Field Line Curvature Research Articles

The Impact of the 8–10 March 2012 Geomagnetic Storm on Inner Zone Protons as Measured by Van Allen Probes

AbstractThe Relativistic Electron Proton Telescope (REPT) instrument on the Van Allen Probes observed a double‐peaked inner zone proton population throughout the 7 year lifetime of the mission. M. Hudson et al. (2023) showed that a strong SEP event accompanied by a CME‐shock in early March 2012 provided the Solar Energetic Proton (SEP) source for the higher L trapped proton population, which then diffused radially inward to be observed by REPT at . The study followed trajectories of SEP protons launched isotropically from a sphere at 7 Re for 2.5 hr in fields calculated by the LFM‐RCM global MHD model, which includes electric fields needed to model the transport and trapping of the protons by the shock, and then a radial diffusion simulation was run for 2 years using the result from the test‐particle simulation as the initial condition. The simulation result was compared with REPT measurement in November 2013 and showed reasonable agreement. However, the simulation overestimated the Phase Space Density by a factor of four due to lack of field line curvature scattering during the storm in the model. In this study, a test‐particle simulation is performed for 2 days following the injection and trapping of protons in March 2012 using TS05 fields to simulate the field line curvature scattering of the trapped SEP due to the buildup of the ring current during the geomagnetic storm. The resulting sample distribution was then weighted using the flux at the end of the two‐hour MHD‐test particle simulation. A radial diffusion simulation is then run using the initial profile that included the loss effect, with improved comparison with REPT measurements after 2 years.

Magnetic field dragging in filamentary molecular clouds

Context. 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. Aims. 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. Methods. 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 Alfvén Mach number and the magnetic Reynolds number. Results. 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. Conclusions. 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.

Field Line Curvature (FLC) Scattering in the Dayside Off‐Equatorial Minima Regions

AbstractMagnetic field line curvature (FLC) scattering is an effective mechanism for collisionless particle scattering. In the terrestrial magnetosphere, the FLC scattering plays an essential role in shaping the outer boundary of protons radiation belt, the rapid decay of ring current, and the formation of proton isotropic boundary (IB). However, previous studies have yet to adequately investigate the influence of FLC scattering on charged particles in the Earth's dayside magnetosphere, particularly in the off‐equatorial magnetic minima regions. This study employs T89 magnetic field model to investigate the impacts of FLC scattering on ring current protons in the dayside magnetosphere, with a specific focus on the off‐equatorial minimum regions. We analyze the spatial distributions of single and dual magnetic minima regions, adiabatic parameter, and pitch angle diffusion coefficients due to FLC scattering as functions of Kp. The results show that the effects of FLC scattering are significant not only on the dusk and dawn sides but also in the off‐equatorial minima regions on the noon. Additionally, we investigate the role of dipole tilt angle in the hemispheric asymmetry of FLC scattering effects. The dipole tilt angle controls the overall displacement of the dayside magnetosphere, resulting in different FLC scattering effects in the two hemispheres. Our study holds significance for understanding the FLC scattering effects in the off‐equatorial region of Earth's dayside magnetosphere and for constructing a more accurate dynamic model of particles.

Towards synthetic magnetic turbulence with coherent structures

Synthetic turbulence is a relevant tool to study complex astrophysical and space plasma environments inaccessible by direct simulation. However, conventional models lack intermittent coherent structures, which are essential in realistic turbulence. We present a novel method featuring coherent structures, conditional structure function scaling and fieldline curvature statistics comparable to magnetohydrodynamic turbulence. Enhanced transport of charged particles is investigated as well. This method presents significant progress towards physically faithful synthetic turbulence.

