Motion Of Field Lines Research Articles

The role of an in-plane electric field during the merging formation of spherical tokamak plasmas

Axial merging of two torus plasmas is utilized as a center-solenoid free start-up scheme for a high-beta spherical tokamak (ST) plasma, in which magnetic reconnection under a strong guide field plays dominant roles in energy conversion and equilibrium formation. The ion heating source in magnetic reconnection is the plasma outflow with E×B drift velocity in the downstream region where the reconnected field lines flow out. Since the inductive reconnection electric field is almost parallel to the magnetic field, particularly in the inboard-side downstream region of magnetic reconnection under a strong guide field, a large electrostatic field in the poloidal plane is spontaneously formed to sustain steady plasma outflow motion in the downstream region. In ST plasma merging experiments, the self-generated electrostatic field in the downstream region does not always balance with the inductive electric field to make the total electric field strictly perpendicular to the total magnetic field. The excess electrostatic field will provide an even faster outflow plasma velocity than the magnetic field line motion and a quick reversal of the toroidal plasma current to form convex flux surfaces.

Magnetic flux expulsion in a superconducting wire

An electric current generates a magnetic field, and magnetic fields cannot exist in the interior of type I superconductors. As a consequence of these two facts, electric currents can only flow near the surface of a type I superconducting wire so that the self-field vanishes in the interior. Here we examine how an electric current flowing through the entire cross-section of a normal conducting wire becomes a surface current when it enters a superconducting portion of the wire. This geometry provides insight into the dynamics of magnetic flux expulsion that is not apparent in the Meissner effect involving expulsion of an externally applied magnetic field. It provides clear evidence that the motion of magnetic field lines in superconductors is intimately tied to the motion of charge carriers, as occurs in classical plasmas (Alfven's theorem) and as proposed in the theory of hole superconductivity [1], in contradiction with the conventional London-BCS theory of superconductivity.

Prediction of temperature barriers in weakly collisional plasmas by a Lagrangian coherent structures computational tool

Analysis of Lagrangian Coherent Structures (LCSs) has been shown to be a valid mathematical approach to explain the formation of transport barriers in magnetized plasmas. Such LCSs, borrowed from fluid dynamics theory, can be considered as the hidden skeleton of the system and can be used for studying a wide spectrum of transport mechanisms, even in plasmas. An LCS can be considered as a generalization for a finite time interval and for a general dynamical system of what manifolds are for Hamiltonian systems. In this paper, we demonstrate that such structures can be particularly useful for underlying the hidden paths governing the motion of magnetic field lines in chaotic magnetic fields.To perform such an analysis, we developed a numerical tool able to detect LCSs for a general dynamical system. The tool is able to deal with general coordinate systems and it is shown to match with other techniques already used to analyse chaotic magnetic fields, e.g. connection length. After the description of the computational tool, we focus on the heat transport equation and the comparison between temperature profile and topology of the LCSs. We provide evidence that numerical simulations are able to reproduce the temperature profiles similar to those observed in reversed field pinch experiments and that our tool successfully predicts the location of temperature gradients. The results suggest that, inside the chaotic region, the field-lines motion is far from stochastic and that the presence of hidden patterns allows the development of high temperature gradients.

A generalized poloidal–toroidal decomposition and an absolute measure of helicity

In fluid mechanics and magneto-hydrodynamics it is often useful to decompose a vector field into poloidal and toroidal components. In a spherical geometry, the poloidal component contains all of the radial part of the field, while the curl of the toroidal component contains all of the radial current. This paper explores how they work in more general geometries, where space is foliated by nested simply connected surfaces. Vector fields can still be divided into poloidal and toroidal components, but in geometries lacking spherical symmetry it makes sense to further divide the poloidal field into a standard part and a ‘shape’ term, which in itself behaves like a toroidal field and arises from variations in curvature.The generalised P–T decomposition leads to a simple definition of helicity which does not rely on subtracting the helicity of a potential reference field. Instead, the helicity measures the net linking of the standard poloidal field with the toroidal field as well as the new shape field. This helicity is consistent with the relative helicity in spherical and planar geometries. Its time derivative due to motion of field lines in a surface has a simple and intuitively pleasing form.

