Curvature Of Magnetic Field Lines Research Articles

Magnetic field dragging in filamentary molecular clouds

Maps of polarized dust emission of molecular clouds reveal the morphology of the magnetic field associated with star-forming regions. In particular, polarization maps of hub-filament systems show the distortion of magnetic field lines induced by gas flows onto and inside filaments. We aim to understand the relation between the curvature of magnetic field lines associated with filaments in hub-filament systems and the properties of the underlying gas flows. We consider steady-state models of gas with finite electrical resistivity flowing across a transverse magnetic field. We derive the relation between the bending of the field lines and the flow parameters represented by the Alfv\'en Mach number and the magnetic Reynolds number. We find that, on the scale of the filaments, the relevant parameter for a gas of finite electrical resistivity is the magnetic Reynolds number, and we derive the relation between the deflection angle of the field from the initial direction (assumed perpendicular to the filament) and the value of the electrical resistivity, due to either Ohmic dissipation or ambipolar diffusion. Application of this model to specific observations of polarized dust emission in filamentary clouds shows that magnetic Reynolds numbers of a few tens are required to reproduce the data. Despite significant uncertainties in the observations (the flow speed, the geometry and orientation of the filament), and the idealization of the model, the specific cases considered show that ambipolar diffusion can provide the resistivity needed to maintain a steady state flow across magnetic fields of significant strength over realistic time scales.

A Survey of Magnetic Field Line Curvature in Jovian Dawn Magnetodisc

AbstractThe Jovian magnetosphere is highly dynamic, influenced by both solar wind and internal processes associated with the rapid planetary rotation and Io's volcanic activities. Accompanying the mass and energy circulations driven by the magnetospheric dynamics, the magnetic configuration also changes dramatically. One of the crucial parameters to characterize the magnetic configuration is magnetic field line curvature (FLC), which generally describes how stretched the field line is. The curvature is pivotal to influence particle behaviors, for example, pitch angle scattering which may lead to auroral particle precipitation. In this work, a method is proposed to investigate the real‐time magnetic FLC in Jovian current sheet using the magnetic field data from the Juno spacecraft. The results indicate that the FLC scattering of ions and relativistic electrons are common in Jovian magnetosphere, providing a crucial insight to understand the particle behaviors.

Quantum mechanical calculations of synchro-curvature radiations: maser possibility

Abstract We calculate the radiative transition rates for synchro-curvature radiation to explore the possibility of maser in the environment that may occur in the magnetosphere of neutron stars (NSs). Unlike previous studies, we employ relativistic quantum mechanics, solving the Dirac equation for an electron in helical magnetic fields. Following Voisin et al. [1,2], we utilize adiabatic spinor rotations, under the assumption that the curvature of magnetic-field lines is much larger than the Larmor radius, to obtain the wave functions of an electron. We classify the electron states either by the spin operator projected on the magnetic field or by the helicity operator. To demonstrate that there is a regime where the true absorption rate becomes negative, we numerically evaluate the obtained formulae for some parameter values that may be encountered in the outer gaps of different types of NSs. We show that there is indeed a range of parameters for the negative true absorption rate to occur. We will also study the dependence on those parameters systematically and discuss the classical limit of our formulae. We finally give a crude estimate of the amplification factor in the same environment.

The Influence of the Magnetic Field Line Curvature on Wall Erosion near the Hall Thruster Exit Plane

