Field Line Curvature Research Articles

The loss rates of O+ in the inner magnetosphere caused by both magnetic field line curvature scattering and charge exchange reactions

With consideration of magnetic field line curvature (FLC) pitch angle scattering and charge exchange reactions, the O+ (>300 keV) in the inner magnetosphere loss rates are investigated by using an eigenfunction analysis. The FLC scattering provides a mechanism for the ring current O+ to enter the loss cone and influence the loss rates caused by charge exchange reactions. Assuming that the pitch angle change is small for each scattering event, the diffusion equation including a charge exchange term is constructed and solved; the eigenvalues of the equation are identified. The resultant loss rates of O+ are approximately equal to the linear superposition of the loss rate without considering the charge exchange reactions and the loss rate associated with charge exchange reactions alone. The loss time is consistent with the observations from the early recovery phases of magnetic storms.

Ion Charge Separation in a Multi‐Species Plasma Flowing through a Magnetic Transport System

AbstractEnergy spectra of ions of various charged states at different cross‐section of a titanium plasma flow produced with a dc vacuum arc were studied. It was established that ions with different charges states were spatially separated during their travel through a plasma transport system based on a curved magnetic field. Ions with greater charge states were concentrated in the inner part of the curved plasma flow, i.e. closer to the centre of curvature of the field lines, so that the average charge state of ions in this area was higher than that at the outer part of the flow. A computer simulation of guiding a multi‐species plasma flow by a curved magnetic field qualitatively agreed with the experimental data. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modulation of auroras by Pc5 pulsations in the dawn sector in association with reappearance of energetic particles at geosynchronous orbit

Geomagnetic Pc5 pulsations were observed in the dawn sector of the auroral zone on 17 January 1994 in association with increased energetic ion fluxes at geosynchronous orbit 10min after the Pi2 onset. The characteristic properties of auroras associated with these pulsations were studied using movies taken by an all-sky imager. It was found that a pulsating aurora (PA) can be an optical manifestation of the Pc5 waves by a strong poloidal component observed with ground-based magnetometers. Goes7 observations showed compressional pulsations with the same period which can be attributed to the influence of the finite pressure of plasma and field line curvature on the poloidally polarized Alfvén waves. These poloidal pulsations may be generated by the ion injection observed with the LANL 1989-046 satellite. Two auroral arcs were observed north of the PA with optical features characteristic for the toroidal field line resonances: strong localization across L-shells, 180° phase change across the resonance, poleward phase propagation. Thus the Pc5 oscillations split into the toroidal and poloidal mode and oscillated coherently at latitudes from 62°N to 70°N. This study provides observational evidence of polarization splitting of the Alfven oscillation spectrum. Such a polarization splitting would occur in association with the reappearance of the energetic particles at geosynchronous orbit.

Application of curvatures and Poisson’s relation to airborne gravity gradient data in oil exploration

SUMMARY The application of equipotential surface curvatures and Poisson’s relation to airborne gravity gradient data is presented. The mean and differential curvature of the equipotential surface, the curvature of the gravity field line, the AGG Geometry Map, the zero contour of the Gaussian curvature of the equipotential surface and the zero contour of the determinant of the gravity gradient tensor should improve the understanding and geological interpretation of gravity gradient data.

Electron pitch-angle diffusion: resonant scattering by waves vs. nonadiabatic effects

Abstract. In this paper we investigate the electron pitch-angle diffusion coefficients in the night-side inner magnetosphere around the geostationary orbit (L ~ 7) due to magnetic field deformation. We compare the effects of resonant wave–particle scattering by lower band chorus waves and the adiabaticity violation of electron motion due to the strong curvature of field lines in the vicinity of the equator. For a realistic magnetic field configuration, the nonadiabatic effects are more important than the wave–particle interactions for high energy (> 1 MeV) electrons. For smaller energy, the scattering by waves is more effective than nonadiabatic one. Moreover, the role of nonadiabatic effects increases with particle energy. Therefore, to model electron scattering and transport in the night-side inner magnetosphere, it is important to take into account the peculiarities of high-energy electron dynamics.

