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Electromagnetic Ion Cyclotron (EMIC) waves mediate energy transfer from the solar wind to the magnetosphere, relativistic electron precipitation, or thermalization of the ring current population, to name a few. How these processes take place depends on the wave properties, such as the wavevector and polarization. However, inferring the wavevector from in‐situ measurements is problematic since one needs to disentangle spatial and time variations. Using 8 years of Magnetospheric Multiscale (MMS) mission observations in the dayside magnetosphere, we present an algorithm to detect proton‐band EMIC waves in the Earth's dayside magnetosphere, and find that they are present roughly 15% of the time. Their normalized frequency presents a dawn‐dusk asymmetry, with waves in the dawn flank magnetosphere having larger frequency than in the dusk, subsolar, and dawn near subsolar region. It is shown that the observations are unstable to the ion cyclotron instability. We obtain the wave polarization and wavevector by comparing Single Value Decomposition and Ampere methods. We observe that for most waves the perpendicular wavenumber (k⊥) is larger than the inverse of the proton gyroradius (ρi), that is, k⊥ρi> 1, while the parallel wavenumber is smaller than the inverse of the ion gyroradius, that is, k‖ρi< 1. Left‐hand polarized waves are associated with small wave normal angles (θBk< 30°), while linearly polarized waves are associated with large wave normal angles (θBk> 30°). This work constitutes, to our knowledge, the first attempt to statistically infer the full wavevector of proton‐band EMIC waves observed in the outer magnetosphere. We conduct a statistical analysis of proton‐band Electromagnetic Ion Cyclotron (EMIC) waves in dayside magnetosphere using 8 years of Magnetospheric Multiscale data and measure full wavevectorsThe normalized frequency of EMIC waves presents a dawn‐dusk asymmetryThe perpendicular wavevector is, for most of the waves, larger than the inverse of proton gyroradius and ion inertial lengths We conduct a statistical analysis of proton‐band Electromagnetic Ion Cyclotron (EMIC) waves in dayside magnetosphere using 8 years of Magnetospheric Multiscale data and measure full wavevectors The normalized frequency of EMIC waves presents a dawn‐dusk asymmetry The perpendicular wavevector is, for most of the waves, larger than the inverse of proton gyroradius and ion inertial lengths

We present a new method for determining the main relevant features of the local magnetic field configuration, based entirely on the knowledge of the magnetic field gradient four‐spacecraft measurements. The method, named “magnetic configuration analysis” (MCA), estimates the spatial scales on which the magnetic field varies locally. While it directly derives from the well‐known magnetic directional derivative and magnetic rotational analysis procedures (Shi et al., 2005, htpps://doi.org/10.1029/2005GL022454; Shen et al., 2007, https://doi.org/10.1029/2005JA011584), MCA was specifically designed to address the actual magnetic field geometry. By applying MCA to multispacecraft data from the Magnetospheric Multiscale (MMS) satellites, we perform both case and statistical analyses of local magnetic field shape and dimensionality at very high cadence and small scales. We apply this technique to different near‐Earth environments and define a classification scheme for the type of configuration observed. While our case studies allow us to benchmark the method with those used in past works, our statistical analysis unveils the typical shape of magnetic configurations and their statistical distributions. We show that small‐scale magnetic configurations are generally elongated, displaying forms of cigar and blade shapes, but occasionally being planar in shape like thin pancakes (mostly inside current sheets). Magnetic configurations, however, rarely show isotropy in their magnetic variance. The planar nature of magnetic configurations and, most importantly, their scale lengths strongly depend on the plasma β parameter. Finally, the most invariant direction is statistically aligned with the electric current, reminiscent of the importance of electromagnetic forces in shaping the local magnetic configuration. We define and use a four‐spacecraft method on MMS data to study the magnetic field configuration at small scales in near Earth regionsCase studies demonstrate the ability of the method to measure local magnetic configuration, benchmarking the method on previous studiesStatistically, low plasma betas are correlated with large length scales and slightly more frequent planar shapes in magnetic configurations

We develop a new asymptotic method of resolution of the two-dimensional equilibrium equation of collisionless plasmas described by the Maxwell–Vlasov equations. This method differs from the classical one proposed by K. Schindler [Earth’s Magnetospheric Processes (ed. B. M. McCormac). Norwood, MA: Reidel, 1972, pp. 200–209.] since we consider free-boundary plasmas. Our method is a generalization of the usual multiscale asymptotic developments. The first-approximation asymptotic solutions are found from the elimination of increasing and singular terms in the next approximation. We apply the method to the mathematical description of nonlinear structures that may form in neutral sheets. Particular solutions describing localized plasmoids (O-point configuration) as well as X-point magnetic configurations are obtained. We also find more general solutions describing a finite number of ‘magnetic islands’ (multiplasmoid solutions) separated by X points.