Introduction

Plasmas, with their inherently high temperatures, may hold the key to the future of efficient power generation, and hence a solution to the world's voracious appetite for energy. In addition to the promise of controlled thermonuclear fusion, now 50 years old, plasmas have the potential to improve the old fashioned internal-combustion engine to unheard of efficiencies, because of their high temperature and low entropy. The essence of all such plasma pipe-dreams lies in confinement of the extremely hot plasma. Confinement hitherto has consisted of various-shaped vacuum vessels wrapped in miles of low-gauge copper wire, backed up by theorists and supercomputer models which attempt to find the island of stability in the ocean of parasitic wave modes. However, as Levitated Dipole Experiment [#!Kesner98!#] has successfully proposed, the lowly dipole field of a simple bar magnet may hold the key to confinement of hot plasma. Not too surprisingly, since a dipole is the simplest magnetic field imaginable, there are many examples of dipole confinement in nature, from the Earth's magnetosphere, to Jupiter, to the Sun, to astrophysical systems. Thus, the study of dipole-trapped plasma is a field in its own right, and the purpose of this paper.

Since the study of laboratory plasmas in strongly inhomogeneous magnetic fields is plagued by the inability to linearize the equations of motion, few, if any, analytic fluid treatments exist. Single fluid treatments such as Magneto-Hydro-Dynamics (MHD) cannot describe the plasma equilibrium due to the strong $\bf\nabla B$ effects, and multi-fluid treatments are at best a discretized solution to what should be a continuous spectrum. Indeed, the Debye length in strongly magnetized plasmas is also not well defined, so that even the assumption of quasi-neutrality only holds on macroscopic, large system-size length scales, as we discussed in our first publication, [#!Sheldon01!#], hereafter SS1. This non-neutrality produces both perpendicular and parallel electric fields that modify the plasma distribution. Without close attention to self-consistency and spacing of energy levels, multispecie treatments (where each specie is a separate energy) are unable to describe these interrelated effects. The consequence of this complexity is that plasma equilibria in a strong dipolar magnetic field possess peculiar non-equilibrium properties, such as discharges and non-thermally heated distributions. These are the properties that we seek to understand and possibly exploit. Our approach, of necessity, will be primarily experimental, with an attempt at heuristic modelling of the physics.

Our goal is to characterize the plasmas trapped in these topologies and to form semi-empirical descriptions of their properties. In section II, we describe the experimental setup and plasma diagnostics. In section III we list the observations. In the discussion section IV we heuristically model the equilibrium properties of the plasma and an empirical model. Finally, in conclusion we show the relevance of these laboratory analogies to space and astrophysical plasmas.