One of the main factors that limit the lifetime of the Hall effect Thrusters (HETs) is the erosion of the acceleration channel caused by the flux of energetic ions. The magnetic field that is curved and convex towards the anode has been widely used in HETs because of its role in reducing the divergence angle of the ion beam and the channel wall erosion. However, the mechanism of the influence of the magnetic field line curvature on the wall erosion is not clear. Therefore, in this paper, a 2D3V numerical model based on the immersed-finite-element and particle-in-cell (IFE-PIC) method is established to simulate the radial-azimuthal plane near the exit of the Hall thruster. The effect of the tilt angle of the magnetic field line on the wall sputtering erosion rate is analyzed. The results show that compared to the case with the electric field E perpendicular to the magnetic field B, the energy of the ions hitting the channel wall is smaller and the wall erosion is weaker when the magnetic field lines are convex to the anode. As the tilt angle of the magnetic field lines increases from 0° to 60°, the erosion rate is reduced by 90%. Conversely, when the magnetic field lines are convex to the exit plane of the channel, the wall erosion is much more serious compared to the case with the orthogonal electric field E and the magnetic field B. As the tilt angle of the magnetic field line changes from 0° to 60°, the erosion rate is enhanced by 171%. The results in this paper are instructive for the design and optimization of the magnetic field of the HETs.

Proton loss of inner radiation belt during geomagnetic storm of 2018 based on CSES satellite observation* *Project supported by the Research Fund from the National Institute of Natural Hazards, Ministry of Emergency Management of China (Grant No. 2021-JBKY- 11), the National Natural Science Foundation of China (Grant Nos. 41904149 and 12173038), and the Stable Support Projects of Basic Scientific Research

The proton distribution in inner radiation belt is often affected by strong geomagnetic storm disturbance. Based on the data of the sun-synchronous CSES satellite, which carries with several high energy particle payloads and was launched in February 2018, we analyzed the extensive proton variations in the inner radiation belt in a wide energy range of 2 MeV– 220 MeV during 2018 major geomagnetic storm. The result indicates that the loss mechanism of protons was energy dependence which is consistent with some previous studies. For protons at low energy 2 MeV–20 MeV, the fluxes were decreased during main phase of the storm and did not come back quickly during the recovery phase, which is likely to be caused by Coulomb collision due to neutral atmosphere density variation. At higher energy 30 MeV–100 MeV, it was confirmed that the magnetic field line curvature scattering plays a significant role in the proton loss phenomenon during this storm. At highest energies > 100 MeV, the fluxes of protons kept a stable level and did not exhibit a significant loss during this storm.

Fitting an Analytic Magnetic Field to a Prestellar Core

Abstract We deploy and demonstrate the capabilities of the magnetic field model developed by Ewertowski & Basu by fitting observed polarimetry data of the prestellar core FeSt 1–457. The analytic hourglass magnetic field function derived directly from Maxwell’s equations yields a central-to-surface magnetic field strength ratio in the equatorial plane, as well as magnetic field directions with relative magnitudes throughout the core. This fit emerges from a comparison of a single plane of the model with the polarization map that results from the integrated properties of the magnetic field and dust throughout the core. Importantly, our fit is independent of any assumed density profile of the core. We check the robustness of the fit by using the POLARIS code to create synthetic polarization maps that result from the integrated scattering and emission properties of the dust grains and their radiative transfer, employing an observationally motivated density profile. We find that the synthetic polarization maps obtained from the model also provide a good fit to the observed polarimetry. Our model fits the striking feature of significant curvature of magnetic field lines in the outer part of FeSt 1–457. Combined with independent column density estimates, we infer that the core of size R gas has a mildly supercritical mass-to-flux ratio and may have formed through dynamical motions starting from a significantly larger radius R. A breakdown of flux freezing through neutral-ion slip (ambipolar diffusion) could be responsible for effecting such a transition from a large-scale magnetic field structure to a more compact gas structure.

Multi-case Study of Current Sheet Flapping Motions Induced by Non-adiabatic Ions

In this paper, the <i>y</i>-component of magnetic field line curvature in the plasma sheet was analyzed, and two kinds of shear structures of the flapping current sheet were found, <i>i.e</i>. symmetric and antisymmetric. The alternating bending orientations of the guiding field are exactly corresponding to alternating north-south asymmetries of the bouncing ion population in the sheet center. Those alternating asymmetric plasma sources consequently induce the current sheet flapping motion as a driver. In addition, a substantial particle population with downward motion was observed in the center of a bifurcated current sheet. This population is identified as the quasi-adiabatic particles, and provides a net current opposite to the conventional cross-tail current.

