Magnetic Curvature Research Articles

Electron Reconnection in the Magnetopause Current Layer

AbstractThe electron dynamics within thin current sheets plays a key role both for the process of magnetic reconnection and other energy transfer mechanisms but, from an observational point of view, is not well understood. In this paper we report observations of a reconnecting current sheet with intermediate guide field BG=0.5Bin, where Bin is the magnetic field amplitude in the inflow regions. The current sheet width is comparable to electron spatial scales. It shows a bifurcated structure and is embedded within the magnetopause current layer with thickness of several ion scales. The electron scale current sheet has strong out‐of‐plane and in‐plane currents, Hall electric and magnetic fields, a finite magnetic field component normal to the current sheet, and nongyrotropic electron distributions formed due to finite gyroradius effects at the boundary of the current sheet. Comparison between test particle simulations and electron data shows that electrons approaching from the edge of the largest magnetic curvature are scattered to perpendicular pitch angles in the center of the current sheet while electrons entering from the opposite side remain close to field aligned. The comparison also shows that an observed depletion in phase space at antiparallel pitch angles can be explained if an out‐of‐plane electric field, which due to the guide field is close to antiparallel to the magnetic field, is present in the center of the current sheet. This electric field would be consistent with the reconnection electric field, and we therefore interpret the depletion of electron phase space density as a manifestation of ongoing reconnection.

Investigation of different small-scale flux-rope acceleration scenarios for energetic particles in the solar wind near Earth

Our previous kinetic transport theoretical development for energetic particle acceleration by and large-scale transport through solar wind regions with numerous dynamic small-scale flux ropes in the strong guide/background field limit is further analyzed and extended. The basic flux-rope acceleration mechanisms and the issue of compressibility are further clarified by applying concepts such as magnetic curvature and shear flow to these structures. A set of new coupled focused-transport-MHD turbulence equations is presented for modeling coherent and stochastic energetic particle acceleration by small-scale flux ropes self-consistently. Furthermore, test particle coherent and stochastic acceleration rates are compared for the different flux-rope acceleration mechanisms, and stochastic acceleration and pitch-angle scattering rates for flux ropes and Alfvén waves are compared, for energetic protons at Earth.

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.

Quasilinear particle transport from gyrokinetic instabilities in general magnetic geometry

The quasilinear particle flux arising from gyrokinetic instabilities is calculated in the electrostatic and collisionless approximation, keeping the geometry of the magnetic field arbitrary. In particular, the flux of electrons and heavy impurity ions is studied in the limit where the former move quickly, and the latter slowly, along the field compared with the mode frequency. Conclusions are drawn about how the particle fluxes of these species depend on the magnetic field geometry, mode structure and frequency of the instability. Under some conditions, such as everywhere favourable or unfavourable magnetic curvature and modest temperature gradients, it is possible to make general statements about the fluxes independently of the details of the instability. In quasi-isodynamic stellarators with favourable bounce-averaged curvature for most particles, the particle flux is always outward if the temperature gradient is not too large, suggesting that it might be difficult to fuel such devices with gas puffing from the wall. In devices with predominantly unfavourable magnetic curvature, the particle flux can be inward, resulting in spontaneous density peaking in the centre of the plasma. In the limit of highly charged impurities, ordinary diffusion (proportional to the density gradient) dominates over other transport channels and the diffusion coefficient becomes independent of mass and charge. An estimate for the level of transport caused by magnetic field fluctuations arising from ion-temperature-gradient instabilities is also given and is shown to be small compared with the electrostatic component.

The Magnetic Field Curvature Correction Algorithm Dedicated for Helmet Mounted Cueing Systems

The Magnetic Field Curvature Correction Algorithm Dedicated for Helmet Mounted Cueing Systems

Strongly driven surface-global kinetic ballooning modes in general toroidal geometry

Kinetic ballooning modes in magnetically confined toroidal plasmas are investigated putting emphasis on specific stellarator features. In particular, we propose a Mercier criterion which is purposely designed to allow for direct comparison with local flux-tube gyrokinetics simulations. We investigate the influence on the marginal frequency of the mode of a magnetic curvature which is inhomogeneous on the magnetic flux surface due to the fieldline-label dependence. This is a typical (surface) global effect present in non-axisymmetry. Finally, we propose an artificial equilibrium model that explicitly retains the fieldline-label dependence in the magnetic drift, and analyse the stability of the system by introducing a representation of the perturbations similar to the flux-bundle model of Sugamaet al. (Plasma Fusion Res., vol. 7, 2012, 2403094). The coupling of flux bundles is shown to have a stabilising effect on the most unstable local flux-tube mode.

