Chapter 12 - The Kappa-Shaped Particle Spectra in Planetary Magnetospheres

Abstract

The kappa distribution function has become an essential form for analyzing trapped distributions of charged particles in space. It is loosely based on the Maxwellian distribution and can be thought of as a generalization of it, specifically with the capacity to describe higher fluxes at high energy, i.e., exhibiting a power law tail at the highest energies that roll over at lower energies to become Maxwellian at the lowest energies. Given that the charged particle populations themselves can have many different kinds of sources (solar wind, atmosphere, volcanic moons, etc.) and sinks (collisions with ambient neutrals or moon or ring surfaces, reconnection, etc.) and move under the influence of strong and dynamic planetary magnetic fields, it is advantageous to have a function flexible enough to capture the essential properties of entire particle distributions, e.g., plasma (<1keV) and energetic ions (>5keV). However, some distributions are well modeled by combinations (or modifications) of kappa distributions, since the most accurate quantitative characterizations often need even more flexibility than afforded by the standard kappa function. In this chapter we will review the use of kappa distributions to describe charged particles in the magnetospheres of the gas giant planets (Jupiter, Saturn, Uranus, and Neptune) and the inner planets (Earth and Mercury) that have allowed the determination of physical quantities of the plasma and energetic particle spectra such as temperatures, densities, pressures, spectral indices, and convection bulk velocities for one or more species, as available. These are critical quantities for understanding the structure and dynamics of magnetospheres. The dependence of these quantities on spatial and magnetic field parameters has rendered the kappa distribution a powerful diagnostic tool for understanding processes in space plasma physics. We also consider the degree to which the kappa distribution succeeds or fails to characterize planetary particle distributions under different conditions.