These look very good, I am currently preparing note 257(3) which will develop the Beltrami equation in electrodynamics, giving the correct phase factor when photon mass is incorporated, expressing the d’Alembertian in terms of the Beltrami equation, and suggesting generalizations. Then in further notes I will look at the mathematics of how B(3) comes out of a helicoidal flow. Plane waves are of course just models with infinite lateral extent.
Sent: 31/01/2014 11:32:15 GMT Standard Time
Subj: 3D vector graphics
Graphics examples of a vector field
v = (vr, vtheta, vz) = (0, sin(r), cos(r0-r))
in cylindrical coordinates. In the projected X-Y plane the vectors v (red) and curl(v) (black) are parallel, but not in a 3D view, see second image. This is not a Beltrami field, but v and curl(v) are parallel at some places. It is difficult to find a good perspective, best is to rotate the view in computer, then you get the best spatial impression.