Length Of Field Lines Research Articles

A Study on the Predawn Ionospheric Heating Effect and Its Main Controlling Factors

We proposed, for the first time, that the angle between the horizontal projection of the magnetic field line and the sunrise line (AMFS) is a crucial factor that controls predawn heating. Through quantitative analysis, we determined that both the AMFS and the length of the magnetic field line (LMF) significantly affect predawn heating. We found that an increased AMFS intensifies predawn heating, while an increased LMF counteracts it. Our research indicates that the optimal conditions for peak predawn heating occur at an AMFS of approximately 30 degrees and an LMF of about 4000 km, where the effect surpasses 400 K. Additionally, we observed that the effects of both the AMFS and the LMF on predawn heating exhibit a saturation effect. This study provides a clearer understanding of the factors driving predawn ionospheric heating, with implications for topside ionosphere research.

Variation in Path Lengths of Turbulent Magnetic Field Lines and Solar Energetic Particles

Modeling of time profiles of solar energetic particle (SEP) observations often considers transport along a large-scale magnetic field with a fixed path length from the source to the observer. Here, we point out that variability in the turbulent field line path length can affect the fits to SEP data and the inferred mean free path and injection profile. To explore such variability, we perform Monte Carlo simulations in representations of homogeneous 2D MHD + slab turbulence adapted to spherical geometry and trace trajectories of field lines and full particle orbits, considering proton injection from a narrow or wide angular region near the Sun, corresponding to an impulsive or gradual solar event, respectively. We analyze our simulation results in terms of field line and particle path length statistics for 1° × 1° pixels in heliolatitude and heliolongitude at 0.35 and 1 au from the Sun, for different values of the turbulence amplitude b/B 0 and turbulence geometry as expressed by the slab fraction f s . Maps of the most probable path lengths of field lines and particles at each pixel exhibit systematic patterns that reflect the fluctuation amplitudes experienced by the field lines, which in turn relate to the local topology of 2D turbulence. We describe the effects of such path length variations on SEP time profiles, both in terms of path length variability at specific locations and the motion of the observer with respect to turbulence topology during the course of the observations.

Inferring Whistler‐Mode Chorus Wave Source Regions in the Martian Mini‐Magnetospheres

AbstractMartian mini‐magnetospheres contain whistler‐mode chorus waves potentially contributing to atmospheric escape, analogous to the Earth's inner magnetosphere. At Earth, the chorus waves have been found to originate from the near‐equatorial region spanning approximately 2% of the entire magnetic field line length. However, because of the lack of wave Poynting flux measurements, the Martian chorus source region remains unclear. By comparing the frequency dependence between observed wave power and modeled linear growth rates, we present the first attempt to explore the chorus wave source distribution along the Martian mini‐magnetospheric field lines. Our data‐to‐model comparisons support that these waves are not generated by a single source tightly confined near the magnetic strength minimal location but by intermittent or continuous sources spanning up to 40% of the entire field line length. These results imply that the Martian mini‐magnetospheres could have more active energy transfer processes mediated by whistler‐mode chorus waves than the expectation.

Anisotropic heat diffusion in stochastic magnetic fields

AbstractThe magnetic topology is a critical issue in fusion plasma research. An example is the Resonant Magnetic Perturbation (RMP), which controls the edge transport in tokamaks. However, the physics of how the RMP affects edge transport is not clear. One reason is the transport process on the stochastic magnetic field is poorly understood. This study examines anisotropic heat diffusion numerically to understand heat transport in stochastic magnetic fields. We developed a numerical model of an anisotropic temperature diffusion model, where the significant deviation of the parallel and perpendicular thermal conductivity exists. We applied this implementation to the realistic stellarator geometry with the stochastic magnetic field in the edge. The smooth temperature profile is obtained for the large perpendicular diffusion, although the magnetic field is stochastic. However, for another case of significant parallel diffusion, the small flattening of the temperature on the magnetic island in the stochastic region appears. That result suggests that the stochastic magnetic field can keep the finite temperature gradient if the connection length of the magnetic field line in the stochastic region is sufficiently long.

