Modeling of anisotropy dynamics of the proton pitch angle distribution in the Earth's magnetosphere

Last years the attention to research of anisotropy of the charged particle pitch angle distribution has considerably increased. Therefore for research of anisotropy dynamics of the proton pitch angle distribution is used the two-dimensional Phenomenological Model of the Ring Current (PheMRC 2-D), which includes the radial and pitch angle diffusions with consideration of losses due to wave-particle interactions. Experimental data are collected on the Polar/MICS satellite during the magnetic storm on October 21–22, 1999. Solving the non-stationary two-dimensional equation of pitch angle and radial diffusions, numerically was determined the proton pitch angle distribution anisotropy index (or parameter of the proton pitch angle distribution) for the pitch angle of $90$ degrees during the magnetic storm, when the geomagnetic activity $Kp$-index changed from $2$ in the beginning of a storm up to $7+$ in the end of a storm. Dependence of the perpendicular proton pitch angle distribution anisotropy index with energy $E = 90$ keV during the different moments of time from the McIlwain parameter $L$ ($2.26 < L < 6.6$) is received. It is certain at a quantitative level for the magnetic storm on October 21–22, 1999, when and where on the nightside of the Earth's magnetosphere ($\mathrm{MLT} = 2300$) to increase in the geomagnetic activity $Kp$-index there is a transition from normal (pancake) proton pitch angle distributions to butterfly proton pitch angle distributions. That has allowed to determine unequivocally and precisely the anisotropy dynamics of the proton pitch angle distribution in the given concrete case. It is shown, that with increase of the geomagnetic activity $Kp$-index the boundary of isotropic proton pitch angle distribution comes nearer to the Earth, reaching $L \thickapprox 3.6$ at $Kp = 7+$.