Meaning of kappa

For vacuum plane waves it is the magnitude of wavenumber, in other circumstances it is related vorticity by
curl v = kappa v
so in general it is a fundamental property of the of the vacuum electromagnetic field. Its meaning is discussed by Reed in some depth, and I am just about to study the book by March kindly sent by Steve Bannister. This book will probably have many valuable new solutions to vacuum electromagnetism. The plane wave is a mathematical idealization with infinite lateral extent. The new Beltrami solutions will have finite lateral extent. As you know Beltrami structures occur in vacuum electrodynamics, plasma flow, hydrodynamics, aerodynamics and cosmology. We have just made the important discovery that the space part of the Cartan identity is a Beltrami equation (see below), so the Cartan identity has a rich variety of Beltrami solutions. This is a sudden large leap forward in understanding.

In a message dated 21/02/2014 17:22:13 GMT Standard Time, writes:

Myron . If Kappa is a constant what might be its physical significance? something like vorticity?torsion? or viscosity ,permittivity, reynolds type number of the vacuum?? Just thinking out loud Regards Norman

On 2/21/2014 11:04 AM, EMyrone wrote:

Many thanks to Horst for checking this, finding the important result that kappa must be a constant independent of X, Y and Z. Agreed about Eq. (35). Eq. (24) follows from Eq. (23) because
del x bold = 0
where
x bold = omega sup a sub b x A sup b

so curl x = kappa x
which is eq. (24). using this result in eq. (27) gives eq. (28).

In a message dated 21/02/2014 12:57:30 GMT Standard Time, writes:

In eq.(9) a factor of kappa is missing at the RHS. Putting this equation into Maxima gives the solution
kappa = constant,
ie kappa is not a function of X,Y,Z. This is obvious because from eq. (9) follows
del (kappa) = – del (kappa),
so the divergence must vanish.
In eq.(35) a kappa is missing at the RHS.
I do not understand how (24) follows from (23).
Similarly: how does (28) follow from (27): Obviously the curl A terms have been compared, but there are additional terms. Or has omega x A = 0 been assumed?
Horst

EMyrone hat am 21. Februar 2014 um 12:18 geschrieben:

These are given in eqs. (9), and eqs. (31) to (35). The magnetic and electric fields, the vector potential, the spin connection vector, and the Cartan identity are all Beltrami equations with a very rich variety of intricate solutions, all with longitudinal solutions, all indicating finite photon mass. The original B(3) field is now recognized as a special case for plane waves and some plane wave equations are summarized in this note. So the standard model of physics is comprehensively and completely refuted in yet another way because Beltrami fields are observable experimentally, including their longitudinal components. In the standard model there are no longitudinal components of the free field. This absurd and dogmatic idea violates geometry, but is needed for zero photon mass, and is needed for the Higgs mechanism. In consequence there is no Higgs boson.

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