The analytical description of the Earth's ring current proton flux for the pitch angle of 90 degrees

As mathematical model is offered the ordinary differential equation for the analytical description of a perpendicular differential flux of the charged particles in the Earth’s magnetosphere which depends on time and several parameters (the McIlwain parameter, the magnetic local time or geomagnetic eastern longitude, the geomagnetic activity index, parameter of the charged particle pitch angle distribution or the pitch angle distribution anisotropy index but is taken for the pitch angle of 90 degrees at = 0, the average parameter of the charged particle pitch angle distribution on an interval of time of calculation, the lifetime due to wave-particle interactions). Under the certain geophysical conditions and on a time interval approximately no more than three hours (when a geomagnetic activity index = const) or on a greater time interval, when ≈ const, the equation is solved analytically. The simple analytical solution is received which depends on time and several parameters...