Quantifying the Effect of Magnetic Field Line Curvature Scattering on the Loss of Ring Current Ions

AbstractDuring geomagnetic storms, the ring current ions sometimes exhibit rapid loss as suggested by the fast recovery of the Dst index on a time scale of a few hours. The effects of magnetic field line curvature (FLC) scattering on the loss of ring current ions, which have not been well quantified, are studied here by test particle simulations under the T89c magnetic field model. Our simulation results show that the prediction of ion loss based on a single‐value cutoff of the κ parameter or maximum of of a single FLC scattering is not accurate. Instead, the e‐folding lifetime (τ) for the loss of ring current ions due to cumulative FLC scattering has been calculated for different initial ion energies, equatorial pitch angles, and L shells under different geomagnetic conditions. The results show that in general the FLC scattering loss is faster for ions of higher energy, higher mass, smaller pitch angle, higher L, and at high Kp level. Specifically, we find that at Kp = 6 the lifetime can be &lt;10 h at L &gt; 5 for 100 s keV protons and at L &gt; 4 for 100 s keV O+, which demonstrates that FLC scattering can be an important mechanism for the observed fast loss (τ &lt; 10 h) of ring current ions during geomagnetic storms. Furthermore, we formulate an empirical formula for τ as a function of ion energy, pitch angle, position, species, and Kp. The empirical formula can be directly included in ring current models to account for the FLC scattering effects.

A Fusion Reactor Scheme Using Magnetic Mirrors

The paper describes a fusion reactor scheme consisting of two 200-m-long magnetic mirrors with a ratio of two connected by semicircular sections to form a racetrack configuration. The two most serious problems of magnetic mirrors, magnetohydrodynamic stability and end losses, are solved by minimizing the negative curvature of the mirror magnetic field lines and using helical windings in the curved sections to add a positive curvature and strong shear to the magnetic field lines at and beyond the mirror throat and for confining the mirror end losses. The reactor should be capable of producing at least 13 GW of fusion power when operating in deuterium-tritium at the same plasma density and temperature as ITER.

Observations of Magnetic Field Line Curvature and Its Role in the Space Plasma Turbulence

Abstract Recent numerical simulations of plasma turbulence showed that magnetic field line curvature plays a key role in particle energization. Based on in situ high-resolution data provided by the four Magnetospheric Multiscale spacecraft, we investigate the magnetic field line curvature and its role in the turbulent magnetosheath plasma. Our analysis reveals that the curvature exhibits two power-law distributions: the low curvature follows the scaling as κ 0.33, and the large curvature has a scaling as κ −2.16. The curvature is anticorrelated with the magnitude of the magnetic field, but positively related to the normal force, the drift electric current, and the curvature drift acceleration term, indicating that intense energy dissipation due to the curvature drift occurs in the large curvature region. One typical example shows a localized increase of electron temperature that coincides with a peak in the curvature and the curvature drift acceleration term, which supports the role of the latter in local energization of electrons, in agreement with simulation results. These observations allow us to better understand the connection between magnetic field line curvature, energy dissipation, and particle energization in space and astrophysical plasmas.

Curvature of Magnetic Field Lines in Compressible Magnetized Turbulence: Statistics, Magnetization Predictions, Gradient Curvature, Modes, and Self-gravitating Media

Abstract Magnetic field lines in interstellar media have a rich morphology, which could be characterized by geometrical parameters such as curvature and torsion. In this paper we explore the statistical properties of magnetic field line curvature κ in compressible magnetized turbulence. We see that both the mean and standard deviation of magnetic field line curvature obey power-law relations to the magnetization. Moreover, the power-law tail of the curvature probability distribution function is also proportional to the Alfvénic Mach number. We also explore whether the curvature method could be used in the field-tracing velocity gradient technique. In particular, we observe that there is a relation between the mean and standard deviation of the curvature probed by velocity gradients to M A . Finally, we discuss how curvature is contributed by different MHD modes in interstellar turbulence and suggests that the eigenvectors of MHD modes could be possibly represented by the natural Frenet–Serret frame of the magnetic field lines. We discuss possible theoretical and observational applications of the curvature technique, including the extended understanding on a special length scale that characterizes the importance of magnetic field curvature in driving MHD turbulence, and how it could be potentially used to study a self-gravitating system.

