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Published October 2023 | Published
Journal Article Embargoed

Energetic electron tail production from binary encounters of discrete electrons and ions in a sub-Dreicer electric field

  • 1. ROR icon California Institute of Technology


During transient instabilities in a 2 eV, highly collisional MHD-driven plasma jet experiment, evidence of a 6 keV electron tail was observed via x-ray measurements. The cause for this unexpected high energy tail is explored using numerical simulations of the Rutherford scattering of a large number of electrons and ions in the presence of a uniform electric field that is abruptly turned on as in the experiment. When the only active processes are Rutherford scattering and acceleration by the electric field, contrary to the classical Fokker–Planck theory of plasma resistivity, it is found that no steady state develops, and instead, the particle kinetic energy increases continuously. However, when a power loss mechanism is introduced mimicking atomic line radiation, a near steady state can develop and, in this case, an energetic electron tail similar to that observed in the experiment can develop. The reasons underlying this behavior are analyzed, and it is shown that an important consideration is that Rutherford scattering is dominated by the cumulative effect of grazing collisions, whereas atomic line radiation requires an approximately direct rather than a grazing collision.

Copyright and License

© 2023 Author(s). Published under an exclusive license by AIP Publishing.


This study was supported by NSF Award No. 2105492 and AFOSR Award No. FA9550–21-1–0379.


Paul M. Bellan: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Resources (lead); Software (lead); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead).

Data Availability

Raw calculated velocity distributions will be posted on the Caltech archival server https://data.caltech.edu.

Conflict of Interest

The authors have no conflicts to disclose.



The files will be made publicly available on October 1, 2024.

Additional details

October 26, 2023
December 5, 2023