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\begin{document}

\title{An Analysis of Magnetosphere-Ionosphere Coupling That Is Independent of
Inertial Reference Frame}



\author[1,1]{Anthony James Mannucci}%
\author[2,2]{Ryan McGranaghan}%
\author[1,1]{Xing Meng}%
\author[1,1]{Olga P. Verkhoglyadova}%
\affil[1]{Jet Propulsion Laboratory, California Institute of Technology}%
\affil[2]{Jet Propulsion Laboratory}%


\vspace{-1em}



  
  \date{June 14, 2024}


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\begin{abstract}
This paper analyses magnetosphere-ionosphere (MI) coupling from a
perspective that is independent of inertial reference frame, explicitly
acknowledging the role of the principle of relativity in MI coupling.
For the first time in the context of MI coupling, we discuss the
literature on the low-velocity limit of the theory of special relativity
applied to electrodynamics. In many MI coupling theories, a particular
low-velocity limit applies, known as the ``magnetic limit''. Two
important consequences of the magnetic limit are: 1) Maxwell's equations
cannot contain a displacement current and be consistent with the
magnetic limit and 2) the magnetic field is not modified by currents
created by charge densities in motion, thus charge density is
approximately zero. We show how reference frame-independent descriptions
of MI coupling require that ion-neutral relative velocities and
ion-neutral collisions are key drivers of the physics. Electric fields,
on the other hand, depend on reference frame, and can be zero in an
appropriate frame. Currents are independent of reference frame and will
flow when the electric field is close to zero. Starting with the same
momentum equations that are typically used to derive Ohm's law, we
derive an equation that relates the perpendicular current to collisions
between ions and neutrals, and electrons and neutrals, without reference
to electric fields. Ignoring the relative motion between ions and
neutrals will result in errors exceeding 100\% for estimates of high
latitude Joule heating during significant geomagnetic storms when
ion-neutral velocity differences are largest near the initiation of
large-scale ion convection.%
\end{abstract}%



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