Electron dynamics near diamagnetic regions of comet 67P/Churyumov- Gerasimenko

The Rosetta spacecraft detected transient and sporadic diamagnetic regions around comet 67P/Churyumov-Gerasimenko. In this paper we present a statistical analysis of bulk and suprathermal electron dynamics, as well as a case study of suprathermal electron pitch angle distributions (PADs) near a diamagnetic region. Bulk electron densities are correlated with the local neutral density and we find a distinct enhancement in electron densities measured over the southern latitudes of the comet. Flux of suprathermal electrons with energies between tens of eV to a couple of hundred eV decreases each time the spacecraft enters a diamagnetic region. We propose a mechanism in which this reduction can be explained by solar wind electrons that are tied to the magnetic field and after having been transported adiabatically in a decaying magnetic field environment, have limited access to the diamagnetic regions. Our analysis shows that suprathermal electron PADs evolve from an almost isotropic outside the diamagnetic cavity to a field-aligned distribution near the boundary. Electron transport becomes chaotic and non-adiabatic when electron gyroradius becomes comparable to the size of the magnetic field line curvature, which determines the upper energy limit of the flux variation. This study is based on Rosetta observations at around 200 ​km cometocentric distance when the comet was at 1.24 AU from the Sun and during the southern summer cometary season.

Why do the microstructures of the main pulse and the interpulse of the pulsar in the Crab nebula differ so dramatically?

Pulsars are magnetized neutron stars. They are not resolved by modern radio telescopes and are studied only by radiation coming from the regions of the magnetic poles. Because of the rotation, this narrow radiation is received as pulses. In a few pulsars whose magnetic axis is almost orthogonal to the rotation axis (the simplest hypothesis), pulses are observed from both poles: the (main) pulse and the interpulse. Such objects primarily include a pulsar in the Crab nebula, observed at many frequencies of the electromagnetic spectrum. In the remarkable work of Hankins and Eilek, a striking difference between the spectra of the main pulse and the interpulse in the Crab nebula in the centimeter wavelength range at microsecond resolution was found (surprising the authors: “In traditional pulsar models... the MP and IP should be the same in their observable quantities (such as spectrum, time signature, or dispersion). We were—and remain—quite surprised that this turns out not to be the case in the Crab pulsar.” See T. H. Hankins and J. A. Eilek, “Radio emission signatures in the Crab pulsar,” Astrophys. J., 670:693–701, 2007). In particular, a wide range of frequencies was observed in the spectra of the main pulse forming “vertical structures,” while “horizontal structures” with distinguished frequencies were observed in the spectra of the interpulse at the same frequencies. Such a difference, related to different radiation mechanisms (nonrelativistic electron emission in a longitudinal accelerating field for the main pulse and relativistic positron radiation due to the curvature of magnetic field lines for the interpulse), is explained by the change from the nonrelativistic to the relativistic mechanism as the frequency increases. Therefore, the frequencies at which the mechanism changes differ for the main pulse and the interpulse. The frequency of observation in the work of Hankins and Eilek is just between these frequencies with which the difference in the microstructure is connected.