Multiprobe estimation of field line curvature radius in the equatorial magnetosphere and the use of proton precipitations in magnetosphere‐ionosphere mapping

Nonadiabatic, chaotic motion of ions under a curved geomagnetic field geometry is well recognized as a key mechanism that leads to the pitch angle scattering of protons in the equatorial magnetosphere. The efficiency of such proton pitch angle scattering process is energy dependent and controlled by the radius of curvature of the magnetic field line (RCMFL). The protons scattered into the loss cone will precipitate into the ionosphere and excite proton auroras there. In this study, we propose techniques to calculate the RCMFL based upon multiprobe measurements under different probe geometries. We also demonstrate how to use the obtained RCMFL to evaluate the proton precipitation fluxes, and further use the proton precipitation features to help estimate the magnetosphere‐ionosphere mapping. Our procedures are summarized as follows: (1) We calculate the RCMFL using Time History of Events and Macroscale Interactions during Substorms (THEMIS) multiprobe measurements. (2) With the obtained RCMFL, we evaluate the scattering efficiency and in turn the loss cone fluxes of the magnetospheric protons at different energy levels. (3) The above evaluation of the in situ loss cone fluxes is compared to the ionospheric measurements of proton precipitation fluxes in various energy ranges and/or the optical proton auroras to estimate the possible footprint of THEMIS probes in the ionosphere.

Propagation of shear Alvén waves in two-ion species plasmas confined by a nonuniform magnetic field

Ray tracing calculations are performed for shear Alfvén waves in two-ion species plasmas in which the magnetic field varies with position. Three different magnetic topologies of contemporary interest are explored: a linear magnetic mirror, a pure toroidal field, and a tokamak field. The wave frequency is chosen to lie in the upper propagation band, so that reflection at the ion-ion hybrid frequency can occur for waves originally propagating along the magnetic field direction. Calculations are performed for a magnetic well configuration used in recent experiments [S. T. Vincena et al., Geophys. Res. Lett. 38, L11101 (2011) and S. T. Vincena et al., Phys. Plasmas 20, 012111 (2013)] in the Large Plasma Device (LAPD) related to the ion-ion hybrid resonator. It is found that radial spreading cannot explain the relatively low values of the resonator quality factor (Q) measured in those experiments, even when finite ion temperature is considered. This identifies that a damping mechanism is present that is at least an order of magnitude larger than dissipation due to radial energy loss. Calculations are also performed for a magnetic field with pure toroidal geometry, without a poloidal field, as in experiments being planned for the Enormous Toroidal Plasma Device. In this case, the effects of field-line curvature cause radial reflections. A poloidal field is included to explore a tokamak geometry with plasma parameters expected in ITER. When ion temperature is ignored, it is found that the ion-ion hybrid resonator can exist and trap waves for multiples bounces. The effects of finite ion temperature combine with field line curvature to cause the reflection point to move towards the tritium cyclotron frequency when electron temperature is negligible. However, for ITER parameters, it is shown that the electrons must be treated in the adiabatic limit to properly describe resonator phenomena.

Application of curvatures to airborne gravity gradient data in oil exploration

We apply equipotential surface curvatures to airborne gravity gradient data. The mean and differential curvature of the equipotential surface, the curvature of the gravity field line, the zero contour of the Gaussian curvature, and the shape index improve the understanding and geologic interpretation of gravity gradient data. Their use is illustrated in model data and applied to FALCON airborne gravity gradiometer data from the Canning Basin, Australia.

Antisunward structure of thin current sheets in the Earth's magnetotail: Implications of quasi‐adiabatic theory

AbstractWe developed a self‐consistent kinetic model of thin current sheets (TCS), taking into account the inhomogeneity of TCS parameters in the antisunward direction. We show that the charged particle dynamics depending on the magnetic field distribution in the downtail direction completely determines the magnetotail equilibrium structure. We demonstrate that transient ions as well as electrons are the main current carriers in this system, but the first ones support mostly the background (1‐D) structure of the current sheet. The influence of electrons and quasi‐trapped ions is found to vary depending upon downtail distance along the sheet. Assuming the conservation of the so‐called quasi‐adiabatic invariant, we show that quasi‐trapped particles are distributed along the current sheet in such a way that they concentrate in the region with large values of normal magnetic field component. As a result quasi‐trapped ions can dominate near the earthward edge of TCS. In contrast, the electron current becomes stronger in the TCS tailward region where the normal magnetic field component becomes weaker, and field line curvature drifts are enhanced. Our quasi‐adiabatic model predicts that thin current sheets in the Earth's magnetotail should have weakly 2‐D configuration which, similar to its 1‐D analog considered earlier, conserves the multiscale “matreshka” structure with multiple embedded layers.

