I'm going with Drs. Corum on this one. Solve equation 28 for tau, get
beta from equation 4. The phase velocity along the axis of the coil is
omega/beta.

The velocity factor in question is that phase velocity over the speed
of light in a vacuum.

The coil modes are surface waves in a weird coordinate system. Note
that the paper is very explicit in saying they're not TEM.

Throw equation 28 into Mathematica or Matlab or something and solve for
tau. The cases given after equation 28 with all the limitations
appear(ed?) to be a point of some contention, but equation 28 seems
*only* to have the limitation of circumferential symmetry of the
surface waves on the coil.


At the junctions between the wire and the coil, there is a transfer of
energy between the surface wave modes on the coil and the usual antenna
mode (I guess it's TEM?)

The coil is like G-line in that it guides surface waves, but the coil
modes are modes specific to the helical geometry; the G-line surface
waves are specific to the straight-wire geometry.

There is a mode on the helix where the waves go round and round the
turns, but the example given is a traveling wave tube for microwave
amplification, and it seems to me that there are a few turns over a few
inches for *microwave* frequencies.

I am not one to argue with a solution to Maxwell's equations.

-Dan