Low-Frequency Continuous MHD Spectrum of Toroidally Rotating Tokamak Plasmas with Anisotropic Pressure

Continuous-spectrum equations for low-frequency ideal magnetohydrodynamic perturbations in toroidally rotating plasmas with anisotropic pressure in axisymmetric tokamaks are derived in the framework of the Chew–Goldberger–Low model. In the rotating coordinate system, these equations describe the toroidal coupling of Alfven and slow magnetosonic modes due to the curvature of magnetic field lines, the pressure anisotropy, and the centrifugal and Coriolis effects. The derived general equations are applied to study the spectra of both the zonal flows and the general electromagnetic modes in low-pressure large-aspect-ratio tokamaks. The condition for the instability of zonal flows due to plasma stratification over the poloidal angle on a magnetic surface is obtained. It is shown that a similar instability takes place for the general modes localized in the vicinities of rational magnetic surfaces. Stabilization of this instability by the Alfven effect for the modes localized far from rational surfaces is shown.

Stellarator microinstabilities and turbulence at low magnetic shear

Gyrokinetic simulations of drift waves in low-magnetic-shear stellarators reveal that simulation domains comprised of multiple turns can be required to properly resolve critical mode structures important in saturation dynamics. Marginally stable eigenmodes important in saturation of ion temperature gradient modes and trapped electron modes in the Helically Symmetric Experiment (HSX) stellarator are observed to have two scales, with the envelope scale determined by the properties of the local magnetic shear and an inner scale determined by the interplay between the local shear and magnetic field-line curvature. Properly resolving these modes removes spurious growth rates that arise for extended modes in zero-magnetic-shear approximations, enabling use of a zero-magnetic-shear technique with smaller simulation domains and attendant cost savings. Analysis of subdominant modes in trapped electron mode (TEM)-driven turbulence reveals that the extended marginally stable modes play an important role in the nonlinear dynamics, and suggests that the properties induced by low magnetic shear may be exploited to provide another route for turbulence saturation.

Stellarator nonlinearly saturated periodicity-breaking ideal magnetohydrodynamic equilibrium states

The relaxation of the constraint of periodicity imposed by the external confining magnetic field coils in a nominally 4-field period Helias advanced stellarator configuration produces weak periodicity-breaking deformations of the plasma. The corrugations are driven by the interaction of the pressure gradient with the magnetic field line curvature and correspond to saturated ideal magnetohydrodynamic interchanges with a mode structure dominated by nonresonant Fourier components. The conditions of quasi-isodynamicity of the Helias reactor system investigated are not significantly altered by the periodicity-breaking distortions.

Formation of 30 KeV Proton Isotropic Boundaries During Geomagnetic Storms

AbstractWe study the origin of the 30 keV proton isotropic boundary (IB) in the nightside auroral zone during geomagnetic storms, particularly, to address the recent results that the adiabaticity parameter K (ratio of the magnetic field line curvature radius to the particle gyroradius at the equator) on the IB field line can be much larger comparing to its theoretical estimate K ∼ 8 for the field line curvature (FLC) scattering mechanism. During nine storms in 2011–2013, we investigate ∼2,000 IBs observed by low‐altitude Polar Operational Environmental Satellites (POES) satellites and apply the TS05 magnetospheric model to estimate the K value in the equatorial part of the IB field line. The statistical distribution of the estimated K parameter, while being rather broad, is centered on K = 9–13. For smaller subset of ∼250 IBs, the concurrent magnetic field measurements on board Time History of Events and Macroscale Interaction During Substorms probes in the equatorial magnetotail were used to correct the estimated K‐values accounting for the TS05 deviations from the real magnetic configuration. After correction, the K distribution becomes narrower, being still centered on K = 9–12. Different estimates give percentages of events with K &lt; 13, which can be attributed to IBs formed by FLC scattering, between 60% and 80%. Finally, we have not found any dependence of the K distribution on magnetic local time and IB latitude, except for events with IB located at extremely low latitudes (&lt;59°). These findings imply that the FLC scattering is a dominant mechanism of IB formation operating in a variety of magnetospheric conditions.