Geometry of duskside equatorial current during magnetic storm main phase as deduced from magnetospheric and low-altitude observations

Abstract. We present the results of a coordinated study of the moderate magnetic storm on 22 July 2009. The THEMIS and GOES observations of magnetic field in the inner magnetosphere were complemented by energetic particle observations at low altitude by the six NOAA POES satellites. Observations in the vicinity of geosynchronous orbit revealed a relatively thin (half-thickness of less than 1 RE) and intense current sheet in the dusk MLT sector during the main phase of the storm. The total westward current (integrated along the z-direction) on the duskside at r ~ 6.6 RE was comparable to that in the midnight sector. Such a configuration cannot be adequately described by existing magnetic field models with predefined current systems (error in B > 60 nT). At the same time, low-altitude isotropic boundaries (IB) of > 80 keV protons in the dusk sector were shifted ~ 4° equatorward relative to the IBs in the midnight sector. Both the equatorward IB shift and the current strength on the duskside correlate with the Sym-H* index. These findings imply a close relation between the current intensification and equatorward IB shift in the dusk sector. The analysis of IB dispersion revealed that high-energy IBs (E > 100 keV) always exhibit normal dispersion (i.e., that for pitch angle scattering on curved field lines). Anomalous dispersion is sometimes observed in the low-energy channels (~ 30–100 keV). The maximum occurrence rate of anomalous dispersion was observed during the main phase of the storm in the dusk sector.

Application of curvatures to airborne gravity gradients

The application of equipotential surface curvatures to airborne gravity gradient data is presented. The differential curvature, as measured by the FALCON? airborne gravity gradiometer system, the mean curvature, and the direction of maximum curvature of the equipotential surface should improve the understanding and geological interpretation of gravity gradient data. It has been shown that the horizontal gradients of the vertical component of the gravity vector form the curvature of the gravity field line. As this line is orthogonal to the equipotential surface, its curvature is related to how successive equipotential surfaces change and it may not be needed to interpret. The theoretical basis for the method is discussed. Practical applications of utilising the curvature method are presented on a synthetic model and FALCON? airborne gravity gradiometer data from the western zone of the Halls Creek Orogen, Western Australia.

A systematic examination of particle motion in a collapsing magnetic trap model for solar flares

Context. It has been suggested that collapsing magnetic traps may contribute to accelerating particles to high energies during solar flares. Aims. We present a detailed investigation of the energization processes of particles in collapsing magnetic traps, using a specific model. We also compare for the first time the energization processes in a symmetric and an asymmetric trap model. Methods. Particle orbits are calculated using guiding centre theory. We systematically investigate the dependence of the energization process on initial position, initial energy and initial pitch angle. Results. We find that in our symmetric trap model particles can gain up to about 50 times their initial energy, but that for most initial conditions the energy gain is more moderate. Particles with an initial position in the weak field region of the collapsing trap and with pitch angles around 90 degrees achieve the highest energy gain, with betatron acceleration of the perpendicular energy the dominant energization mechanism. For particles with smaller initial pitch angle, but still outside the loss cone, we find the possibility of a significant increase in parallel energy. This increase in parallel energy can be attributed to the curvature term in the parallel equation of motion and the associated energy gain happens in the center of the trap where the field line curvature has its maximum. We find qualitatively similar results for the asymmetric trap model, but with smaller energy gains and a larger number of particles escaping from the trap.

