Mathematical Models of Magnetospheric Convection and its Coupling to the Ionosphere

Abstract

The phrase ‘magnetospheric model’ can have several different meanings. Here I am using the term ‘model’ in the sense described by Parker (1968): “We construct idealized and simplified theoretical models for the purpose of demonstrating how the basic laws of physics lead to a certain observed effect.” A model in this sense is a solution of the equations that describe the system under consideration. Obtaining an exact solution of the equations governing a system as complex as the magnetosphere is clearly impossible, and to construct a theoretical model the equations must be simplified (often drastically) to the point of tractability. The aim is to isolate those aspects of the physical situation that are essential to the particular phenomenon one is attempting to understand. One thus proceeds by solving the basic equations under a variety of simplifying assumptions and noting what assumptions are required to reproduce the essential features of the phenomenon under study. Of course, no model will predict in precise quantitative detail all the features of the observations, but then our primary goal is understanding, not forecasting.