Formation of Dawn‐Dusk Asymmetry in Earth's Magnetotail Thin Current Sheet: A Three‐Dimensional Particle‐In‐Cell Simulation

AbstractUsing a three‐dimensional particle‐in‐cell simulation, we investigate the formation of dawn‐dusk asymmetry in Earth's magnetotail. The magnetotail current sheet is compressed by an external driving electric field down to a thickness on the order of ion kinetic scales. In the resultant thin current sheet (TCS) where the magnetic field line curvature radius is much smaller than ion gyroradius, a significant portion of the ions becomes unmagnetized and decoupled from the magnetized electrons, giving rise to a Hall electric field Ez and an additional cross‐tail current jy caused by the unmagnetized ions being unable to comove with the electrons in the Hall electric field. The Hall electric field transports via E × B drift magnetic flux and magnetized plasma dawnward, causing a reduction of the current sheet thickness and the normal magnetic field Bz on the duskside. This leads to an even stronger Hall effect (stronger jy and Ez) in the duskside TCS. Thus, due to the internal kinetic effects in the TCS, namely, the Hall effect and the associated dawnward E × B drift, the magnetotail dawn‐dusk asymmetry forms in a short time without any global, long‐term effects. The duskside preference of reconnection and associated dynamic phenomena (such as substorm onsets, dipolarizing flux bundles, fast flows, energetic particle injections, and flux ropes), which has been pervasively observed by spacecraft in the past 20 years, can thus be explained as a consequence of this TCS asymmetry.

On the Origin of the Bi-drifting Subpulse Phenomenon in Pulsars

Abstract The unique and highly unusual drift feature reported for PSR J0815+0939, wherein one component’s subpulses drift in the direction opposite of the general trend, is a veritable challenge to pulsar theory. In this paper, we observationally quantify the drift direction throughout its profile, and find that the second component is the only one that exhibits “bi-drifting,” meaning that only the second component moves in the direction opposite of the others. We present a model that shows that the observed bi-drifting phenomenon follows from the insight that the discharging regions, i.e., sparks, do not rotate around the magnetic axis per se, but rather around the point of maximum potential at the polar cap. We show that a purely dipolar surface magnetic field cannot exhibit bi-drifting behavior. though certain non-dipolar configurations can. We can distinguish two types of solutions, with relatively low ( ) and high ( ) surface magnetic fields. Depending on the strength of the surface magnetic field, the radius of the curvature of magnetic field lines ranges from to . Pulsar J0815+0939 allows us to gain an understanding of the polar-cap conditions essential for plasma generation processes in the inner acceleration region, by linking the observed subpulse shift to the underlying spark motion.

A model of energetic ion effects on pressure driven tearing modes in tokamaks

The effects that energetic trapped ions have on linear resistive magnetohydrodynamic (MHD) instabilities are studied in a reduced model that captures the essential physics driving or damping the modes through variations in the magnetic shear. The drift-kinetic orbital interaction of a slowing down distribution of trapped energetic ions with a resistive MHD instability is integrated to a scalar contribution to the perturbed pressure, and entered into an asymptotic matching formalism for the resistive MHD dispersion relation. Toroidal magnetic field line curvature is included to model trapping in the particle distribution, in an otherwise cylindrical model. The focus is on a configuration that is driven unstable to the m/n = 2/1 mode by increasing pressure, where m is the poloidal mode number and n is the toroidal. The particles and pressure can affect the mode both in the core region where there can be low and reversed shear and outside the resonant surface in significant positive shear. The results show that the energetic ions damp and stabilize the mode when orbiting in significant positive shear, increasing the marginal stability boundary. However, the inner core region contribution with low and reversed shear can drive the mode unstable. This effect of shear on the energetic ion pressure contribution is found to be consistent with the literature. These results explain the observation that the 2/1 mode was found to be damped and stabilized by energetic ions in δf-MHD simulations of tokamak experiments with positive shear throughout, while the 2/1 mode was found to be driven unstable in simulations of experiments with weakly reversed shear in the core. This is also found to be consistent with related experimental observations of the stability of the 2/1 mode changing significantly with core shear.