Staged cooling of a fusion-grade plasma in a tokamak thermal quench

In tokamak disruptions where the magnetic connection length becomes comparable to or even shorter than the plasma mean-free-path, parallel transport can dominate the energy loss and the thermal quench of the core plasma goes through four phases (stages) that have distinct temperature ranges and durations. The main temperature drop occurs while the core plasma remains nearly collisionless, with the parallel electron temperature dropping in time t as and a cooling time that scales with the ion sound wave transit time over the length of the open magnetic field line. These surprising physics scalings are the result of effective suppression of parallel electron thermal conduction in an otherwise bounded, quasineutral, and collisionless plasma, which is different from what are known to date on electron thermal conduction along the magnetic field in a nearly collisionless and quasineural plasma.

Solar energetic particle event onsets at different heliolongitudes: The effect of turbulence in Parker spiral geometry

Context. Solar energetic particles (SEPs), accelerated during solar eruptions, are observed to rapidly reach a wide heliolongitudinal range in the interplanetary space. Turbulence-associated SEP propagation across the mean Parker spiral direction has been suggested to contribute to this phenomenon. Aims. We study SEP propagation in turbulent magnetic fields to evaluate SEP spatial distribution in the heliosphere, their path lengths, and the overall evolution of SEP intensities at 1 au. Methods. We use full-orbit test particle simulations of 100-MeV protons in a novel analytic model of the turbulent heliospheric magnetic field, where the turbulence is dominated by modes that are transverse and 2D with respect to the Parker spiral direction. Results. We find that by propagating along meandering field lines, SEPs reach a 60°-wide heliolongitudinal range at 1 au within an hour of their injection for the turbulence parameters considered. The SEP onset times are asymmetric with respect to the location connected to the source along the Parker spiral, with the earliest arrival times being 15° westwards from the well-connected Parker spiral longitude. The inferred path length of the first arriving particles is 1.5−1.8 au within 30° of the well-connected longitude; 20−30% longer than the length of the random-walking field lines, increasing monotonously at longitudes further away; and 30−50% longer than the Parker spiral. The global maximum intensity is reached 15° west from the well-connected longitude an hour after the SEP injection. Subsequently, the SEP distribution broadens, consistent with diffusive spreading of SEPs across the field lines. Conclusions. Our results indicate that magnetic field line meandering can explain rapid access of SEPs to wide longitudinal ranges, as well as several other features of SEP event intensity evolution.

Simulation of the Solar Energetic Particle Event on 2020 May 29 Observed by Parker Solar Probe

This paper presents a stochastic three-dimensional focused transport simulation of solar energetic particles (SEPs) produced by a data-driven coronal mass ejection (CME) shock propagating through a data-driven model of coronal and heliospheric magnetic fields. The injection of SEPs at the CME shock is treated using diffusive shock acceleration of post-shock suprathermal solar wind ions. A time-backward stochastic simulation is employed to solve the transport equation to obtain the SEP time–intensity profile at any location, energy, and pitch angle. The model is applied to a SEP event on 2020 May 29, observed by STEREO-A close to ∼1 au and by Parker Solar Probe (PSP) when it was about 0.33 au away from the Sun. The SEP event was associated with a very slow CME with a plane-of-sky speed of 337 km s−1 at a height below 6 R S as reported in the SOHO/LASCO CME catalog. We compute the time profiles of particle flux at PSP and STEREO-A locations, and estimate both the spectral index of the proton energy spectrum for energies between ∼2 and 16 MeV and the equivalent path length of the magnetic field lines experienced by the first arriving SEPs. We find that the simulation results are well correlated with observations. The SEP event could be explained by the acceleration of particles by a weak CME shock in the low solar corona that is not magnetically connected to the observers.