Photoelectrons in the quiet polar wind

AbstractThis study presents a newly coupled model capable of treating the superthermal electron population in the global polar wind solution. The model combines the hydrodynamic Polar Wind Outflow Model (PWOM) with the kinetic SuperThermal Electron Transport (STET) code. The resulting PWOM‐STET coupled model is described and then used to investigate the role of photoelectrons in the polar wind. We present polar wind results along single stationary field lines under dayside and nightside conditions, as well as the global solution reconstructed from nearly 1000 moving field lines. The model results show significant day‐night asymmetries in the polar wind solution owing to the higher ionization and photoelectron fluxes on the dayside compared to the nightside. Field line motion is found to modify this dependence and create global structure by transporting field lines through different conditions of illumination and through the localized effects of Joule heating.

Resonance of relativistic electrons with electromagnetic ion cyclotron waves

Relativistic electrons have been thought to more easily resonate with electromagnetic ion cyclotron EMIC waves if the total density is large. We show that, for a particular EMIC mode, this dependence is weak due to the dependence of the wave frequency and wave vector on the density. A significant increase in relativistic electron minimum resonant energy might occur for the H band EMIC mode only for small density, but no changes in parameters significantly decrease the minimum resonant energy from a nominal value. The minimum resonant energy depends most strongly on the thermal velocity associated with the field line motion of the hot ring current protons that drive the instability. High density due to a plasmasphere or plasmaspheric plume could possibly lead to lower minimum resonance energy by causing the He band EMIC mode to be dominant. We demonstrate these points using parameters from a ring current simulation.

A model of plasma heating by large-scale flow

In this work we study the process of energy dissipation triggered by a slow large scale motion of a magnetized conducting fluid. Our consideration is motivated by the problem of heating the solar corona, which is believed to be governed by fast reconnection events set off by the slow motion of magnetic field lines anchored in the photospheric plasma. To elucidate the physics governing the disruption of the imposed laminar motion and the energy transfer to small scales, we propose a simplified model where the large-scale motion of magnetic field lines is prescribed not at the footpoints but rather imposed volumetrically. As a result, the problem can be treated numerically with an efficient, highly-accurate spectral method, allowing us to use a resolution and statistical ensemble exceeding those of the previous work. We find that, even though the large-scale deformations are slow, they eventually lead to reconnection events that drive a turbulent state at smaller scales. The small-scale turbulence displays many of the universal features of field-guided MHD turbulence like a well developed inertial range spectrum. Based on these observations, we construct a phenomenological model that gives the scalings of the amplitude of the fluctuations and the energy dissipation rate as functions of the input parameters. We find a good agreement between the numerical results and the predictions of the model.

Dynamics of Line Preserving Field Line Motions

AbstractWe develop the theory of line preserving flows and the magnetic reconnection using the Euler potentials formalism. In addition to our recently proposed model, we formulate new equations describing the time evolution of the Euler potentials in the line preserving regime. We also look at a special case of the flows represented by the ideal plasma flows. We consider the magnetic reconnection as a breakage of the line preservation regime. Because general solutions of the obtained dynamics equations do not have their closed-form expressions, we provide two different approaches to the possible solutions, in particular, a linear approximation and a solution by finding a Lagrangian and a Hamiltonian that generate the dynamics equations. We also provide some simple examples of the physical interpretation of the solutions obtained.

Detection of magnetic barriers in a chaotic domain: first application of finite time Lyapunov exponent method to a magnetic confinement configuration

Magnetic field lines embedded in a plasma confinement system are often characterized by a chaotic motion. This weakens the confinement properties of any magnetic configuration. However, even in case of chaotic domains, magnetic barriers can emerge and limit the field line motion itself. In the context of the numerical simulation of a Reversed-Field Pinch configuration a new magnetic topology analysis, borrowed from previous fluid dynamic studies, is discussed. This methodology relies on the behavior of the Finite Time Lyapunov Exponent (FTLE) associated with the magnetic field. By referring to a previous work in which the magnetic field is given in terms of analytical function (Borgogno et al 2011 Phys. Plasmas 18 102307) the FTLE field shows the presence of ridges, special gradient lines normal to the direction of minimum curvature, forming magnetic barriers. These ridges can be recognized as Lagrangian Coherent Structures (LCSs) for the system, actually opposing the penetration of magnetic field lines across them. In this article a more general numerical scheme for the detection of the LCSs has been adopted that allows analysis of realistic cases in which the magnetic fields are numerically known on a discrete mesh. After a validation test performed on the analytical case, a first application to a numerical magnetohydrodynamics simulation of the RFP, characterized by a broad chaotic region, has been performed. A strong magnetic barrier has been observed that effectively limits the field lines motion inside the chaotic sea.

