Review of modeling of losses and sources of relativistic electrons in the outer radiation belt I: Radial transport

In this paper, we focus on the modeling of radial transport in the Earth's outer radiation belt. A historical overview of the first observations of the radiation belts is presented, followed by a brief description of radial diffusion. We describe how resonant interactions with poloidal and toroidal components of the ULF waves can change the electron's energy and provide radial displacements. We also present radial diffusion and guiding center simulations that show the importance of radial transport in redistributing relativistic electron fluxes and also in accelerating and decelerating radiation belt electrons. We conclude by presenting guiding center simulations of the coupled particle tracing and magnetohydrodynamic (MHD) codes and by discussing the origin of relativistic electrons at geosynchronous orbit. Local acceleration and losses and 3D simulations of the dynamics of the radiation belt fluxes are discussed in the companion paper

Review of modeling of losses and sources of relativistic electrons in the outer radiation belt II: Local acceleration and loss

This paper focuses on the modeling of local acceleration and loss processes in the outer radiation belt. We begin by reviewing the statistical properties of waves that violate the first and second adiabatic invariants, leading to the loss and acceleration of high energy electrons in the outer radiation belt. After a brief description of the most commonly accepted methodology for computing quasi-linear diffusion coefficients, we present pitch-angle scattering simulations by (i) plasmaspheric hiss, (ii) a combination of plasmaspheric hiss and electromagnetic ion cyclotron (EMIC) waves, (iii) chorus waves, and (iv) a combination of chorus and EMIC waves. Simulations of the local acceleration and loss processes show that statistically, the net effect of chorus waves is acceleration at MeV energies and loss at hundreds of keV energies. The combination of three-dimensional (3D) simulations of the local processes and radial transport show that the complexity of the behavior of the radiation belts is due to a number of competing processes of acceleration and loss, and depends on the dynamics of the plasmasphere, ring current, and solar wind conditions

Non-variant phenomena in heterogeneous systems. New type of solubility diagrams points

The article gives a general classification of non-invariant points in phase equilibrium diagrams of all possible types. The complete topological isomorphism of the diagrams of fusibility, solubility, and liquid-vapor equilibria in various sets of variables is demonstrated. The stability of mono-variant equilibria near the non-variant points is investigated. Recurrent formulas for calculating the number of topological elements of phase diagrams are given. A previously undescribed type of non-invariant points and phase processes in the solubility diagrams is described and characterized. The last ones have no topological analogs in other types of diagrams. Thus, we have carried out, as far as is available to the authors, a complete classification of invariant points and invariant processes in phase equilibrium diagrams of an arbitrary type and with an arbitrary number of components