Modelling the Magnetosphere with Maple

Abstract

Environmental systems are often large and complex. It is by modeling and simulation that such systems can be understood and environmental changes predicted. This approach involves both mathematical (paper and pencil) and computational (numerical) activities. The former requires knowledge and focused concentration to avoid errors in the intermediate steps. Development of skills for the latter component typically represents an obstacle as well. This working landscape is changing with the advent of interactive mathematical systems, like Maple. A Maple document captures the analytic modelling, driven by a large body of mathematical algorithms, as well as numerical experiments, supported with an efficient computational engine. In this paper, we illustrate the application of Maple as a modeling tool to mathematically describe the earth’s magnetosphere. Instead of using empirical data, the description includes a simplified analytic model of the interaction between the solar wind and the earth magnetic field. This allows for plotting and visualization of the relevant phenomena directly from the model. This equation based approach, derived directly from first principles and a fundamental understanding of the magnetosphere, can provide adequate understanding and prediction capabilities without resorting to classical brute force finite element and finite difference simulation models.