Chaos in magnetic flux ropes

Magnetic flux ropes immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Each collision results in magnetic field line reconnection and the generation of a quasi-separatrix layer. Three-dimensional magnetic field lines are computed by conditionally averaging the data using correlation techniques. Conditional averaging is possible for only a number of rotation cycles as the field line motion becomes chaotic. The permutation entropy can be calculated from the time series of the magnetic field data (this is also done with flows) and is used to calculate the positions of the data on a Jensen–Shannon complexity map. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The Lyapunov and Hurst exponents are calculated and the complexity and permutation entropy of the flows and field components are shown throughout the volume.

Magnetic-flutter-induced pedestal plasma transport

Plasma toroidal rotation can limit reconnection of externally applied resonant magnetic perturbation (RMP) fields δB on rational magnetic flux surfaces. Hence it causes the induced radial perturbations δBρ to be small there, thereby inhibiting magnetic island formation and stochasticity at the top of pedestals in high (H-mode) confinement tokamak plasmas. However, the δBρs induced by RMPs increase away from rational surfaces and are shown to induce significant sinusoidal radial motion (flutter) of magnetic field lines with a radial extent that varies linearly with δBρ and inversely with distance from the rational surface because of the magnetic shear. This produces a radial electron thermal diffusivity that is (1/2)(δBρ/B0)2 times a kinetically derived, electron-collision-induced, magnetic-shear-reduced, effective parallel electron thermal diffusivity in the absence of magnetic stochasticity. These low collisionality flutter-induced transport processes and thin magnetic island effects are shown to be highly peaked in the vicinity of rational surfaces at the top of low collisionality pedestals. However, the smaller but finite level of magnetic-flutter-induced electron heat transport midway between rational surfaces is the primary factor that determines the electron temperature difference between rational surfaces at the pedestal top. The magnetic-flutter-induced non-ambipolar electron density transport can be large enough to push the plasma toward an electron density transport root. Requiring ambipolar density transport is shown to determine the radial electric field, the plasma toroidal rotation (via radial force balance), a reduced electron thermal diffusivity and increased ambipolar density transport in the pedestal. At high collisionality the various flutter effects are less strongly peaked at rational surfaces and generally less significant. They are thus less likely to exhibit flutter-induced resonant behaviour and transition toward an electron transport root. Magnetic-flutter-induced plasma transport processes provide a new paradigm for developing an understanding of how RMPs modify the pedestal structure to stabilize peeling–ballooning modes and thereby suppress edge localized modes in low collisionality tokamak H-mode plasmas.

Comparison of electromagnetic and gravitational radiation: What we can learn about each from the other

We compare the nature of electromagnetic fields and gravitational fields in linearized general relativity. We carry out this comparison both mathematically and visually. In particular, the “lines of force” visualizations of electromagnetism are contrasted with the recently introduced tendex/vortex eigenline technique for visualizing gravitational fields. Specific solutions, visualizations, and comparisons are given for an oscillating point quadrupole source. Among the similarities illustrated are the quasistatic nature of the near fields, the transverse 1/r nature of the far fields, and the interesting intermediate field structures connecting these two limiting forms. Among the differences illustrated are the meaning of field line motion and of the flow of energy.

Model of line preserving field line motions using Euler potentials

We consider behavior of finite magnetic field lines during reconnection processes. We portray field line motions using Euler potentials representation. Here, we propose a new insight into plasma flow fields related with magnetic reconnection. In this approach reconnection is treated as a breakage of magnetic topology, which results in deviation from the line preserving flow regime. We derive constraints and the general equations for these flows. In our approach the flux preserving flows are treated as a special case of line preserving regime. We also derive a constraint on a non-ideal term in Ohm’s Law within diffusion regions, which relates plasma flow with resistivity, and which must hold for non-reconnective diffusion. We also propose a new method of detecting magnetic reconnection.

Excitation of the third harmonic mode in meridian planes for Pi2 in the auroral zone

Polarizations of Pi2 pulsations in the magnetosphere and on the ground in the auroral zone are inconsistent when field line motions in the meridian and transverse planes are both in the fundamental harmonic. To resolve these inconsistencies, we propose a third harmonic mode in the meridian planes. The excitation of the third harmonic is explained by dusk‐to‐dawn currents at the equatorial plane, which are driven by diamagnetic currents during substorm injections. We propose diamagnetic currents in the equatorial plane and compressional input at the outer boundary as the source of Pi2 pulsations in the magnetosphere.

