Ring current proton dynamics driven by wave-particle interactions during a nonstorm period

Modeling of pitch angle scattering of ring current protons at interaction with electromagnetic ion cyclotron waves during a nonstorm period was considered very seldom. Therefore it is used correlated observation of enhanced electromagnetic ion cyclotron (EMIC) waves and dynamic evolution of ring current proton flux collected by Cluster satellite near the location $L = 4.5$ during March $26--27$, $2003$, a nonstorm period ($Dst > -10$ nT). Energetic ($5$–$30$ keV) proton fluxes are found to drop rapidly (e.g., a half hour) at lower pitch angles, corresponding to intensified EMIC wave activities. As mathematical model is used the non-stationary one-dimensional pitch angle diffusion equation which allows to compute numerically density of phase space or pitch angle distribution of the charged particles in the Earth's magnetosphere. The model depends on time $t$, a local pitch angle and several parameters (the mass of a particle, the energy, the McIlwain parameter, the magnetic local time or geomagnetic eastern longitude, the geomagnetic activity index, parameter of the charged particle pitch angle distribution taken for the $90$ degrees pitch angle at $t = 0$, the lifetime due to wave–particle interactions). This model allows numerically to estimate also for different geophysical conditions a lifetime due to wave–particle interactions. It is shown, that EMIC waves can yield decrements in proton flux within $30$ minutes, consistent with the observational data. The good consent is received. Comparison of results on full model for the pitch angle range from $0$ up to $180$ degrees and on the model for the $90$ degrees pitch angle is lead. For a perpendicular differential flux of the Earth's ring current protons very good consent with the maximal relative error approximately $3.23 \%$ is received.