Measurements of the rf electric field have been made along the z axis of a helicon reactor using a retarding field energy analyzer. A fluid code and a simple analytical model have been developed to analyze the ion energy distribution functions, especially in the case of bimodal distributions where the ion transit time through the sheath in front of the analyzer is comparable to the rf period. A generalized curve ͑and an analytical approximation to that curve͒ has been developed from the analytical model and confirmed by the self-consistent fluid model for high, low, and intermediate ion transit time, which can be used by experimenters to quickly convert the experimental results ͑energy peak separation, plasma potential and density, electron temperature͒, which are related to rf sheath oscillations, to absolute values of the rf electric field. An analysis of the errors involved in the derivation of the field is given. The results agree qualitatively with rf pickup measured with a floating Langmuir probe.

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

We present simulations of the outer radiation belt electron flux during the March 2015 and 2013 storms using a radial diffusion model. Despite differences in disturbance short‐time intensity between the two storms, the response of the ultra‐relativistic electrons in the outer radiation belt was remarkably similar, both showing a sudden drop in the electron flux followed by a rapid enhancement in the outer belt flux to levels over an order of magnitude higher than those observed during the pre‐storm interval. Simulations of the ultra‐relativistic electron flux during the March 2015 storm show that outward radial diffusion can explain the flux dropout down to L*~4. However, in order to reproduce, the observed flux dropout at L* < 4 requires the addition of a loss process characterized by an electron lifetime of around 1 hr operating below L*~3.5 during the flux dropout interval. Nonetheless, during the pre‐storm and recovery phase of both storms, the radial diffusion simulation reproduces the observed flux dynamics. For the March 2013 storm, the flux dropout across all L‐shells is reproduced by outward radial diffusion activity alone. However, during the flux enhancement interval at relativistic energies, there is evidence of a growing local peak in the electron phase space density at L*~3.8, consistent with local acceleration such as by very low frequency chorus waves. Overall, the simulation results for both storms can accurately reproduce the observed electron flux only when event specific radial diffusion coefficients are used, instead of the empirical diffusion coefficients derived from ultra‐low frequency wave statistics.

The sudden enhancements of magnetic strength, named magnetic peaks (MPs), are often observed in the magnetosheath of magnetized planets. They are usually identified as flux ropes (FRs) or magnetic mirror mode structures. Previous studies of MPs are mostly on the magnetohydrodynamics (MHD) scale. In this study, an electron scale MP is reported in the Earth magnetosheath. We present a typical case with a scale of ~7 electron gyroradii and a duration of ~0.18 s. A strong magnetic disturbance and associated electrical current are detected. Electron vortex is found perpendicular to the magnetic field line and is self‐consist with the peak. We use multipoint spacecraft techniques to determine the propagation velocity of the MP structure and find that the magnetic peak does propagate relative to the plasma (ion) flow. This is very different from the magnetic mirror mode that does not propagate relative to the plasma flow. Furthermore, we developed an efficient method that can effectively distinguish “magnetic bottle like” and “FRs like” structures. The MP presented in this study is identified as magnetic bottle like type. The mechanism to generate the electron scale magnetic bottle like structure is still unclear, suggesting that new theory needs to be developed to understand such small‐scale phenomena.

Mirror‐mode structures are widely observed in space plasma environments. Although plasma features within the structures have been extensively investigated in theoretical models and numerical simulations, relatively few observational studies have been made, due to a lack of high‐cadence measurements of particle distributions in previous space missions. In this work, electron dynamics associated with mirror‐mode structures are studied based on Magnetospheric Multiscale observations of electron pitch angle distributions. We define mirror‐mode peaks/troughs as the region where the magnetic field strength is greater/smaller than the mean field. The observations show that most electrons are trapped inside the mirror‐mode troughs and display a donut‐like pitch angle distribution configuration. Besides the trapped electrons in mirror‐mode troughs, we find that electrons are also trapped between ambient mirror‐mode peaks and coexisting untrapped electrons within the mirror‐mode structure. Analysis shows that the observed donut‐like electron distributions are the result of betatron cooling and the spatial dependence of electron pitch angles within the structure.