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.

Barriers in the transition to global chaos in collisionless magnetic reconnection. II. Field line spectroscopy

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. The identification of the ridges in the field of the finite time Lyapunov exponent as barriers to the field line motion is carried out adopting the technique of field line spectroscopy to analyze the radial position of a field line while it winds its way through partial stochastic layers and to compare the frequencies of the field line motion with the corresponding frequencies of the distinguished hyperbolic field lines that are the nonlinear generalizations of linear X-lines.

Stochastic flux freezing and magnetic dynamo

Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr(m)) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr(m)=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered.

Multipoint Spectroscopy Measurement of Spherical Tokamak Heating by Magnetic Reconnection in UTST

The temporal evolution of ion temperature and flow was observed to investigate the heating effect of plasma merging in the UTST device by using a multipoint Doppler spectroscopy measurement system. The bulk plasma ion temperature measured by a carbon impurity line was about 15-20 eV after plasma merging. In addition, anomalous broadening of the carbon line width was observed only in the early phase of plasma merging. Since carbon impurity emission comes mainly from the X-point and the vicinity of the center stack, the broad spectrum is considered to consist of a radially bi-directional outflow component from the X-point and a stationary component near the center stack. The outflow velocity estimated from the spectroscopy was about 24 km/s, which agreed well with both an Alfven velocity of 22 km/s and a velocity of the reconnected field line motion of 35 km/s.

THE ROLE OF ACTIVE REGION TOPOLOGY IN EXCITATION, TRAPPING, AND DAMPING OF CORONAL LOOP OSCILLATIONS

We investigate the role of magnetic field topology in dense coronal loop oscillation by the means of three-dimensional magnetohydrodynamic numerical simulations of two models of idealized active regions (ARs). The first AR model is initialized as a straight cylinder surrounded by the field lines of the same length and orientation. The second model consists of a potential dipole magnetic configuration and contains a loop with a higher density than its surroundings. Dipole field lines have position-dependent length and orientation in contrary to straight ones. We study different ways of excitation of transverse loop oscillations by an external pulse and a nearly eigenmode excitation implemented inside the loop. We find that perturbation acting directly on a single loop excites oscillations both in cylindrical and dipole loops. However, the leakage of the wave energy is larger in a curved loop compared to a straight loop. External excitation of the whole AR is efficient in the excitation of oscillation in the straight field configuration, but results in less efficient excitation in the case of dipole field. We show that excitation of collective motion of straight field lines having the same wave periods and planes of the oscillations requires much less energy than excitation of dipole field lines having position-dependent orientation and wave periods and being excited individually, not having a collective mode of oscillation. We conclude that coherent motion of straight field lines is one of the factors that decrease the energy leakage from an oscillating loop, while individual motions of dipole field lines require more energy from the source to produce the loop oscillations, and also lead to higher damping rate compared to the straight field case. We discuss Transition Region and Coronal Explorer (TRACE) observations of coronal loop oscillations in view of our theoretical findings. We show several examples of time signatures of transversal loop oscillations observed by TRACE that agree with numerical simulations of externally excited oscillations.

Resonant drift echoes in electron phase space density produced by dayside Pc5 waves following a geomagnetic storm

The interaction between relativistic, equatorially mirroring electrons and Pc5 Ultra Low Frequency (ULF) waves in the magnetosphere is investigated using a numerical MagnetoHydroDynamic (MHD) model for waves and a test‐kinetic model for electron phase space density (PSD). The temporal and spatial characteristics of a ULF wave packet are constrained using ground‐based observations of narrowband ULF activity following a geomagnetic storm on 24 March 1991, which occurred from 1200 to 1340 Universal Time (UT). A salient feature of the ULF waves during this interval was the apparent localization of the ULF wave power to the dayside of the magnetosphere and the antisunward propagation of ULF wave phase in the morning and afternoon sectors. This is interpreted to imply a localized source of ULF wave power close to noon Magnetic Local Time (MLT) at the magnetopause. The expected electron dynamics are investigated using model wavefields to predict the observable characteristics of the interaction in satellite electron flux data. The wave and kinetic models show that the localized radial motion of magnetic field lines associated with MHD fast waves propagating from the ULF source region acts to periodically inject electrons from high L to lower L within the magnetosphere. This action becomes resonant when the drift period of the electrons matches a multiple of the ULF wave period and leads to an enhancement in radial transport.