Test of Ion Cyclotron Resonance Instability Using Proton Distributions Obtained From Van Allen Probe-A Observations

Anisotropic velocity distributions of protons have long been considered as free energy sources for exciting electromagnetic ion cyclotron (EMIC) waves in the Earth\textquoterights magnetosphere. Here we rigorously calculated the proton anisotropy parameter using proton data obtained from Van Allen Probe-A observations. The calculations are performed for times during EMIC wave events (distinguishing the times immediately after and before EMIC wave onsets) and for times exhibiting no EMIC waves. We find that the anisotropy values are often larger immediately after EMIC wave onsets than the times just before EMIC wave onsets and the non-EMIC wave times. The increase in anisotropy immediately after the EMIC wave onsets is rather small but discernible, such that the average increase is by ~15\% relative to the anisotropy values during the non-EMIC wave times and ~8\% compared to those just before the EMIC wave onsets. Based on the calculated anisotropy values, we test the criterion for ion cyclotron instability suggested by Kennel and Petschek (1966, https://doi.org/10.1029/JZ071i001p00001) by applying it to the EMIC wave events. We find that despite the weak increase in anisotropy, the majority of the EMIC wave events satisfy the instability criterion. We suggest that the proton distributions often remain close to the marginal state to ion cyclotron instability, and consequently, the proton anisotropy values should often be observed near threshold values for ion cyclotron instability. Additionally, we demonstrate the usefulness and limitation of the instability criteria expressed in the form of an inverse relation between the anisotropy and plasma beta.