I would dissagree with this last statement. The root mean square
is a type of averaging (not really just the average though), so how
could it be a function of position??
Well, not surprising. You seem to dissssagree with just about
everything...
The RMS is of course an average, "the square root of the mean
[average] squared value...," but it's a time average, not a position
average. There is an RMS current associated with every point along
the line, and because of standing waves, it's not the same everywhere.
Similarly with RMS voltage. If you wish, you can use instantaneous
current and voltage and integrate over time as well, but that's just
performing the RMS function. Putting it another way that's even
easier to see, would you expect the RMS current in my refrigerator
power cord to be the same as in my blender power cord? Clearly, RMS
current CAN be a function of location. And with standing waves, or
with attenuation along the line, or both, it SHOULD be pretty clear
that it can be a function of position along a TEM line.