An Analytical Model of Turbulence in Parker Spiral Geometry and Associated Magnetic Field Line Lengths

Understanding the magnetic connections from the Sun to interplanetary space is crucial for linking in situ particle observations with the solar source regions of the particles. A simple connection along the large-scale Parker spiral magnetic field is made complex by the turbulent random walk of field lines. In this paper, we present the first analytical model of heliospheric magnetic fields where the dominant 2D component of the turbulence is transverse to the Parker spiral. The 2D wave field is supplemented with a minor wave field component that has asymptotic slab geometry at small and large heliocentric distances. We show that turbulence spreads field lines from a small source region at the Sun to a 60° heliolongitudinal and heliolatitudinal range at 1 au, with a standard deviation of the angular spread of the field lines of 14°. Small source regions map to an intermittent range of longitudes and latitudes at 1 au, consistent with dropouts in solar energetic particle intensities. The lengths of the field lines are significantly extended from the nominal Parker spiral length of 1.17 au up to 1.6 au, with field lines from sources at and behind the west limb considerably longer than those closer to the solar disk center. We discuss the implications of our findings for understanding charged particle propagation and the importance of understanding the turbulence properties close to the Sun.

Standing Alfvén Waves Within Equatorial Plasma Bubbles

AbstractPlasma depletions in the disturbed equatorial ionosphere are known to be associated with magnetic fluctuations and Alfvén waves. Here, using data from the Swarm B satellite's vector field magnetometer and electric fields instrument at an altitude of ∼500 km, we present evidence of standing Alfvén modes trapped within strong density depletions. Fourier transforms of electric (δE) and magnetic (δB) perturbations reveal harmonic structure with anticorrelated peaks and relative phase shifts approaching ±90°, in agreement with a simple model of standing waves sampled from a moving spacecraft. The mode frequencies allow us to estimate the field‐aligned length of the bubbles, which we find to be in the range of 110–200 km. This value is much smaller than the overall field line length mapped to the two E‐region footprints, indicating that the waves we observe do not couple to the lower ionosphere.

Magnetic reconnection and the Kelvin-Helmholtz instability in the solar corona

Context. The magnetic Kelvin-Helmholtz instability (KHI) has been proposed as a means of generating magnetohydrodynamic turbulence and encouraging wave energy dissipation in the solar corona, particularly within transversely oscillating loops. Aims. Our goal is to determine whether the KHI encourages magnetic reconnection in oscillating flux tubes in the solar corona. This will establish whether the instability enhances the dissipation rate of energy stored in the magnetic field. Methods. We conducted a series of three-dimensional magnetohydrodynamic simulations of the KHI excited by an oscillating velocity shear. We investigated the effects of numerical resolution, field line length, and background currents on the growth rate of the KHI and on the subsequent rate of magnetic reconnection. Results. The KHI is able to trigger magnetic reconnection in all cases, with the highest rates occurring during the initial growth phase. Reconnection is found to occur preferentially along the boundaries of Kelvin-Helmholtz vortices, where the shear in the velocity and magnetic fields is greatest. The estimated rate of reconnection is found to be lowest in simulations where the KHI growth rate is reduced. For example, this is the case for shorter field lines or due to shear in the background field. Conclusions. In non-ideal regimes, the onset of the instability causes the local reconnection of magnetic field lines and enhances the rate of coronal wave heating. However, we found that if the equilibrium magnetic field is sheared across the Kelvin-Helmholtz mixing layer, the instability does not significantly enhance the rate of reconnection of the background field, despite the free energy associated with the non-potential field.

Magnetic field line random walk and solar energetic particle path lengths

Context. In 2020 May-June, six solar energetic ion events were observed by the Parker Solar Probe/IS⊙IS instrument suite at ≈0.35 AU from the Sun. From standard velocity-dispersion analysis, the apparent ion path length is ≈0.625 AU at the onset of each event. Aims. We develop a formalism for estimating the path length of random-walking magnetic field lines to explain why the apparent ion path length at an event onset greatly exceeds the radial distance from the Sun for these events. Methods. We developed analytical estimates of the average increase in path length of random-walking magnetic field lines, relative to the unperturbed mean field. Monte Carlo simulations of field line and particle trajectories in a model of solar wind turbulence were used to validate the formalism and study the path lengths of particle guiding-center and full-orbital trajectories. The formalism was implemented in a global solar wind model, and the results are compared with ion path lengths inferred from IS⊙IS observations. Results. Both a simple estimate and a rigorous theoretical formulation are obtained for field-lines’ path length increase as a function of path length along the large-scale field. From simulated field line and particle trajectories, we find that particle guiding centers can have path lengths somewhat shorter than the average field line path length, while particle orbits can have substantially longer path lengths due to their gyromotion with a nonzero effective pitch angle. Conclusions. The long apparent path length during these solar energetic ion events can be explained by (1) a magnetic field line path length increase due to the field line random walk and (2) particle transport about the guiding center with a nonzero effective pitch angle due to pitch angle scattering. Our formalism for computing the magnetic field line path length, accounting for turbulent fluctuations, may be useful for application to solar particle transport in general.