Dipolarization fronts and associated auroral activities: 1. Conjugate observations and perspectives from global MHD simulations

Earthward‐propagating dipolarization fronts (DFs) are often found to be associated with magnetic reconnection and bursty bulk flows (BBFs) in the magnetotail. Recent THEMIS (Time History of Events and Macroscale Interactions During Substorms) probe observations have shown a DF propagating over 10REfrom the mid‐tail region to the near‐Earth tail region, and THEMIS All‐Sky Imager data show a north‐south auroral form and intensification of westward auroral zone currents. In this study, we examine THEMIS in situ observations of DFs in the magnetotail and simultaneous observations of the proton aurora from ground‐based CANOPUS (the Canadian Auroral Network for the OPEN Program Unified Study) Meridian Scanning Photometers (MSPs). We find that earthward‐moving DFs are often associated with intensification of proton aurora when the THEMIS probes are conjugate to the meridian of the MSP. The proton auroral intensifications are transient and in some cases detached from the background proton precipitation. Just before the DFs, the ion distribution is anisotropic in the field‐aligned direction (mostly earthward) and the ion energy increases. These observations suggest that plasma sheet protons can be reflected and energized by earthward‐moving DFs as they propagate through the magnetotail. We postulate that this population of ions is the source of the proton auroral intensification observed on the ground. This conjecture is tested using our global MHD simulation results, where the proton precipitation is calculated with the field‐line curvature (FLC) model. The MHD simulation results show that proton precipitation enhancement can be caused by compression of plasma by approaching DFs/BBFs, which is consistent with ion reflection at DFs. Thus, using the conjugate observations from THEMIS spacecraft and MSP in this study, we are able to directly link the magnetotail dynamics, i.e., dipolarization fronts, with ground auroral activities. However, understanding of DF‐associated ion energization requires detailed test‐particle simulations with an analytical magnetotail model, such as those in our companion paper.

On the ballooning instability of the coupled Alfvén and drift compressional modes

The paper examines the ballooning instability in gyrokinetic approximation taking into account the effects of finite-β, magnetic field line curvature, and diamagnetic drift. We used a simple model with a constant curvature of magnetic field lines which enabled us to obtain analytical results. The possible plasma oscillatory modes comprise the poloidal Alfvén and drift compressional modes, coupled due to the magnetic field line curvature and plasma inhomogeneity. The frequencies of these modes depend on the westward current value. As this value grows, the frequencies of these two branches approach to each other, and the branches are merged at some critical value of the current. Then an instability develops which is called the drift ballooning coupling instability. There are three major differences of the drift ballooning coupling instability from the ordinary MHD ballooning instability: (1) the drift ballooning coupling instability is not aperiodic, there is a real part of the oscillation frequency of the order of the drift frequency, (2) only the mode with the same direction of the azimuthal phase speed as the velocity of the ion diamagnetic drift can be unstable, (3) the instability threshold depends on the diamagnetic drift frequency.

BUOYANCY INSTABILITIES IN A WEAKLY COLLISIONAL INTRACLUSTER MEDIUM

The intracluster medium of galaxy clusters is a weakly collisional, high-beta plasma in which the transport of heat and momentum occurs primarily along magnetic-field lines. Anisotropic heat conduction allows convective instabilities to be driven by temperature gradients of either sign, the magnetothermal instability (MTI) in the outskirts of non-isothermal clusters and the heat-flux buoyancy-driven instability (HBI) in their cooling cores. We employ the Athena MHD code to investigate the nonlinear evolution of these instabilities, self-consistently including the effects of anisotropic viscosity (i.e. Braginskii pressure anisotropy), anisotropic conduction, and radiative cooling. We highlight the importance of the microscale instabilities that inevitably accompany and regulate the pressure anisotropies generated by the HBI and MTI. We find that, in all but the innermost regions of cool-core clusters, anisotropic viscosity significantly impairs the ability of the HBI to reorient magnetic-field lines orthogonal to the temperature gradient. Thus, while radio-mode feedback appears necessary in the central few tens of kpc, conduction may be capable of offsetting radiative losses throughout most of a cool core over a significant fraction of the Hubble time. Magnetically-aligned cold filaments are then able to form by local thermal instability. Viscous dissipation during the formation of a cold filament produces accompanying hot filaments, which can be searched for in deep Chandra observations of nearby cool-core clusters. In the case of the MTI, anisotropic viscosity maintains the coherence of magnetic-field lines over larger distances than in the inviscid case, providing a natural lower limit for the scale on which the field can fluctuate freely. In the nonlinear state, the magnetic field exhibits a folded structure in which the field-line curvature and field strength are anti-correlated.

