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Plasma kinetic theory predicts that sufficiently anisotropic proton distribution will excite electromagnetic ion cyclotron (EMIC) waves, which in turn relax the proton distribution to a marginally stable state creating an upper bound on the relaxed proton anisotropy. Here, using EMIC wave observations and coincident plasma measurements made by Van Allen Probes in the inner magnetosphere, we show that the proton distributions are well constrained by this instability to a marginally stable state. Near the threshold, the probability of EMIC wave occurrence is highest, having left-handed polarization and observed near the magnetic equator with relatively small wave normal angles, indicating that these waves are locally generated. In addition, EMIC waves are distributed in two magnetic local time regions with different intensity. Compared with helium band waves, hydrogen band waves behave similarly except that they are often observed in low-density regions. These results reveal several important features regarding EMIC waves excitation and propagation.

Plain Language Summary Electromagnetic ion cyclotron (EMIC) waves play a very important role in controlling plasma dynamics. In particular, EMIC wave-particle interaction is a significant loss process for ring current ions and radiation belt relativistic electrons due to pitch angle scattering into the atmosphere. To understand the relationship between the generation of EMIC waves and the underlying plasma distributions, we perform a statistical survey to link the observed EMIC wave properties to the associated macroscopic state of the proton distributions by using 4 years of Van Allen Probe observations. We have found that close to the threshold of proton anisotropy instability, high occurrences of left-hand polarized EMIC waves are usually observed near the magnetic equator with relatively small wave normal angles. In addition, there are two distinct magnetic local time regions of observed EMIC waves, with intense waves occurring on the duskside associated with high AE levels and relatively weak waves occurring in the noon sector accompanied by low AE levels. Furthermore, hydrogen band waves behave similarly to helium band waves except that these waves are often observed in low-density regions while helium band waves are usually present in high-density regions. These results provide important insights for studying the excitation mechanism of EMIC waves.