Quantitative models of magnetic and electric fields in the magnetosphere
In order to represent the magnetic field B in the magnetosphere various auxiliary functions can be used: the current density, the scalar potential, toroidal and poloidal potentials, and Euler potentials -- or else, the components of B may be expanded directly. The most versatile among the linear representations is the one based on toroidal and poloidal potentials; it has seen relatively little use in the past but appears to be the most promising one for future work. Other classifications of models include simple testbed models vs. comprehensive ones and analytical vs. numerical representations. The electric field E in the magnetosphere is generally assumed to vary only slowly and to be orthogonal to B, allowing the use of a scalar potential which may be deduced from observations in the ionosphere, from the shape of the plasmapause, or from particle observations in synchronous orbits.