Solenoidal components, 0 electrodynamics

In this final section, it is shown that the three magnetic field components of electromagnetic radiation in 0(3) electrodynamics are Beltrami vector fields, illustrating the fact that conventional Maxwell-Heaviside electrodynamics are incomplete. Therefore Beltrami electrodynamics can be regarded as foundational, structuring the vacuum fields of nature, and extending the point of view of Heaviside, who reduced the original Maxwell equations to their presently accepted textbook form. In this section, transverse plane waves are shown to be solenoidal, complex lamellar, and Beltrami, and to obey the Beltrami equation, of which B is an identically nonzero solution. In the Beltrami electrodynamics, therefore, the existence of the transverse 1 = implies that of , as in 0(3) electrodynamics. 

Beltrami fields have been advanced [4] as theoretical models for astrophy-sical phenomena such as solar flares and spiral galaxies, plasma vortex filaments arising from plasma focus experiments, and superconductivity. Beltrami electrodynamic fields probably have major potential significance to theoretical and empirical science. In plasma vortex filaments, for example, energy anomalies arise that cannot be described with the Maxwell-Heaviside equations. The three magnetic components of 0(3) electrodynamics are Beltrami fields as well as being complex lamellar and solenoidal fields. The component is identically nonzero in Beltrami electrodynamics if is so. In the Beltrami... 

The three components of the cyclic theorem (411) are solenoidal, complex lamellar, and Beltrami. This is a remarkable property of Beltrami electrodynamics when recognized as 0(3) electrodynamics for the special case when... 

The Bii] component [which is nonzero only on the 0(3) level] is a solution of the Beltrami equation (885) with k = 0. Therefore, in Beltrami electrodynamics, Bii] is a solenoidal, irrotational, complex lamellar and Beltrami field in the vacuum, and is also a propagating field. The B 1 component in Beltrami... 

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