John Popelish wrote:
"it seems that these references are not particularly concerned with
dimensions of the coil with respect to wavelength, or to the mode of
propagation within the coil.

OK. I gave an example of a traveling wave tube which uses a coil
specifically to retard wave progress ao that an electron beam could keep
up with a signal winding its way through the coil.Terman describes the
Traveling Wave Tube (TWT) starting on page 678 of his 1955 edition of
"Electronic and Radio Engineering".

Here is another version of how the TWT works. The TWT was developed to
provide wideband gain, about 10 to 60 dB over 10% of the operating
frequency or more, and produce a power output of one kilowatt, if
needed.

The TWT consists of an electron gun similar to those used in CRTs, a
wire helix, and a collector. The gun at one end of the helix produces a
focused beam of electrons directed through the center of the helix. The
helix is a uniform coil of wire used to slow down the forward progress
of an RF signal fed into the gun-end of the helix inside a glass vacuum
tube. Output is taken from the helix at the collector end of the helix.
The collector and the helix are positively charged. The collector is the
electrode which catches the spent electrons which have traveled through
the length of the tube.

A magnetic field distributed along the length of the TWT is used to keep
rhe electron beam from spreading during flight.

Transfer of power from the direct current of the electron beam to the RF
signal is by velocity modulation of the beam into periodic bunches of
electrons. these accelerating electron bunches generate a stronger
signal along its path. Interaction between the electron beam and the
helix is continuous and accumulative. Amplitude of the signal grows as
it travels down the helix.

The axial wave velocity is fixed by the helix while the initial
eleectron velocity (before modulation) is proportional to the positive
potential on the helix and collector.

The signal to be amplified is fed to the end of the helix nearer the
electron gun. This RF signal travels as a surface wave around the turns
of the helix, toward the collector, at about the velocity of light. The
forward or axial movement of the signal is slower, of course, because of
the pitch and diameter of the helix. This forward movement of the wave
is analogous to the travel of a finely threaded screw where many turns
are required to drive it into position. The signal wave generates an
axial electric field which travels with it along the longitudinal axis
of the helix. This velocity modulates (slows down and speeds up) the
electrons of the beam current.

So, the wave traveling from one end of the coil towards the other is a
"slow-wave" while the wave travelimg around the coil turns is only
slightly slowed below the speed of light. This is how a coil works.
Frequency and coil form matter but don`t change the basics.

Best regards, Richard Harrison, KB5WZI