Gene Fuller wrote:
Isw = 2Io cos (kz) cos (wt)

What can be seen immediately is that the standing wave current still has
exactly the same time dependence that the traveling waves had. The
magnitude of the current is now a function of z, unlike the constant
magnitude in the traveling waves. The "current" is still defined as
above, namely the charge that moves back-and-forth in the z-direction.

On the contrary, when kz is not linked by a plus or minus sign
to wt, the wave doesn't move anymore. Maybe you need a review?

Gene, you are a genius. Why didn't I think of that? I recognize
that equation from "Optics", by Hecht. Pick any point, 'z', and
see what you get. Hecht says, "It doesn't rotate at all, and the
resultant wave it represents *DOESN'T PROGRESS THROUGH SPACE* - it's
a standing wave." The RF equivalent of a standing wave of light that
doesn't progress through space is an RF standing wave that doesn't
progress through a wire. That's what I have been telling you guys.
Standing waves don't move. Standing wave current doesn't flow!
Even in empty space, a light standing wave doesn't progress
through space, i.e. IT DOESN'T MOVE!
That is on page 289 of "Optics", by Hecht, 4th edition.

From "Fields and Waves ...", by Ramo & Whinnery, in describing the
standing wave situation: "The total energy in any length of line
a multiple of a quarter wavelength long is constant, *merely
interchanging between energy in the electric field of the voltages
and energy in the magnetic field of the currents*." Again, proof
that standing wave energy doesn't flow. It just stands there
being exchanged between the E-fields and the H-fields.
That is from page 40 of "Fields and Waves in Communications
Electronics", by Ramo, Whinnery, and Van Duzer.

Now I did make a mistake in what I said earlier and I apologize for
that. I said the energy in the E-field and H-field exchanges at a
"point" on the line. Obviously, since a current maximum occurs at
a voltage zero, that can't be true so I mis-spoke. Since the voltage
maximum is 1/4 wavelength away from the current maximum, as Ramo &
Whinnery say, one has to consider 1/4WL of line, and not a point as
I said.

Consider a 1/4WL section of line with a voltage maximum at Z and
a current maximum at Z+(1/4WL). The current at Z is zero and the
voltage at Z+(1/4WL) is zero. The net energy in that 1/4WL of line
is constant. No net energy is flowing into or out of that 1/4WL
of line. At some point the E-field energy is strongest toward
the Z end and 1/4 cycle later, it is strongest toward the Z+(1/4WL)
end. Since there is no net energy flow into or out of the line,
there is no net current flow into or out of the line.

The current oscillation factor (wt) is now decoupled from "z", unlike
the traveling wave case. The "wave" is stationary. The current itself,
however, behaves exactly the same as in the case of the traveling waves.

Sorry, you are wrong there, Gene. On that same page, Hecht says, "The
standing wave does not move through space: it is clearly not of the
form f(x +/- vt). For your equations that statement would be: The
standing wave current does not move through the wi it is clearly
not of the form f(z +/- wt). When you separate the 'z' function from
the 'wt' function, the wave doesn't move anymore. It, well, it just
stands there, like a good little standing wave.

Of course there are important differences in radiation patterns for
traveling waves and standing waves. The magnitude of the current is
different along the wire. However, except at the standing wave nodes,
the standing wave current is very real and non-zero.

And stationary as Hecht says. Your own equation indicates that it
is stationary, i.e. not moving.

I am almost embarrassed to write this, ...

As you should be for not realizing that [Isw = 2Io cos (kz) cos (wt)]
is "clearly not of the form f(z +/- wt)", i.e. of the form of a current
traveling wave that moves. Time to refresh you memory on that subject.
--
73, Cecil http://www.qsl.net/w5dxp