Abstract
Dispersion relations from the Darwin (a.k.a., magnetoinductive or magnetostatic) model are given and compared with those of the full electromagnetic model. Analytical and numerical solutions show that the errors from the Darwin approximation can be large even if phase velocity for a low-frequency wave is close to or larger than the speed of light. Besides missing two wave branches associated mainly with the electron dynamics, the coupling branch of the electrons and ions in the Darwin model is modified to become a new artificial branch that incorrectly represents the coupling dynamics of the electrons and ions.
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