Gravitational instability of solar prominence threads

Context. Prominence threads are dense and cold structures lying on curved magnetic fields that can be suspended in the solar atmosphere against gravity. Aims. The gravitational stability of threads, in the absence of non-ideal effects, is comprehensively investigated in the present work by means of an elementary but effective model. Methods. Based on purely hydrodynamic equations in one spatial dimension and applying line-tying conditions at the footpoints of the magnetic field lines, we derive analytical expressions for the different feasible equilibria (se) and the corresponding frequencies of oscillation (ω). Results. We find that the system allows for stable and unstable equilibrium solutions subject to the initial position of the thread (s0), its density contrast (ρt) and length (lt), and the total length of the magnetic field lines (L). The transition between the two types of solutions is produced at specific bifurcation points that have been determined analytically in some particular cases. When the thread is initially at the top of the concave magnetic field, that is at the apex, we find a supercritical pitchfork bifurcation, while for a shifted initial thread position with respect to this point the symmetry is broken and the system is characterised by an S-shaped bifurcation. Conclusions. The plain results presented in this paper shed new light on the behaviour of threads in curved magnetic fields under the presence of gravity and help to interpret more complex numerical magnetohydrodynamics simulations about similar structures.

A Simple Analytical Model of Static Eccentricity for PM Brushless Motors and Validation through FEM Analysis

The paper firstly summarizes a simple analytical model of the air gap flux-density distribution for isotropic permanent magnet (PM) synchronous machines, in the presence of static eccentricity. The model was proposed by the authors in a previous paper and is based on an efficacious analytical expression of the variable length of air gap magnetic field lines which occur in eccentric brushless machines with surface-mounted permanent magnets. The approximate expression of the air gap field makes it possible to achieve a mathematical model with concentrated parameters close to that of a PM machine without eccentricity. The expression of the armature voltages and electromagnetic torque are found, also with reference to steady-state operating conditions at fixed rotor speed and impressed currents. The differences introduced by the considered type of eccentricity are evaluated and highlighted especially with reference to the air gap inductance and to waveforms and frequency spectra of voltages and shaft torque. Numerical results in a case-study of an 8-pole, 110 kW PM motor are compared to those obtained by using finite element analysis.

Torsional Alfvénic Oscillations Discovered in the Magnetic Free Energy during Solar Flares

Abstract We report the discovery of torsional Alfvénic oscillations in solar flares, which modulate the time evolution of the magnetic free energy E f (t), while the magnetic potential energy E p (t) is uncorrelated, and the nonpotential energy varies as E np (t) = E p + E f (t). The mean observed time period of the torsional oscillations is P obs = 15.1 ± 3.9 minutes, the mean field line length is L = 135 ± 35 Mm, and the mean phase speed is v phase = 315 ± 120 km s−1, which we interpret as torsional Alfvénic waves in flare loops with enhanced electron densities. Most of the torsional oscillations are found to be decay-less, but exhibit a positive or negative trend in the evolution of the free energy, indicating new emerging flux (if positive), magnetic cancellation, or flare energy dissipation (if negative). The time evolution of the free energy has been calculated in this study with the Vertical-current Approximation (Version 4) Non-linear Force-free Field code, which incorporates automatically detected coronal loops in the solution and bypasses the non-force-freeness of the photospheric boundary condition, in contrast to traditional NLFFF codes.

