Nonlinear effect for anisotropy of charged particle pitch angle distribution at geostationary orbit

The new phenomenological model of a prediction of perpendicular anisotropy index of charged particle pitch angle distribution at geostationary (geosynchronous) orbit (GEO) in the Earth's magnetosphere, and also in any circular orbit depending from the local time LT in an orbit and the geomagnetic activity index $Kp$ is offered. Comparison of model with the numerous experimental data is lead. It is proved, that the general analytical dependence of perpendicular anisotropy index of charged particle pitch angle distribution on GEO received as a first approximation can be used for conditions of magnetically quiet time for quantitative forecasts and comparisons with experimental data on GEO. The nonlinear effect is theoretically predicted for a difference between the maximal value of perpendicular anisotropy index of charged particle pitch angle distribution and the minimal value of perpendicular anisotropy index (in local midnight LT = 0 h) on GEO from the $Kp$-index of geomagnetic activity. The nonlinear effect for anisotropy of charged particle pitch angle distribution will be, possibly, to some extent and on other radial distances from the Earth.