We present a systematic and physically motivated characterization of incoherent or coherent electric and magnetic fields, as measured for instance by the low frequency receiver on-board the Solar Orbiter spacecraft. The characterization utilizes the 36 auto/cross correlations of the 3+3 complex Cartesian components of the electric and magnetic fields; hence, they are second order in the field strengths and so have physical dimension energy density. Although such 6x6 correlation matrices have been successfully employed on previous space missions, they are not physical quantities; because they are not manifestly space-time tensors. In this paper we propose a systematic representation of the 36 degrees-of-freedom of partially coherent electromagnetic fields as a set of manifestly covariant space-time tensors, which we call the Canonical Electromagnetic Observables (CEO). As an example, we apply this formalism to analyze real data from a chorus emission in the mid-latitude magnetosphere, as registered by the STAFF-SA instrument on board the Cluster-II spacecraft. We find that the CEO analysis increases the amount of information that can be extracted from the STAFF-SA dataset; for instance, the reactive energy flux density, which is one of the CEO parameters, identifies the source region of electromagnetic emissions more directly than the active energy (Poynting) flux density alone.
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