Theoretical study of pre-ionization by inductive field in tokamaks

A one-dimensional fluid model is developed for a numerical study of pre-ionization in a tokamak device under a given external inductive field. The calculation space is a magnetic field line connecting the bottom and the top limiters, and the spatial profiles of ion and electron densities and their time evolutions are calculated, assuming density growth by the Townsend avalanche. It was found that at a low initial density, electrons are evacuated and exponential growth can be stopped (i.e. stagnation phase), and at a high density, formation of an ambipolar diffusion state may suppress further avalanche by compensating the external inductive field. The numerical study revealed that these two obstacles for pre-ionization can be avoided or mitigated under a certain condition. A high ion impact secondary electron emission efficiency at the limiter, a long field line length and a large Townsend’s coefficient are preferable to avoid the stagnation phase or to resume growth from the stagnation phase. The ambipolar diffusion state can be mitigated or avoided using the following four mechanisms: drift induced diffusion, and curvature drifts, a high ion impact secondary electron emission efficiency and AC inductive field. Among them, only the first is practically useful in weak inductive field large devices. Various analytical expressions describing these behaviors and the conditions for a successful pre-ionization are obtained.

Analysis of peak heat load on the blanket module for JA DEMO

Plasma heat flux in the peripheral plasma reaches the first wall (FW) along a magnetic field line, and it sometimes causes several MW/m2 orders of magnitude high heat flux concentration at narrow region, such as the edge of the blanket module. Thus, to assess and to reduce the heat load is key issue in the DEMO design activity. In this research, a new heat load analysis code is introduced based on the e-folding model. In this code, the decay length λ is changed depending on wall connection length of magnetic field line (defined as the length of magnetic field line from the wall to the wall), and parallel heat flux q// is calculated in each flux tube. This code can calculate the FW heat load simulating actual blanket module shapes. The 0.23 MW/m2 peak heat load at inner midplane in the case of the ideal FW (without gaps between blanket modules) is increased to 22 MW/m2 at toroidal module edge in the case of box shaped module. To shadow the edge and reduce such peak heat load, toroidal, and poloidal roof shaping is applied. Required roof height is analyzed from this code calculation. After shaping, peak heat load is reduced to 1.2 MW/m2. This value is under the allowable value 1.5 MW/m2, and in this case, surface temperature is also less than allowable temperature.

Helically self-organized pinches: dynamical regimes and magnetic chaos healing

This paper deals with helical self-organization in current-carrying toroidal pinches for the magnetic confinement of fusion plasmas. We perform our study in the framework of 3D nonlinear visco-resistive magnetofluid modelling, where a large set of simulations is now available. A global picture is derived about how visco-resistive transport coefficients and magnetic boundary conditions rule the self-organized helical states for the reversed-field pinch configuration. Decreasing visco-resistive dissipation causes a transition from steady ohmic helical equilibria to intermittent states (sawtoothing activity), while selected helical magnetic perturbations applied at the boundary favor steady global quasi-helical solutions. The sawtoothing frequency decreases together with visco-resistive dissipation, while sawtoothing amplitude decreases when applying non-resonant magnetic perturbations. Simulations of the tokamak configuration allow us to draw a tight parallelism with reversed-field pinches: a similar role of dissipation and magnetic boundary conditions on the dynamics of the internal kink mode is found, with decreasing sawtoothing frequency and amplitude by decreasing dissipation and by applying suitable helical boundary conditions. Magnetic chaos healing is the topological feature of the transition from intermittent to quasi-quiescent helical states in reversed-field pinches. Bundles of Lagrangian coherent structures (LCS) in the weakly stochastic region surrounding the helical core constitute the skeleton of chaos healing, and behave as barriers to the transport of magnetic field lines. In this work, they are detected during the whole temporal evolution and it is proved that they can withstand the nonlinear dynamics even during sawtoothing activity. Furthermore, we show that LCS are connected to regions with strong gradients of the connection length of magnetic field lines to the edge. This provides a further indication of their possible role in the formation of electron temperature barriers. As a final result it is shown that a reasonable value of plasma rotation can further enhance the intensity of the dominant helical mode.