SuperDARN observations of high‐m ULF waves with curved phase fronts and their interpretation in terms of transverse resonator theory

The Hankasalmi SuperDARN radar in Finland, while operating in a high spatial and temporal resolution mode, has measured the ionospheric signature of a naturally occurring ULF wave in scatter artificially induced by the Tromsø Heater. The wave had a period of 100 s and exhibited curved phase fronts across the heated volume (about 180 km along a single radar beam). Spatial information provided by the radar has enabled an m‐number for the wave of about 38 to be determined. It is demonstrated here that the curved phase fronts are a generic feature of nonstationary poloidal waves in a transverse resonator, caused by the common action of the field line curvature, the plasma pressure, and the equilibrium current. Some features of the observed event agree with the resonator in the vicinity of the ring current, where it is proposed that the wave is excited by a moving source in the form of a proton cloud drifting in the magnetosphere in the azimuthal direction.

Global simulation of proton precipitation due to field line curvature during substorms

The low latitude boundary of the proton aurora (known as the Isotropy Boundary or IB) marks an important boundary between empty and full downgoing loss cones. There is significant evidence that the IB maps to a region in the magnetosphere where the ion gyroradius becomes comparable to the local field line curvature. However, the location of the IB in the magnetosphere remains in question. In this paper, we show simulated proton precipitation derived from the Field Line Curvature (FLC) model of proton scattering and a global magnetohydrodynamic simulation during two substorms. The simulated proton precipitation drifts equatorward during the growth phase, intensifies at onset and reproduces the azimuthal splitting published in previous studies. In the simulation, the pre‐onset IB maps to 7–8 RE for the substorms presented and the azimuthal splitting is caused by the development of the substorm current wedge. The simulation also demonstrates that the central plasma sheet temperature can significantly influence when and where the azimuthal splitting takes place.

Magnetization of type-II superconductors in the form of short cylinders and the screening supercurrent distribution in the Bean model

The simplest analytical form of the screening supercurrent distribution is found, and the magnetization of type-II (hard) superconductors in the form of finite-length cylinders and disks (pellets) is calculated. Calculations are carried out in terms of the Bean model taking into account the curvature of magnetic field lines. From this distribution, the total magnetic field intensity and the magnetization hysteresis loop are calculated for such samples in different cases.

What geometrical factors determine the in situ solar wind speed?

At present it remains to address why the fast solar wind is fast and the slow wind is slow. Recently we have shown that the field line curvature may substantially influence the wind speed v, thereby offering an explanation for the Arge et al. finding that v depends on more than just the flow tube expansion factor. Here we show by extensive numerical examples that the correlation between v and field line curvature is valid for rather general base boundary conditions and for rather general heating functions. Furthermore, the effect of field line curvature is even more pronounced when the proton-alpha particle speed difference is examined. We suggest that any solar wind model has to take into account the field line shape for any quantitative analysis to be made.

Modeling the Parker instability in a rotating plasma screw pinch

We analytically and numerically study the analogue of the Parker (magnetic buoyancy) instability in a uniformly rotating plasma screw pinch confined in a cylinder. Uniform plasma rotation is imposed to create a centrifugal acceleration, which mimics the gravity required for the classical Parker instability. The goal of this study is to determine how the Parker instability could be unambiguously identified in a weakly magnetized, rapidly rotating screw pinch, in which the rotation provides an effective gravity and a radially varying azimuthal field is controlled to give conditions for which the plasma is magnetically buoyant to inward motion. We show that an axial magnetic field is also required to circumvent conventional current driven magnetohydrodynamic (MHD) instabilities such as the sausage and kink modes that would obscure the Parker instability. These conditions can be realized in the Madison plasma Couette experiment (MPCX). Simulations are performed using the extended MHD code NIMROD for an isothermal compressible plasma model. Both linear and nonlinear regimes of the instability are studied, and the results obtained for the linear regime are compared with analytical results from a slab geometry. Based on this comparison, it is found that in a cylindrical pinch, the magnetic buoyancy mechanism dominates at relatively large Mach numbers (M > 5), while at low Mach numbers (M < 1), the instability is due to the curvature of magnetic field lines. At intermediate values of Mach number (1 < M < 5), the Coriolis force has a strong stabilizing effect on the plasma. A possible scenario for experimental demonstration of the Parker instability in MPCX is discussed.