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 < 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 (<59°). These findings imply that the FLC scattering is a dominant mechanism of IB formation operating in a variety of magnetospheric conditions.

A Statistical Study of Spatial Variation of Relativistic Electron Precipitation Energy Spectra With Polar Operational Environmental Satellites

AbstractThe mechanisms that drive relativistic electron precipitation (REP) from the radiation belts can be better understood with a better knowledge of the particle energies involved. National Oceanic and Atmospheric Administration Polar Operational Environmental Satellites, being a network of multiple satellites, can provide multiple point spectral data over a long time period, including the Van Allen Probe's era. The number of energy channels is limited, but the particle detectors on Polar Operational Environmental Satellites have a narrow field of view allowing an investigation of bounce loss cone particles. We use the ratio of count rates in the E3 (>300 keV) and the P6 (>700 keV) channels as a parameter to define spectral hardness. Using this parameter, the spatial variation of spectral hardness of REP events was investigated. It was found that very soft events were mostly found in the dusk‐midnight‐early morning magnetic local time sectors and L∼ 5–7 while the hardest events were located in the postnoon sector peaking at L∼ 4–5. The hardest events peaked at lower L shells, and less than 20% were coincident with low‐energy (30–80 keV) proton precipitation. Further, around 70% of nightside REP coincident with proton precipitation was associated with stretched magnetic field lines indicating that curvature scattering may have been an important driver. Around 62% of nightside REP coincident with proton precipitation associated with relaxed magnetic field lines, suggesting a mechanism other than magnetic field curvature scattering, was highly energetic.

Study on the Curvature and Gradient of the Magnetic Field in Earth's Cusp Region Based on the Magnetic Curvature Analysis Method

AbstractThis paper uses the multiple‐point magnetic measurements from the Cluster mission to investigate the curvature and gradient of the magnetic field as well as their relations with the current density inside the cusp region under different interplanetary magnetic field (IMF) conditions. From two event studies, it is shown that the curvature radius of magnetic field line is on average 5.13 RE under southward IMF and 19.75 RE under northward IMF condition. The directional angle of curvature is more distributed in a wider range under southward condition. The gradient of the magnetic field strength B is larger with a larger standard deviation under southward IMF condition. These results imply that the cusp region has more complicated magnetic structures under southward IMF condition. Through the correlation analysis between the magnetic field parameters and the current density, it is found that the magnetic gradient has a strong relation with total current density jt and perpendicular current density j⊥ when the ratio of parallel component j// to jt decreases, possibly due to gradient B drift. Furthermore, we present a statistical study on the 19 cusp crossing events from July 2003 to September 2003. The results from the statistical study are consistent with the event studies.

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.

Stability of a slab collisional microtearing mode

The stability of a collisional microtearing mode (MTM) is investigated by means of linear gyro‐kinetic simulations and a theoretical linear dispersion relation. The electric potential fluctuations and the magnetic curvature are neglected in the simulations to match the theoretical model assumptions. In these conditions, the stability domain, the mode growth rate, and the mode frequency predicted by the theory and the simulations are in satisfactory agreement. The radial structure of the mode has been also investigated, and the localization of the parallel current around the resonant surface predicted by the theory is recovered by the simulations.

Influence of toroidal rotation on magnetic islands in tokamaks

The dynamics of magnetic islands including toroidal rotation in tokamaks is studied. It is found that the contribution of toroidal rotation to the dynamics of magnetic islands is mainly through the coupling of magnetic curvature with pressure and density. In the presence of toroidal rotation, pressure and density are poloidal asymmetric. Then, their coupling with magnetic curvature provides a perpendicular current, and a corresponding return parallel current is induced to affect the dynamics of magnetic islands. It is found that the effect of toroidal rotation depends on its magnitude, rather than the shear. It also depends on the relative magnitude of the island propagation frequency to sound frequency. When the Mach number is large enough, the effect of toroidal rotation is stabilizing and dramatic, and overcomes the contribution of polarization current, namely the onset threshold of NTMs increases. Further, it is also suggested that the toroidal rotation plays an important role in the stability of small scale magnetic islands.