Magnetohydrodynamic waves in braided magnetic fields

Aims. We investigate the propagation of transverse magnetohydrodynamic (MHD) wave fronts through a coronal plasma containing a braided magnetic field. Methods. We performed a series of three dimensional MHD simulations in which a small amplitude, transverse velocity perturbation is introduced into a complex magnetic field. We analysed the deformation of the wave fronts as the perturbation propagates through the braided magnetic structures and explore the nature of Alfvénic wave phase mixing in this regime. We considered the effects of viscous dissipation in a weakly non-ideal plasma and evaluate the effects of field complexity on wave energy dissipation. Results. Spatial gradients in the local Alfvén speed and variations in the length of magnetic field lines ensure that small scales form throughout the propagating wave front due to phase mixing. Additionally, the presence of complex, intricate current sheets associated with the background field locally modifies the polarisation of the wave front. The combination of these two effects enhances the rate of viscous dissipation, particularly in more complex field configurations. Unlike in classical phase mixing configurations, the greater spatial extent of Alfvén speed gradients ensures that wave energy is deposited over a larger cross-section of the magnetic structure. Further, the complexity of the background magnetic field ensures that small gradients in a wave driver can map to large gradients within the coronal plasma. Conclusions. The phase mixing of transverse MHD waves in a complex magnetic field will progress throughout the braided volume. As a result, in a non-ideal regime wave energy will be dissipated over a greater cross-section than in classical phase mixing models. The formation rate of small spatial scales in a propagating wave front is a function of the complexity of the background magnetic field. As such, if the coronal field is sufficiently complex it remains plausible that phase mixing induced wave heating can contribute to maintaining the observed temperatures. Furthermore, the weak compressibility of the transverse wave and the observed phase mixing pattern may provide seismological information about the nature of the background plasma.

Impact of the Space Charge Distribution in the Model Source of Quasi-Electrostatic Whistler-Mode Waves on the Effective Length of a Short Receiving Antenna

In our previous paper [1] it was shown, using the theory of antennas in plasmas, that the effective length leff of a receiving dipole antenna can be much larger than its geometric length in case quasielectrostatic chorus emissions propagating close to the resonance cone are received. In order to simplify calculations of leff, it was proposed to use a model (“effective”) source of such emissions because taking into account all of the real source properties (that are determined by the nonlinear processes of interaction between waves and charged particles in a wide region of space) would lead to unreasonably cumbersome calculations. The present paper analyzes how the effective length of the spacecraft-borne receiving antenna depends on the parameters of the space charge distribution in the model source of quasi-electrostatic chorus emissions. It is found that the length leff decreases as a power function (with exponent −1/2) with increasing distance (along the group velocity resonance cone) between the model source and the receiving antenna. This relationship is correct up to the distance at which the effective length becomes of the order of the geometric length. At longer distances, the radiation field loses its resonance nature because of the excitation of an electromagnetic (quasi-longitudinal) wave. It is shown that under conditions of the Earth’s magnetosphere, the approximation we used can remain valid up to distances of the order of the geomagnetic field line length, which confirms the importance of the discussed effect for correct interpretation of the electric wave measurement data in the whistler-mode frequency range. It is also shown that the length leff changes by less than 10% when the characteristic scale of spectrum of the charge distribution along the model source varies as Δ ∼ (0.1–1.0) kobs, where the wave number kobs corresponds to the observed spectral maximum of radiation at a given frequency.

Standing Alfvén Waves in Jupiter's Magnetosphere as a Source of ∼10‐ to 60‐Min Quasiperiodic Pulsations

AbstractEnergy transport inside the giant magnetosphere at Jupiter is poorly understood. Since the Pioneer era, mysterious quasiperiodic (QP) pulsations have been reported. Early publications successfully modeled case studies of ∼60‐min (rest‐frame) pulsations as standing Alfvén waves. Since then, the range of periods has increased to ∼10–60 min, spanning multiple data sets. More work is required to assess whether a common QP modulation mechanism is capable of explaining the full range of wave periods. Here we have modeled standing Alfvén waves to compute the natural periods of the Jovian magnetosphere, for varying plasma sheet thicknesses, field line lengths, and Alfvén speeds. We show that variability in the plasma sheet produces eigenperiods that are consistent with all the reported observations. At least the first half‐dozen harmonics (excluding the fundamental) may contribute but are indistinguishable in our analysis. We suggest that all QP pulsations reported at Jupiter may be explained by standing Alfvén waves.