Electron Power-Law Spectra in Solar and Space Plasmas

Particles are accelerated to very high, non-thermal energies in solar and space plasma environments. While energy spectra of accelerated electrons often exhibit a power law, it remains unclear how electrons are accelerated to high energies and what processes determine the power-law index delta . Here, we review previous observations of the power-law index delta in a variety of different plasma environments with a particular focus on sub-relativistic electrons. It appears that in regions more closely related to magnetic reconnection (such as the 'above-the-looptop' solar hard X-ray source and the plasma sheet in Earth's magnetotail), the spectra are typically soft (delta greater than or similar to 4). This is in contrast to the typically hard spectra (delta less than or similar to 4) that are observed in coincidence with shocks. The difference implies that shocks are more efficient in producing a larger non-thermal fraction of electron energies when compared to magnetic reconnection. A caveat is that during active times in Earth's magnetotail, delta values seem spatially uniform in the plasma sheet, while power-law distributions still exist even in quiet times. The role of magnetotail reconnection in the electron power-law formation could therefore be confounded with these background conditions. Because different regions have been studied with different instrumentations and methodologies, we point out a need for more systematic and coordinated studies of power-law distributions for a better understanding of possible scaling laws in particle acceleration as well as their universality.