A clear understanding of the basic forms of motion of charged particles in the magnetic and electric fields of the outer magnetosphere is an essential ingredient to the study of the earth's radiation belts and plasma. To achieve this, one must work with a reliable quantitative model of the magnetospheric field. The main purpose of any such model is to provide a mathematical description of the field that is reasonably accurate within a given spatial and temporal domain and that can be used to analyze in a quantitative way any proce• influenced or governed by this field in the corresponding domain. In this review, magnetic field models of the magnetosphere are critically examined and their fit to in-situ field measurements is discussed. Spe.cial attention is paid to the analysis of typical long-term time variations of the field configuration and the matching changes in model parameters. Implications for adiabatic particle motion, such as she11 geometry, regions of pseudo-trapping, and adiabatic effects of slow time variations of the field, are analyzed.
Why do we want a quantitative model of the magnetosphere?
How do we test the validity of a model? 3. How can we build long-term time variations into a model? 4. What needs to be done in the near future to improve the quantitative description of the magnetospheric field?Each of these questions will be discussed, in turn, in the four sections that follow.
THE NEED FOR A MAGNETOSPHERIC MODELThe broad purpose of a magnetospheric model is to provide a mathematical description of the field (analytical or numerical) that is reasonably accurate within a given limited spatial and temporal domain and that can be used to 77 78 JUAN G. 1tOEDERER study in a quantitative way any physical process influenced or governed by this field. This means that whenever one refers to a given model, one has to specify its spatial domain of validity, the time interval to which it is to be applied, and the type of physical processes for whose study the model is intended.Our discussion will be restricted to the magnetospheric domain between, say, 4 and 15 R• from the center of the earth, which we (arbitrarily) define as the 'outer magnetosphere.' Beyond about 4 R• only the dipole terms of the int. ernal-field expansion survive, making its representation easy. Beyond about 15 R• we essentially have 'pure tail field,' a subject discussed in another review paper at this symposium [Ness, 1969]. Only quiet or slightly disturbed intervals of time will be considered. In other words, only slow time variations of the field configuration will be envisaged.Among the physical processes whose description requires a magnetospheric model, six are described in the following paragraphs a. Trapped-particle motion. There has been a tendency in the past to use a dipole field configuration as a first approximation in the treatment of particle motion. However, the azimuthal asymmetry of the magnetic field in the outer magnetosphere does introduce quite important differences in the particles' kinematic behavior, which ...