Modeling Field Line Curvature Scattering Loss of 1–10 MeV Protons During Geomagnetic Storms

AbstractThe proton radiation belt contains high fluxes of adiabatically trapped protons varying in energy from ∼one to hundreds of megaelectron volts (MeV). At large radial distances, magnetospheric field lines become stretched on the nightside of Earth and exhibit a small radius of curvature RC near the equator. This leads protons to undergo field line curvature (FLC) scattering, whereby changes to the first adiabatic invariant accumulate as field strength becomes nonuniform across a gyroorbit. The outer boundary of the proton belt at a given energy corresponds to the range of magnetic L shell over which this transition to nonadiabatic motion takes place, and is sensitive to the occurrence of geomagnetic storms. In this work, we first find expressions for nightside equatorial RC and field strength Be as functions of Dst and L* to fit the TS04 field model. We then apply the Tu et al. (2014, https://doi.org/10.1002/2014ja019864) condition for nonadiabatic onset to solve the outer boundary L*, and refine our expression for RC to achieve agreement with Van Allen Probes observations of 1–50 MeV proton flux over the 2014–2018 era. Finally, we implement this nonadiabatic onset condition into the British Antarctic Survey proton belt model (BAS‐PRO) to solve the temporal evolution of proton fluxes at L ≤ 4. Compared with observations, BAS‐PRO reproduces storm losses due to FLC scattering, but there is a discrepancy in mid‐2017 that suggests a ∼5 MeV proton source not accounted for. Our work sheds light on outer zone proton belt variability at 1–10 MeV and demonstrates a useful tool for real‐time forecasting.

Experimental study of the effect of geodesic curvature on turbulent transport in magnetically confined plasma

An experimental study has demonstrated the impact of the geodesic curvature of the magnetic field line on turbulent ion-heat transport in magnetically confined plasma using the large helical device. Statistical analyses with corrected Akaike Information Criterion and multiple regression have revealed that the geodesic curvature indicates a dominant contribution to the ion-heat transport. Geodesic curvature dependence of the zonal-flow effect is evaluated by using a gyrokinetic-simulation-based reduced model. Then, the analysis implies a significant enhancement of the zonal-flow effect with a small geodesic curvature. These two independent analyses indicated the possibility of external zonal-flow control with the geodesic curvature of the magnetic field.

Modeling the Simultaneous Dropout of Energetic Electrons and Protons by Magnetopause Shadowing

AbstractMagnetopause shadowing (MPS) effect could drive a concurrent dropout of radiation belt electrons and ring current protons. However, its relative role in the dropout of both plasma populations has not been well quantified. In this work, we study the simultaneous dropout of MeV electrons and 100s keV protons during an intense geomagnetic storm in May 2017. A radial diffusion model with an event‐specific last closed drift shell is used to simulate the MPS loss of both populations. The model well captures the fast shadowing loss of both populations at L* > 4.6, while the loss at L* < 4.6, possibly due to the electromagnetic ion cyclotron wave scattering, is not captured. The observed butterfly pitch angle distributions of electron fluxes in the initial loss phase are well reproduced by the model. The initial proton losses at low pitch angles are underestimated, potentially also contributed by other mechanisms such as field line curvature scattering.

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.

Comparison of Ring Current Proton Losses Between Contributions From Scattering by Field Line Curvature and EMIC Waves

AbstractAlthough both the field line curvature (FLC) and electromagnetic ion cyclotron (EMIC) waves are recognized to contribute importantly to the loss of energetic protons in the Earth's ring current, their quantitative differences in scattering ring current protons are still not fully understood. In this study, using a realistic, nondipolar magnetic field model, we perform a detailed analysis of the scattering effects of ring current protons and the resultant proton lifetimes due to FLC and EMIC waves at different L‐shells under different levels of geomagnetic activity. We find that compared with EMIC wave‐driven scattering, FLC scattering has a stronger dependence on L‐shell and geomagnetic activity. Pitch angle scattering efficiency due to FLC enhances significantly as proton energy increases. In contrast, scattering by H+ band EMIC waves tends to be weaker with increasing proton energy, while the scattering rates by He+ band EMIC waves increase first and then decrease. The results of proton lifetime against pitch angle scattering show that EMIC wave‐driven scattering dominates the loss of ring current protons at lower L‐shells (L < 6), especially during geomagnetically quiet conditions. During geomagnetically active conditions at L ≥ 6, EMIC wave‐driven scattering dominates at lower proton energies, while FLC scattering dominates at higher proton energies. This study improves the current understanding of the relative contributions of scattering by FLC and EMIC waves to the Earth's ring current proton dynamics.

