in the electric field at the X-line.

Field Gradient Analysis Based on a Geometrical Approach

AbstractUsing multi‐point observations from a spacecraft constellation, the spatial gradients of measured physical quantities can be calculated, and thus other derived parameters for the plasma (e.g., current density, topology of magnetic field lines, and wave vectors) can also be calculated. In this research, a geometrical method based on integral theorems has been applied to deduce estimators of the linear gradients of various fields based on constellation measurements. Integral forms are best suited to the particular case of four‐point measurements and indeed using this geometrical approach, it is very easy to derive the field gradients for observations made by a planar constellation (e.g., as defined by three spacecraft). It is verified here that the method based on integral theorems and the method based on spatial interpolation are equivalent for deriving formulas for the gradients. An error analysis found that the accuracy of the estimators is very high and enters at the second order of the tetrahedron size. This makes the estimates, derived from the integral approach rather stable.

Lagrangian evolution of field gradient tensor invariants in magneto-hydrodynamic theory

In 1982 in a series of works Vielliefosse [1, 2] discussed a nonlinear homogeneous evolution equation for the velocity gradient tensor in fluid dynamics. Later Cantwell [3] extended this formalism to the non-homogeneous case including the effects of viscous diffusion and cross derivatives of pressure field. Here, we derive the evolution equations of the geometrical invariants of the magnetic and velocity field gradient tensors in the case of magneto-hydrodynamics for both non-homogeneous and homogeneous cases, i.e., considering or neglecting viscous effects and source terms. The inclusion of dissipation effects and higher-order gradient terms introduces a non trivial evolution of invariants, which can be treated as a stochastic evolution equation. Conversely, in the homogeneous case, the magnetic field invariants do not evolve, i.e., the magnetic field line topology is conserved, while the corresponding velocity invariants are affected by magnetic forces. By writing the equations of the velocity field invariants as a dynamical system we can identify the role of the different terms in the evolution equations. In detail, in the homogenous case we show that the term associated with the current density drives transitions between hyperbolic and elliptical structures. Evolution equations are also discussed in the perspective of an application to the analysis of magneto-hydrodynamic turbulence.

Validation scheme for solar coronal models: Constraints from multi-perspective observations in EUV and white light

Context. In this paper, we present a validation scheme to investigate the quality of coronal magnetic field models, which is based on comparisons with observational data from multiple sources. Aims. Many of these coronal models may use a range of initial parameters that produce a large number of physically reasonable field configurations. However, that does not mean that these results are reliable and comply with the observations. With an appropriate validation scheme, which is the aim of this work, the quality of a coronal model can be assessed. Methods. The validation scheme was developed with the example of the EUropean Heliospheric FORecasting Information Asset (EUHFORIA) coronal model. For observational comparison, we used extreme ultraviolet and white-light data to detect coronal features on the surface (open magnetic field areas) and off-limb (streamer and loop) structures from multiple perspectives (Earth view and the Solar Terrestrial Relations Observatory – STEREO). The validation scheme can be applied to any coronal model that produces magnetic field line topology. Results. We show its applicability by using the validation scheme on a large set of model configurations, which can be efficiently reduced to an ideal set of parameters that matches best with observational data. Conclusions. We conclude that by using a combined empirical visual classification with a mathematical scheme of topology metrics, a very efficient and objective quality assessment for coronal models can be performed.

Radial Evolution of a CIR: Observations From a Nearly Radially Aligned Event Between Parker Solar Probe and STEREO‐A

AbstractThe addition of Parker Solar Probe (PSP) to the Heliophysics System Observatory has allowed for the unprecedented ability to study Corotating Interaction Regions (CIRs) at multiple radial distances without significant temporal/longitudinal variations. On September 19, 2019, PSP observed a CIR at ∼0.5 au when it was nearly radially aligned with the Solar Terrestrial Relations Observatory‐Ahead (STEREO‐A) spacecraft at ∼1 au, allowing for an unambiguous assessment of the radial evolution of a single CIR. Bulk plasma and magnetic field signatures of the CIR evolve in a fashion characteristic to previous observations; however, the suprathermal ions are enhanced over a larger longitudinal range at PSP than at STEREO‐A, although at much lower intensities. The longitudinal spread appears to be largely a consequence of magnetic field line topology at CIRs between the compressed slow solar wind upstream and high‐speed stream following the CIR, underscoring the importance of the large‐scale topology of these structures.

