Determining EMIC Wave Vector Properties Through Multi‐Point Measurements: The Wave Curl Analysis. Issue 4 (28th March 2021) - Vines, S. K.; Anderson, B. J.; Allen, R. C.; Denton, R. E.; Engebretson, M. J.; Johnson, J. R.; Toledo‐Redondo, S.; Lee, J. H.; Turner, D. L.; Ergun, R. E.; Strangeway, R. J.; Russell, C. T.; et al.
Abstract: 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. Plain Language Summary: Waves generated within space plasmas play important roles in accelerating, heating, and depleting charged particles in Earth's magnetosphere. The wave vector, k, mathematically relates the wavelength, direction of wave motion, and wave type to the conditions that produced it. This also tells us if a wave can interact with electrons and ions in ways that will affect the radiation belts. A key problem in understanding waves in space is that k is very difficult to determine observationally. We present a method for calculating k using Magnetospheric Multiscale (MMS) mission data. The "wave curl analysis" uses magnetic field measurements from all four MMS spacecraft to determine the electric current of the magnetic field fluctuations, which allows for direct calculation of k . We test the method on mathematically generated waveforms with properties that mimic electromagnetic ion cyclotron (EMIC) waves previously observed by MMS. We then applied this method to EMIC wave observations and compared the results to theoretical predictions and other methods for estimating k from spacecraft measurements. The wave curl analysis opens up a new way to use MMS to understand how EMIC waves are generated, how they travel and evolve, and how they affect plasma in the near‐Earth space environment. Key Points: The wave curl analysis is a new implementation of determining k using observed wave magnetic field and associated current density The wave curl analysis reliably determines k for both synthetic waves and Magnetospheric MultiScale observations of electromagnetic ion cyclotron waves The calculated k is robust relative to time and frequency ranges used in the analysis, and agrees well with linear dispersion theory