Dispersion and spatial structure of coupled Alfvén and slow magnetosonic modes in the dipole magnetosphere

Numerical analysis of the coupling between the Alfvén and slow azimuthally small scale modes in the dipolar model of the magnetosphere is performed. The field line curvature, inhomogeneity both across the magnetic shells and along the field lines, and finite plasma pressure are taken into account. The field line curvature causes coupling Alfvén and slow modes, while the contribution from the fast mode is neglected due to the assumed small scale of the oscillations in the azimuthal direction. The plasma pressure decreases with distance from the Earth, which is a characteristic for the ring current region. The wave's transverse dispersion, that is, dependence of the radial wave vector kr on the frequency ω, was studied. It was found that the wave can exist in two frequency ranges. Both ranges are bounded by resonant frequency on one side and the cutoff frequency on the other. The higher frequency range corresponds to the Alfvén mode. However, its properties are modified due to the coupling with the slow mode. For example, the divergence of the plasma displacement and the magnetic field compressional component appear. In the slow magnetosonic region, in contrast, the cutoff frequency is always smaller than the resonant one. If the pressure gradient is strong and negative, the slow mode cutoff frequency can disappear, that is, the radial wave vector squared even for the zero frequency. It means that the kr value goes to zero at imaginary frequency. Mode structure along the field line for different plasma pressure values and its pressure gradients was calculated.

Dispersion and spatial structure of the coupled Alfvén and slow magnetosonic oscillations in the Solar corona

Abstract Numerical and analytical analysis of the magnetohydrodynamic (MHD) waves in Solar coronal arcades is performed. A semi-cylinder slab model of arcade is used where the field lines are represented by half-circles intersecting the photosphere, the magnetic shells are represented by nested coaxial semi-cylinders. The finite plasma pressure is taken into account. The “corrugational”perturbations are considered, that is, the perturbations with short wavelength in the direction along the arcade. In this limit, there are two oscillation modes, the Alfvén and slow magnetosonic modes, coupled due to the field line curvature. The transverse dispersion of the modes, that is, the dependence of the radial wave vector’s component kr on the wave frequency ω, is considered. It was found that the wave is concentrated in two regions of mode’s existence, where $k_r^2>0$: the Alfvén and magnetosonic transparent regions. On one side, each of them is bounded by the resonance surface, where $k_r^2 \rightarrow \infty$. On the resonance surface, the wave’s frequency is determined by the Alfvén and slow magnetosonic modes dispersion relations, respectively. On the other side, the transparent regions are bounded by cut-off frequencies where $k_{r}^2 =0$. In both transparent regions, the perturbations have both transverse electric field (characteristic for the Alfvén mode) and field aligned velocity (characteristic for the slow mode). The wave structure along the field line for several models of plasma parameters is calculated.

Field‐Line Curvature Scattering at the Outer Boundary of the Proton Radiation Belt

AbstractA model balancing diffusive field‐line curvature (FLC) scattering loss with other local source, loss, and transport processes is used to compute the L‐shell location of the proton radiation belt outer boundary, where intensity falls below observable levels. The FLC scattering rate increases with increasing L and proton energy, decreasing equatorial pitch angle, and increasing geomagnetic activity, as determined with the Kp‐dependent T89 external magnetic field combined with a dipole internal field. Simulated proton intensity near the outer boundary is compared to measurements from both the low‐altitude SAMPEX satellite and the high‐altitude Van Allen Probes satellites, with correction for instrumental biases caused by field‐of‐view, energy range, and the east‐west effect. Good agreement between observations and simulations is obtained for average boundary locations, time‐dependent variations caused by magnetic storms, and average equatorial pitch‐angle distributions.

