Quasi-linear theory (QLT) has been commonly used to study the Landau resonant interaction between radiation belt electrons and magnetosonic (MS) waves. However, the long-parallel wavelengths of MS waves can exceed their narrow spatial confinement and cause a transit-time effect during interactions with electrons. We perform a careful investigation to validate the applicability of QLT to interactions between MS waves, which have a distribution in frequency and wave normal angle, and radiation belt electrons using test particle simulations. We show agreement between these two methods for scattering rate of intense MS waves at L = 4.5 inside the plasmapause, but find a significant inconsistency for MS waves outside the plasmapause, due to the broad transit-time region in (E k , ) space. Consequently, we introduce a particle-independent criterion to justify the validity of QLT for MS waves: the wave spatial confinement should be longer than two parallel wavelengths.

Magnetic holes (MHs), with a scale much greater than ρi (proton gyroradius), have been widely reported in various regions of space plasmas. On the other hand, kinetic‐size magnetic holes (KSMHs), previously called small‐size magnetic holes, with a scale of the order of magnitude of or less than ρi have only been reported in the Earth's magnetospheric plasma sheet. In this study, we report such KSMHs in the magnetosheath whereby we use measurements from the Magnetospheric Multiscale mission, which provides three‐dimensional (3‐D) particle distribution measurements with a resolution much higher than previous missions. The MHs have been observed in a scale of 10–20 ρe (electron gyroradii) and lasted 0.1–0.3 s. Distinctive electron dynamics features are observed, while no substantial deviations in ion data are seen. It is found that at the 90° pitch angle, the flux of electrons with energy 34–66 eV decreased, while for electrons of energy 109–1024 eV increased inside the MHs. We also find the electron flow vortex perpendicular to the magnetic field, a feature self‐consistent with the magnetic depression. Moreover, the calculated current density is mainly contributed by the electron diamagnetic drift, and the electron vortex flow is the diamagnetic drift flow. The electron magnetohydrodynamics soliton is considered as a possible generation mechanism for the KSMHs with the scale size of 10–20 ρe.

[1] Recently, observational results on currents around the dipolarization fronts (DFs) of earthward flow bursts have attracted much research attention. These currents are found to have close association with substorm intensifications. This paper devotes to further study of the current system ahead and within the DFs with high-resolution magnetic field measurements from Cluster constellation in 2003. The separation of four spacecraft is much smaller than the scales of spatial structures ahead and within the DF layer so that the currents can be reliably obtained. Based on features of the magnetic field variations prior to the fronts, we categorized the DFs into two types: DFs with magnetic dips immediate ahead of the fronts (type I) and DFs without magnetic dips (type II). For type I DFs, it is found that dawnward currents along the DFs exist in the dip region; duskward currents exist within the fronts. Furthermore, the dawnward currents in the dip region are found to be mainly parallel to the local magnetic field with a spatial scale of~1000 km, whereas the duskward currents within the fronts have both significant parallel and perpendicular components. On the other hand, for type II DFs, only significant duskward and mainly perpendicular currents show up within the fronts; no dawnward currents exist ahead of DFs. The dawnward and mainly parallel current in the type I DFs is important in the current coupling process between magnetosphere and ionosphere and may lead to local current disruptions for substorm initiations.

In the analysis of in-situ space plasma and field data, an establishment of the coordinate system and the frame of reference, helps us greatly simplify a given problem and provides the framework that enables a clear understanding of physical processes by ordering the experimental data. For example, one of the most important tasks of space data analysis is to compare the data with simulations and theory, which is facilitated by an appropriate choice of coordinate system and reference frame. While in simulations and theoretical work the establishment of the coordinate system (generally based on the dimensionality or dimension number of the field quantities being studied) and the reference frame (normally moving with the structure of interest) is often straightforward, in space data analysis these are not defined a priori, and need to be deduced from an analysis of the data itself. Although various ways of building a dimensionality-based (D-based) coordinate system (i.e., one that takes account of the dimensionality, e.g., 1-D, 2-D, or 3-D, of the observed system/field), and a reference frame moving along with the structure have been used in space plasma data analysis for several decades, in recent years some noteworthy approaches have been proposed. In this paper, we will review the past and recent approaches in space data analysis for the determination of a structure's dimensionality and the building of D-based coordinate system and a proper moving frame, from which one can directly compare with simulations and theory. Along with the determination of such coordinate systems and proper frame, the variant axis/normal of 1-D (or planar) structures, and the invariant axis of 2-D structures are determined and the proper frame velocity for moving structures is found. These are found