Non-equilibrium statistical mechanics tool for the study of the Earth's radiation belts: AnalytIcal and computational results.

Abstract:

Throughout our lives we have witnessed the interaction between the planet we inhabit and our star. The Earth's magnetosphere is one of its main consequences, originated by the interaction of the Earth's magnetic field and the solar wind. The solar activity is the main driver of this interaction, giving rise to many natural phenomena that may intervene in our daily lives, such as geomagnetic storms, responsible for affecting navigation instruments. Many effects of this interaction are permanent, for example the radiation belts, composed of charged particles that were trapped in the magnetic field, whose variability in the outer belt is intimately related to solar activity and the solar wind. Most of these phenomena are mediated by collisonless plasma processes, in which the presence of long-range interactions gives rise to stationary states (but not thermodynamic equilibrium) described by non-Maxwellian distributions such as the kappa distribution. An interesting problem in plasma physics, when approached from the point of view of non-equilibrium Statistical Mechanics is to obtain properties of collisionless plasmas, through the Vlasov equation, that corresponds to the Liuoville theorem when the Hamiltonian describes electromagnetic interactions. Here, by means of theoretical analysis and numerical calculations we show that starting from the Vlasov equation, and using a classical analog of Ehrenfest theorem, it is possible to derive relations for the expectation values of time-dependent observables. For this case, the three adiabatic invariants are studied indirectly, using an expression for average magnetic moment, pitch angle, and radius of particle orbits. We derive the main equations and perform test particle computer simulation in order to compare and test the Ehrenfest approach. We expect our results to be a good indication to consider the Ehrenfest procedure as a useful tool to address widely studied plasma systems as is the case of the outer radiation belt.