Determining EMIC Wave Vector Properties Through Multi-Point Measurements: The Wave Curl Analysis.

Electromagnetic ion cyclotron (EMIC) waves play important roles in particle loss processes in the magnetosphere. Determining the evolution of EMIC waves as they propagate and how this evolution affects wave-particle interactions requires accurate knowledge of the wave vector, k. We present a technique using the curl of the wave magnetic field to determine k observationally, enabled by the unique configuration and instrumentation of the Magnetospheric MultiScale (MMS) spacecraft. The wave curl analysis is demonstrated for synthetic arbitrary electromagnetic waves with varying properties typical of observed EMIC waves. The method is also applied to an EMIC wave interval observed by MMS on October 28, 2015. The derived wave properties and k from the wave curl analysis for the observed EMIC wave are compared with the Waves in Homogenous, Anisotropic, Multi-component Plasma (WHAMP) wave dispersion solution and with results from other single- and multi-spacecraft techniques. We find good agreement between k from the wave curl analysis, k determined from other observational techniques, and k determined from WHAMP. Additionally, the variation of k due to the time and frequency intervals used in the wave curl analysis is explored. This exploration demonstrates that the method is robust when applied to a wave containing at least 3-4 wave periods and over a rather wide frequency range encompassing the peak wave emission. These results provide confidence that we are able to directly determine the wave vector properties using this multi-spacecraft method implementation, enabling systematic studies of EMIC wave k properties with MMS.