High-order coupling of shear and sonic continua in JET plasmas

A recent model coupling the shear-Alfvén and acoustic continua, which depends strongly on the equilibrium shaping and on elongation in particular, is employed to explain the properties of Alfvénic activity observed on JET plasmas below but close to the typical frequency of toroidicity-induced Alfvén eigenmodes (TAEs). The frequency gaps predicted by the model result from high-order harmonics of the geodesic field-line curvature caused by plasma shaping (as opposed to lower-order toroidicity) and give rise to high-order geodesic acoustic eigenmodes (HOGAEs), their frequency value being close to one-half of the TAEs one. The theoretical predictions of HOGAE frequency and radial location are found to be in fair agreement with measurements in JET experiments, including magnetic, reflectometry and soft x-ray data. The stability of the observed HOGAEs is evaluated with the linear hybrid magnetohydrodynamic/drift-kinetic code CASTOR-K, taking into account the energetic-ion populations produced by neutral beam injection and ion cyclotron resonance heating systems. Wave-particle resonances, along with drive/damping mechanisms, are also discussed in order to understand the conditions leading to HOGAEs destabilisation in JET plasmas.

Об определении понятия альфвеновской моды в неоднородном магнитном поле

The article is methodological and defines the concept of the linear Alfvén mode. There are two definitions — electrodynamic and hydrodynamic. In the former, the Alfvén mode is considered a wave with a potential transverse electric field. In the latter, waves are more often identified with the Alfvén mode, plasma motion in which is purely vortex. While these definitions are equivalent for homogeneous plasma, they are incompatible if the field line curvature is taken into account: if the transverse electric field is purely potential, the plasma speed has not only a vortex component, but also a potential one, and vice versa. The electrodynamic and hydrodynamic definitions are equivalent only if the wave electric field completely lacks a component along the binormal to the external magnetic field. However, such waves do not exist in nature.

Об определении понятия альфвеновской моды в неоднородном магнитном поле

The article is methodological and defines the concept of the linear Alfvén mode. There are two definitions — electrodynamic and hydrodynamic. In the former, the Alfvén mode is considered a wave with a potential transverse electric field. In the latter, waves are more often identified with the Alfvén mode, plasma motion in which is purely vortex. While these definitions are equivalent for homogeneous plasma, they are incompatible if the field line curvature is taken into account: if the transverse electric field is purely potential, the plasma speed has not only a vortex component, but also a potential one, and vice versa. The electrodynamic and hydrodynamic definitions are equivalent only if the wave electric field completely lacks a component along the binormal to the external magnetic field. However, such waves do not exist in nature.

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.

An Empirical Model of the Proton Isotropic Boundary (IB)

AbstractAt mid‐ and high‐latitudes, energetic protons of magnetospheric origin precipitate down to the upper atmosphere, manifested as one of the most important coupling processes between the ionosphere and magnetosphere. The equatorward boundary of the energetic proton precipitation, or called isotropic boundary (IB), is usually believed to coincide with the boundary in the magnetosphere where field line curvature scattering of protons transits from strong to weak. In this study, we statistically examine the global distribution of the IB for 39 and 115 keV ring current protons as detected by the NOAA/Polar Operational Environmental Satellites in 2013–2018 and propose an empirical model of the IB as a function of solar wind conditions, magnetic local time, and geomagnetic activity index. The IB is well ordered by SYM‐H index and interplanetary magnetic field Bz, moving to lower latitudes with more negative SYM‐H index and Bz values, and with larger AE index and solar wind pressure. Energy dispersions of the IB are also explored, consistent with the scenario of field curvature scattering in the magnetosphere. This empirical model can be used as an indirect measure of the strength of the magnetospheric stretching and may be applied in magnetosphere‐ionosphere mapping studies.

