Quasi‐static magnetospheric MHD processes and the “ground state” of the magnetosphere

Abstract

From the viewpoint of magnetic equilibrium and convection theories, we discuss whether there exists a theoretically well‐defined ground state of the Earth's magnetosphere. As a basis for this discussion, we review the quasi‐static MHD theory and show in a two‐dimensional (2‐D) model that the convecting magnetosphere can (mathematically) reach a steady state. The steady state configuration has fairly stretched magnetotail field lines and is, therefore, likely to be unstable to the tearing mode instability which ultimately leads to substorm onset in magnetotail regions with stretched field lines. We present an interpretation of the substorm phenomenon in terms of sequences of quasi‐static MHD equilibrium states and argue that, under the influence of convection, magnetic substorms occur periodically in Earth's magnetosphere, thus being an integral part of the entire convection cycle. After explosively releasing plasma and magnetic field energies in a substorm, the magnetosphere starts the convection process again from a low‐energy state. In addition to “smooth” tail field configurations, there exist oscillatory equilibrium tail structures with lower potential energy.We discuss the concept of the ground state of the magnetosphere within the context of 2‐D quasi‐static MHD models for the near‐Earth magnetosphere. However, we are unable to find a definition of a single magnetospheric ground state that is conceptually simple and computationally feasible. The term “ground state” denotes the lowest energy state of a system, which for a magnetosphere in quasi‐static force equilibrium is the empty vacuum magnetic field configuration with zero thermal plasma pressure. The real magnetosphere never approaches that state. Therefore we propose the term “average magnetosphere” for defining a baseline configuration that corresponds to average solar wind conditions. Earth's magnetosphere is convectively driven and powered by the solar wind. Thus all potential energy states W = ∫ [P/(γ − 1) + B²/2µ0] dV that belong to a particular convection time sequence between substorm events are transient in time. Therefore the newly defined “average magnetosphere” has a potential energy 〈W − Wvacuum〉 representing the time average of equilibrium states over the substorm cycle. Thus a “quiet” magnetosphere would have a net potential energy lower than the average, whereas an “active” magnetosphere would have a higher energy. It is an unresolved theoretical problem, however, to determine the lowest and highest possible energy states for the magnetosphere that are compatible with the thermodynamic condition of quasi‐static convection.Three‐dimensional (3‐D) magnetospheric equilibria have not been computed yet, but we describe our experience with Stern's stretch transformations and a magnetofrictional method for calculating 3‐D magnetospheric MHD equilibria.