Theoretically, kV field-aligned potentials have been surprisingly hard to explain [1,2]. The highly successful formalism of magnetohydrodynamics (MHD), which generally works well on large magnetized plasma systems, completely excludes the possibility of field aligned potentials for the simple reason that electrons travelling along the field lines would be accelerated by such potentials and quickly redistribute the charge . Second order effects, such as polarization drifts have been shown to provide a very small parallel potential, but always on the order of the thermal energy of the electrons. Despite the very real observational data on parallel fields, theoretical explanations generally fall back on an a priori boundary condition, such as an externally imposed pitchangle distribution, or a large field-aligned current, or the presence of a specific wave model. One explanation for why all previous theoretical efforts have found so little quasi-static parallel potential may perhaps be related to their assumption of quasi-neutrality early in the calculation, and therefore they naturally find only small deviations from it [4,5]. The assumption is normally valid, because unshielded charge can create truly large voltages, so that a few Coulombs at the top of a thundercloud are thought to produce gamma rays !
However, the data are showing that large parallel voltages in plasmas do exist [7,8], and have important consequences for both space physics and astrophysics, much as they do in meteorology. In space physics, we believe parallel potentials explain much of the phenomenology of a geomagnetic storm , and are implicated as a source of the Earth's aurora . At the Sun, parallel potentials may be significant in coronal loops that flare and produce copious X-rays . At Jupiter, observations of beaming electrons near the orbit of Io implicate a parallel acceleration mechanism . In astrophysics, the observation of highly collimated jets arising from rapidly spinning magnetic fields encircled by hot accretion disks are ubiquitous ; seen in young stellar objects (YSO), Herbig-Haro objects, microquasars, galaxies and active galactic nuclei (AGN). If these jets are all a result of parallel potentials, then we may have found a unifying theory to explain their mysterious origin. And since one would expect nonthermal X-rays to be another signature of parallel potentials, it may be that the 50% of the near continuum of discrete sources of the X-ray background observed by Chandra  are all powered by such a mechanism.
The goal of this paper is to motivate the proposal that large parallel potentials can develop in a plasma by considering first space charge ] production in thunderstorms, then spacecraft data taken in the Earth's magnetosphere, followed by observations of astrophysical jets. Finally we present initial results of a tabletop laboratory experiment that is suggestive of the production of parallel potentials much larger than the few eV permitted by standard plasma theory.