Magnetic winding – a key to unlocking topological complexity in flux emergence

Magnetic helicity is an invariant of ideal magnetohydrodynamics (MHD) that encodes information on the topology of magnetic field lines. It has long been appreciated that magnetic topology is an important constraint for the evolution of magnetic fields in MHD. In applications to the solar atmosphere, understanding magnetic topology is crucial for following the evolution and eruption of magnetic fields. At present, magnetic helicity flux can be measured in solar observations but the interpretation of results is difficult due to the combination of confounding factors. We propose that a renormalization of helicity flux, the magnetic winding, can be used to detect more detailed topological features in magnetic fields and thus provide a more reliable signature for predicting the onset of solar eruptions.

The Influence of Solar Wind Pressure on Martian Crustal Magnetic Field Topology

AbstractWe present a study of changes in Martian magnetic topology induced by upstream solar wind ram pressure variations. Using electron energy spectra and pitch angle distributions measured by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft, we classify the topology of magnetic field lines in the Martian space environment across a range of solar wind conditions. We find that during periods of high solar wind dynamic pressure, draped fields are pushed to lower altitudes on the dayside of the planet, compressing closed fields. At the same time, open topology becomes more prevalent on the nightside due to the broadening of crustal cusp regions. The result is a decrease in closed topology at all locations around Mars, suggesting that the Martian ionosphere becomes significantly more exposed to solar wind energy input during high solar wind pressure. This could likely contribute to elevated levels of ion escape during these periods.

Evolution of a Pinch Column During the Acceleration of Fast Electrons and Deuterons in a Plasma-Focus Discharge

Plasma in a pinch column, as produced by a plasma-focus discharge at the deuterium filling and the current intensity reaching 1 MA, was investigated at the total neutron yield reaching about 10 10 per discharge. The use was made of neutron diagnostics, laser interferometry, soft X-ray measurements, optical emission spectroscopy, magnetic probes, as well as electron and ion measurements with the temporal, spatial, and energetic resolutions. The detailed studies showed the ordered toroidal, helical, and plasmoidal structures which could contain currents with poloidal and toroidal components and their associated magnetic fields. Their spontaneous transformations were explained by changes in a topology of magnetic field lines due to magnetic reconnections. A nonthermal acceleration of fast electrons and ions (producing hard X-rays and fusion neutrons, respectively) corresponded to: 1) the formation of plasmoids in the pinch column and 2) a decay of pinch constrictions and secondary plasmoids during the evolution of instabilities. A filamentary structure of the current flow could explain the high energy density and fast transformations of the magnetic energy into kinetic energy of electron and ion beams (reaching energy of hundreds of kiloelectronvolt). This paper summarizes the results obtained with the PF-1000 facility in 2009-2017, and describes the internal transformations in a dense plasma column during the evolution of MHD instabilities.

Electron Magnetohydrodynamics Magnetic Reconnection Experiment on Keda Linear Magnetized Plasma Device**Supported by the National Natural Science Foundation of China under Grant Nos 41331067 and 41527804, the Key Research Program of Frontier Sciences of Chinese Academy of Sciences under Grant No QYZDJ-SSW-DQC010, and the Fundamental Research Funds for the Central Universities.

We conduct an electron magnetohydrodynamics magnetic reconnection experiment with guide-field in our Keda linear magnetized plasma device, in which two pulsed currents with the same direction are conducted in parallel with the axial direction of the main chamber of the device using two long aluminum sticks. After approximately , an X-type magnetic field line topology is formed at the center of the chamber. With the formation of the X-type topology of magnetic field lines, we can also find the rapid increase of the current and ratio of the common flux to the private flux in this area. Additionally, a reduction in the plasma density and the plasma density concentration along one pair of separatrices can also be found.

Variational integrators for inertial magnetohydrodynamics

Recently, an extended version of magnetohydrodynamics that incorporates electron inertia, dubbed inertial magnetohydrodynamics, has been proposed [Lingam et al., Phys. Lett. A, 379, 570–576 (2015)]. This model features a noncanonical Hamiltonian formulation with a number of conserved quantities, including the total energy and modified versions of magnetic and cross helicity. In this work, a variational integrator is presented which preserves these conservation laws to machine accuracy. As long as effects due to finite electron mass are neglected, the scheme preserves the magnetic field line topology so that unphysical reconnection is absent. Only when the effects of finite electron mass are added, magnetic reconnection takes place. The excellent conservation properties of the method are illustrated by numerical examples in 2D.

