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Author: Scott E Kruger
Requested Type: Pre-Selected Invited
Submitted: 2018-02-28 12:38:16


Contact Info:
Tech-X Corporation
5621 Arapahoe Ave
Boulder, CO   80026

Abstract Text:
It is well-known that the low-velocity limit of Einstein's
Special Relativity is Newtonian mechanics, which is Galilean
covariant. In 1973, Le Bellac and Levy-Leblond [1]
presented two mutually-incompatible, Galilean covariant
limits of Maxwell's equations (the electro-quasistatic (EQS)
and magneto-quasistatic (MQS) regimes). These limits are
valid for low-frequency, long-wavelength regimes. Formal
investigations of these two limits are useful for engineering
applications [2], and in interpreting many laboratory
experiments [3]. Here, a unified derivation [4] is
presented of these two limits and of the Darwin limit, the
only low-velocity limit presented in the most popular
graduate-level EM textbook [5]. To gain intuition, the
relationship of these limits to circuit equations is briefly
reviewed. Applying these formal investigations to plasmas
provides a new way of looking at old concepts. The EQS
limit provides a new approach to studying collisional
sheaths, and may offer a better approach than the more
commonly-used Darwin approximation. The quasineutrality
approximation is seen as a natural consequence of many
particles within a Debye sphere and leads to the same
equations as the MQS limit, also known as the ``pre-Maxwell
equations'' in the plasma physics literature [6]. This
view of quasineutrality is more illuminating than the more
typical n_e ~ n_i formulation of quasineutrality.

[1] M. Le Bellac, J.M. Levy-Leblond, ``Galilean
Electrodynamics'', Nuovo Cimento B 14, 217 (1973).
[2] H.H. Woodson and J.R. Melcher, Electromechanical Dynamics,
Wiley, New York (1968).
[3] G. Rousseaux, ``Forty years of Galilean Electromagnetism:
1973-2013'' EPJ Plus, 128, 105207 (2013)
[4] Kruger, to be submitted to American Journal of Physics
[5] J.D. Jackson, Classical Electromagnetics, (Wiley, New York, 1999, 3nd ed.)
[6] J.P. Freidberg, Ideal Magnetohydrodynamics (Plenum Press, New York, 1987).