Rotational Discontinuities in the Magnetopause of an Open Magnetosphere

AbstractIn this paper, we analyze the fine structure of rotational discontinuities (RDs) in the magnetopause of an open magnetosphere using four‐point magnetic field measurements recorded by the Magnetospheric MultiScale mission. An RD is commonly observed within the magnetopause when reconnection occurs in the magnetopause. Furthermore, an RD usually occurs closer to the magnetosheath side of the magnetopause. The magnetic structure of RD is usually much thinner than 110 km. The magnetic field rotation maxima and magnetic strength minima are within the RD. The radius of curvature of the magnetic field lines reaches a minimum in the RD (∼83–1,491 km). In addition, the radius of curvature of the magnetic field lines of the RD is usually much larger than the thickness of the magnetic structure of the RD, indicating that the magnetic field lines almost lie in the RD. Generally, a field‐aligned current dominates in the RD.

Modification of the Loss Cone for Energetic Particles in the Earth's Inner Magnetosphere

AbstractThe behavior of energetic particles in the Earth's dipole and stretched magnetic‐field models is explored with a focus on the shift of the atmospheric loss cone away from the magnetic‐field direction and on non‐adiabatic behavior occurring when the particle gyroradius becomes comparable with the gradient scale length of the local magnetic field. It is shown that the equatorial loss cone is aberrated away from the magnetic‐field direction (pitch angle of 0°) by the perpendicular drift of a charged particle (which is referred to as the “Mozer transform” described in Mozer (1966, https://doi.org/10.1029/JZ071i011p02701). It is found that the Mozer coordinate transformation in pitch‐angle/gyrophase‐angle space better organizes the behavior of bounce times, mirror altitudes, drift speeds, and first adiabatic invariant. It also describes the loss‐cone shift accurately for a certain range of values of the adiabaticity parameter ϵ, defined by the ratio of the particle gyroradius to the local radius of curvature of the magnetic field. For particles with larger ϵ, the Mozer transform (evaluated with the standard gradient‐curvature drift) breaks down and the “central trajectory” theory can be used to calculate the angular shift of the loss cone, which now includes an Earthward shift. When ϵ becomes relatively large, stochastic field line curvature (FLC) scattering occurs: we show the intimate connection between the strength of FLC scattering and the loss‐cone shift. By comparing ion orbits in the dipole and Tsyganenko (Ts89 and Ts04) magnetic fields, we conclude that the loss cone of ring‐current ions is significantly modified during geomagnetically active times.

On the Small-scale Turbulent Dynamo in the Intracluster Medium: A Comparison to Dynamo Theory* * Released on August, 19th, 2021.

We present non-radiative, cosmological zoom-in simulations of galaxy-cluster formation with magnetic fields and (anisotropic) thermal conduction of one massive galaxy cluster with M vir ∼ 2 × 1015 M ⊙ at z ∼ 0. We run the cluster on three resolution levels (1×, 10×, 25×), starting with an effective mass resolution of 2 × 108 M ⊙, subsequently increasing the particle number to reach 4 × 106 M ⊙. The maximum spatial resolution obtained in the simulations is limited by the gravitational softening reaching ϵ = 1.0 kpc at the highest resolution level, allowing one to resolve the hierarchical assembly of the structures in fine detail. All simulations presented are carried out with the SPMHD code gadget3 with an updated SPMHD prescription. The primary focus of this paper is to investigate magnetic field amplification in the intracluster medium. We show that the main amplification mechanism is the small-scale turbulent dynamo in the limit of reconnection diffusion. In our two highest resolution models we start to resolve the magnetic field amplification driven by the dynamo and we explicitly quantify this with the magnetic power spectra and the curvature of the magnetic field lines, consistent with dynamo theory. Furthermore, we investigate the ∇ · B = 0 constraint within our simulations and show that we achieve comparable results to state-of-the-art AMR or moving-mesh techniques, used in codes such as enzo and arepo. Our results show for the first time in a cosmological simulation of a galaxy cluster that dynamo action can be resolved with modern numerical Lagrangian magnetohydrodynamic methods, a study that is currently missing in the literature.