Transpolar arcs observed simultaneously in both hemispheres

AbstractTwo coexisting transpolar arcs are observed on 31 August 2005. We track the formation and motion of the arcs in both the Northern and Southern Hemispheres, using data from two independent satellites (Imager for Magnetopause to Aurora Global Exploration and a Defence Meteorological Satellite Program satellite). The observations are supported by supplementary ground‐based ionospheric convection data from the Super Dual Auroral Radar Network. The two arcs form during a period of northward interplanetary magnetic field. Following a change in the direction of the interplanetary magnetic field BY component from negative to positive, the dawnside arc traverses the polar cap to the duskside in the Northern Hemisphere. Over the same time period and in the Southern Hemisphere, the duskside arc traverses the polar cap to the dawnside. A complex magnetic field line topology resulting in the coexistence of two tongues of closed field lines protruding into the otherwise open polar cap is implied. We discuss these observations in terms of magnetic conjugacy and a model of transpolar arcs formation.

On the occurrence of magnetic reconnection equatorward of the cusps at the Earth's magnetopause during northward IMF conditions

AbstractMagnetic reconnection changes the topology of magnetic field lines. This process is most readily observable with in situ instrumentation at the Earth's magnetopause as it creates open magnetic field lines to allow energy and momentum flux to flow from the solar wind to the magnetosphere. Most models use the direction of the interplanetary magnetic field (IMF) to determine the location of these magnetopause entry points, known as reconnection lines. Dayside locations of magnetic reconnection equatorward of the cusps are generally found during sustained intervals of southward IMF, while high‐latitude region regions poleward of the cusps are observed for northward IMF conditions. In this study we discuss Double Star magnetopause crossings and a conjunction with a Polar cusp crossing during northward IMF conditions with a dominant IMF BY component. During all seven dayside magnetopause crossings, Double Star detected switching ion beams, a known signature for the presence of reconnection lines. In addition, Polar observed a cusp ion‐energy dispersion profile typical for a dayside equatorial reconnection line. Using the cutoff velocities for the precipitating and mirrored ion beams in the cusp, the distance to the reconnection site is calculated, and this distance is traced back to the magnetopause, to the vicinity of the Double Star satellite locations. Our analysis shows that, for this case, the predicted line of maximum magnetic shear also coincides with that dayside reconnection location.

Study of charged particle acceleration by magnetic reconnection in a plasma

Magnetic reconnection, which occurs in high conducting plasmas, changes the topology of magnetic field lines and converts magnetic energy into the kinetic and thermal energy of plasma and also accelerates charged particles. This phenomenon plays an important role in changing the dynamic of laboratory and space plasmas such as fusion tokamaks and sun’s corona. The electric and magnetic fields generated by magnetic reconnection result in acceleration and drift motion of charged particles. Therefore, charged particles, depending on their injection position and initial kinetic energy, can be accelerated and escape or can be trapped in magnetic fields. In this study by considering different injection positions and initial kinetic energies, we investigate how a particle (proton) is accelerated or trapped. Our numerical analyses show that the spine structure for three-dimensional magnetic reconnection can be considered as a potential mechanism for particle acceleration. In this model, a proton can be accelerated up to a few MeV within a few milliseconds. The particle’s trajectory and final kinetic energy strongly depend on its injection position.

MHD MODELING OF THE OUTER HELIOSPHERIC STRUCTURES AROUND THE HELIOPAUSE

Voyager 1 (V1) observed the first step increase of the galactic cosmic ray (GCR) flux for energies >70 MeV and >211 MeV near the heliopause at 2012.31, just before the magnetic field polarity changed from away to toward at 2012.47. This event was not accompanied by an anomalous cosmic ray (ACR) flux change. The second GCR step increase, together with an ACR decrease, was observed at 2012.65. The magnetic field change was observed with its polarity changing from a toward to an apparent away direction at 2012.56, at ~122 AU from the Sun, with an eventual orientation of 22°. The later magnetic field has been identified as the interstellar magnetic field and the current sheet at the polarity change is identified as the boundary of the interstellar magnetic field. We present a three-dimensional stationary MHD simulation with a heliopause located at ~122 AU and a magnetic field polarity change across the heliopause. The apparent away polarity of the magnetic field is confirmed to be that of the interstellar magnetic field in this simulation. We present a detailed analysis of the magnetic field line topology in the vicinity of the heliopause and argue for a favorable condition of the first GCR step increase with no concurrent ACR flux change before the time corresponding to the magnetic polarity change at 2012.47.

