Propagation velocity in long helical coils.
I believe I have solved the propagation equation numerically.
The surprising result is the velocity as a function of wavelength repeats
with a similar form to a 1/2 wave resonance. In fact beating between the
coupling function and wavelength.
This produces several possible modes of propagation at least in very long
The effect should readily be detectable in a coil 15 diameters long and
in the progression of harmonics in a smaller coil i.e. the frequencies will
be both higher and lower than a 1/4 wave progression with constant
dispersion. I will post the results when I have them tidy.
Sorry its only numeric I know this is not much better than simulation but
diabolical integrals are hard even for waveophiles.