AN ANALYTICAL SOLUTION OF THE COSMIC RAYS TRANSPORT EQUATION IN THE PRESENCE OF THE GEOMAGNETIC FIELD

Abstract

In this work, I study the propagation of cosmic rays inside the magnetic field of the earth, at distances d≤500 km from its surface; at these distances, the geomagnetic field deeply influences the diffusion motion of the particles. I compare the different effects of the interplanetary and of the geomagnetic fields, by also discussing their role in the cosmic rays transport equation; then, I present an analytical method to solve such an equation through a factorization technique. In this way, it is possible to reduce the initial second-order, partial derivatives differential equation into a more simple, Riccati-like equation, which, finally, can be solved by using standard Runge–Kutta–Merson routines. The results here obtained may have some interest in view of the future AMS (Alpha Magnetic Spectrometer) data, which will be collected at an altitude of about 400 km above the earth surface. Moreover, the study of the propagation of particles having different charges and masses may also help in testing the presence of antimatter and antinuclei in cosmic rays; some theoretical implications of this possibility will also be discussed in the light of the perspectives opened by the AMS Experiment.