Instability of the current sheet in the Earth's magnetotail with normal magnetic field

Instability of a current sheet in the Earth's magnetotail has been investigated by two-dimensional fully kinetic simulations. Two types of magnetic configuration have been studied; those with uniform normal magnetic field along the current sheet and those in which the normal magnetic field has a spatial hump. The latter configuration has been proposed by Sitnov and Schindler [Geophys. Res. Lett. 37, L08102 (2010)] as one in which ion tearing modes might grow. The first type of configuration exhibits electron tearing modes when the normal magnetic field is small. The second type of configuration exhibits an instability which does not tear or change the topology of magnetic field lines. The hump in the initial configuration can propagate Earthward in the nonlinear regime, leading to the formation of a dipolarization front. Secondary magnetic islands can form in regions where the normal magnetic field is very weak. Under no conditions do we find the ion tearing instability.

RECONNECTION AND ELECTRON TEMPERATURE ANISOTROPY IN SUB-PROTON SCALE PLASMA TURBULENCE

Turbulent behavior at sub-proton scales in magnetized plasmas is important for a full understanding of the energetics of astrophysical flows such as the solar wind. We study the formation of electron temperature anisotropy due to reconnection in the turbulent decay of sub-proton scale fluctuations using two dimensional, particle-in-cell (PIC) plasma simulations with realistic electron-proton mass ratio and a guide field out of the simulation plane. A fluctuation power spectrum with approximately power law form is created down to scales of order the electron gyroradius. In the dynamic magnetic field topology, which gradually relaxes in complexity, we identify the signatures of collisionless reconnection at sites of X-point field geometry. The reconnection sites are generally associated with regions of strong parallel electron temperature anisotropy. The evolving topology of magnetic field lines connected to a reconnection site allows spatial mixing of electrons accelerated at multiple, spatially separated reconnection regions. This leads to the formation of multi-peaked velocity distribution functions with a strong parallel temperature anisotropy. In a three-dimensional system, supporting the appropriate wave vectors, the multi-peaked distribution functions would be expected to be unstable to kinetic instabilities, contributing to dissipation. The proposed mechanism of anisotropy formation is also relevant to space and astrophysical systems where the evolution of the plasma is constrained by linear temperature anisotropy instability thresholds. The presence of reconnection sites leads to electron energy gain, nonlocal velocity space mixing and the formation of strong temperature anisotropy; this is evidence of an important role for reconnection in the dissipation of turbulent fluctuations.

Mimetic Methods for Lagrangian Relaxation of Magnetic Fields

We present a new code that performs a relaxation of a magnetic field toward a force-free state (Beltrami field) using a Lagrangian numerical scheme. Beltrami fields are of interest for the dynamics of many technical and astrophysical plasmas as they are the lowest energy states that the magnetic field can reach. The numerical method strictly preserves the magnetic flux and the topology of magnetic field lines. In contrast to other implementations we use mimetic operators for the spatial derivatives in order to improve accuracy for high distortions of the grid. Compared with schemes using direct derivatives we find that the final state of the simulation approximates a force-free state with a significantly higher accuracy. We implement the scheme in a code which runs on graphical processing units, which leads to an enhanced computing speed compared to previous relaxation codes.

Ionospheric Joule heating, fast flow channels, and magnetic field line topology for IMF By‐dominant conditions: Observations and comparisons with predicted reconnection jet speeds

When the interplanetary magnetic field (IMF) is dawnward or duskward, magnetic merging between the IMF and the geomagnetic field occurs near the cusp on the dayside flanks of the magnetosphere. While these periods are usually considered “quiet,” they can lead to intense localized energy deposition into the dayside ionosphere. We analyze two intervals during the geomagnetic storm on 24 August 2005: one with steady duskward IMF and one with steady dawnward IMF. Using outputs from the Assimilative Mapping of Ionospheric Electrodynamics (AMIE) and data from the Defense Meteorological Satellite Program, we show that intense Joule heating exists on fast ionospheric flow channels which lie on open field lines. In addition, the flow channels on open field lines have large components in the sunward direction and therefore resist the bulk solar wind and magnetosheath flow. We compare observed velocities with predicted reconnection jet speeds using magnetosheath and cusp parameters from an MHD simulation. Results suggest that the fast ionospheric flow corresponds to portions of the reconnection jet populated by low‐density plasma. The importance of ionospheric conductance in determining the ionospheric flow is also discussed.