Four‐Spacecraft Magnetic Curvature and Vorticity Analyses on Kelvin‐Helmholtz Waves in MHD Simulations

AbstractFour‐spacecraft missions are probing the Earth's magnetospheric environment with high potential for revealing spatial and temporal scales of a variety of in situ phenomena. The techniques allowed by these four spacecraft include the calculation of vorticity and the magnetic curvature analysis (MCA), both of which have been used in the study of various plasma structures. Motivated by curved magnetic field and vortical structures induced by Kelvin‐ Helmholtz (KH) waves, we investigate the robustness of the MCA and vorticity techniques when increasing (regular) tetrahedron sizes, to interpret real data. Here for the first time, we test both techniques on a 2.5‐D MHD simulation of KH waves at the magnetopause. We investigate, in particular, the curvature and flow vorticity across KH vortices and produce time series for static spacecraft in the boundary layers. The combined results of magnetic curvature and vorticity further help us to understand the development of KH waves. In particular, first, in the trailing edge, the magnetic curvature across the magnetopause points in opposite directions, in the wave propagation direction on the magnetosheath side and against it on the magnetospheric side. Second, the existence of a “turnover layer” in the magnetospheric side, defined by negative vorticity for the duskside magnetopause, which persists in the saturation phase, is reminiscent of roll‐up history. We found significant variations in the MCA measures depending on the size of the tetrahedron. This study lends support for cross‐scale observations to better understand the nature of curvature and its role in plasma phenomena.

An investigation of the effective parameters causing the critical current drop in a small high temperature superconducting D-shaped coil

In this paper, the dependency of the critical current on the magnetic field, temperature, and different curvature radii for a specific sample of Bi-2223/AgMg composite tape are investigated. By using this superconducting tape, a D-shaped pancake coil is designed and built. The coil critical current degradation at liquid nitrogen temperature with respect to a straight short sample of the same tape is reported, and also the portion of the bending and self-field contribution in the critical current drop is indicated separately. The hysteresis behavior as a function of the current rate during ramp up and ramp down cases on the voltage-current curve at liquid nitrogen temperature is examined. In addition, the quenching propagation speed is measured at two different radii of curvature of the designed magnet.

Collisionless microinstabilities in stellarators. Part 4. The ion-driven trapped-electron mode

Optimised stellarators and other magnetic-confinement devices having the property that the average magnetic curvature is favourable for all particle orbits are called maximum-$J$ devices. They have recently been shown to be immune to trapped-particle instabilities driven by the density gradient. Gyrokinetic simulations reveal, however, that another instability can arise, which is also associated with particle trapping but causes less transport than typical trapped-electron modes. The nature of this instability is clarified here. It is shown to be similar to the ‘ubiquitous mode’ in tokamaks and is driven by ion free energy, but requires trapped electrons to exist.

Eulerian approach to bounce-transit and drift resonance with magnetic drifts in tokamaks

Bounce-transit and drift resonance can be important to plasma confinement in tokamaks with a broken symmetry. The resonance usually is either treated by integrating along the unperturbed orbits or calculated using an action-angle approach. An Eulerian approach has been developed to take into account the momentum conservation property of the Coulomb collision operator. The difference between the Eulerian approach and other approaches is in the thermodynamic forces of the transport fluxes, and the corresponding toroidal plasma viscosity. The mass and heat flows that are parallel to the equilibrium magnetic field B appear in the thermodynamic forces in the Eulerian approach. However, in the existing Eulerian approach, only the E × B drift is kept in the theory; the magnetic drifts, i.e., ∇B, and curvature drifts are neglected by adopting the large aspect ratio assumption, where E is the electric field and B = |B|. Here, the Eulerian approach is extended to include the magnetic drifts, which is important for energetic alpha particles as well, to calculate neoclassical toroidal plasma viscosity in finite aspect ratio tokamaks. The relation to the nonlinear plasma viscosity in the plateau regime will also be discussed.

Four-Spacecraft Magnetic Curvature Analysis on Kelvin-Helmholtz Waves in MHD Simulations

AbstractFour-spacecraft missions are probing the Earth’s magnetospheric environment with high potential for revealing spatial and temporal scales of a variety of in-situ phenomena. Magnetic curvature is intrinsic to curved magnetic fields where the magnetic energy is stored in the form of magnetic tension. In-situ magnetic curvature has been resolved by the four-spacecraft technique called “magnetic curvature analysis” (MCA). We test the MCA on 2.5D MHD simulations of curved magnetic structures induced by Kelvin-Helmholtz (KH) waves, with increasing (regular) tetrahedron sizes of virtual spacecraft. We have found variations of the curvature vectors both in radii and orientations depending on the sizes of the tetrahedron. This is helpful to better understand the MCA measures when the technique is applied to in-situ data without knowing the scale sizes of plasma structures under consideration. This study lends support for cross-scale observations to better understand the nature of curvature and its role in plasma phenomena.

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.

Particle-Hole Duality in the Lowest Landau Level.

We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several nontrivial checks of the relations, including for the Jain states and their PH conjugates.