Quantitative models of the magnetosphere

Abstract

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 ...

LLL electron and proton spectrometer on NASA's Orbiting Geophysical Observatory 5

“…Assuming adiabaticity, we find that the equatorially mirroring particles follow contours of constant B. Constant-B contours obtained by Fairfield (1968) for an average magnetosphere are shown in Fig. 30, Conversely, as shown by Roederer (1967Roederer ( , 1969, particles with small equatorial pitch-angles drift so as to keep the length of their bounce path approximately constant, all-the-while maintaining a constant mirror field. If, for example, we examine data at 9 R_ and 0900 local time and contrast them with data at 9 R £ and 1500 local time, we might expect to find changes in electron fluxes having pitch-angles near 90 deg.…”

Seasonal cusp radiation belt on dayside magnetosphere

“…2b) exhibits three local minima with related two local maxims as is was predicted in [3] on the base of MeadWilliams model. The picture for an autumn equinox does not differ significantly from the spring equinox one.…”

“…possessing a hole on its dayside. Roederer [1969] [3] basing on MeadWilliams model [4] accounting magnetospheric tail current found even two bifurcation points related to three minima and two maxima at the subsol meridian.…”

High Latitude Boundary of the Stably-Trapped Radiation Zone on the Day-Side of the Magnetosphere

“…The 'brim' region covers the off-equatorial minima of magnetic field intensity in the H-T model along field lines of force that are close to the day-side magnetospheric boundary, indicating that particles are bouncing back and forth within this brim region. The off equatorial minima are also found in the M-W magnetosphere in addition to the minimum on the equatorial plane, Roederer (1969), however, found no topological connection of drift paths of particles between the night-side equatorial region and the off-equatorial minimum-B region in the day-side magnetosphere. Shabansky (private communication), on the other hand, argues that the appearance of the brim region is not a result of using the H-T model instead of the M-W model but is a result of a severe disturbance of the second invariant of motion of particles on the way of their drift around the earth.…”

“…Detailed description of the two models is not given here, and readers may refer to a fine review article on this topic by Roederer (1969). Briefly, M-W is a 'physical' model which introduces the magnetic field due to the surface current in addition to those of a dipole and of a tail current, H T, on the other hand, is a 'mathematical' model which uses the magnetic field due to an image dipole instead of that of the surface current.…”