TL;DR
This paper analyzes Aristotelian electrodynamics (AE), a plasma regime with strong electric fields, showing how null directions govern AE and how it transitions to force-free electrodynamics, with criteria for AE's validity based on field curvature scalars.
Contribution
It reveals the role of principal null directions and eigenvalues of the field tensor in governing AE and derives a smooth transition to force-free electrodynamics.
Findings
AE governed by principal null directions and eigenvalues.
Force-free electrodynamics as a limit of AE when eigenvalues vanish.
Proposed criteria for AE validity using field curvature scalars.
Abstract
Aristotelian electrodynamics (AE) describes the regime of a plasma with a very strong electric field that is not shorted out, with charge current determined completely by pair production and the balance of Lorentz 4-force against curvature radiation reaction. Here it is shown how the principal null directions and associated eigenvalues of the field tensor govern AE, and how force-free electrodynamics arises smoothly from AE when the eigenvalues (and therefore the electric field in some frame) vanish. A criterion for validity of AE is proposed in terms of a pair of "field curvature scalars" formed from the first derivative of the principal null directions.
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