Jim Kelley wrote:
What happens to the intrinsic energy pre-
existing in those waves before they cancel each other?

The answer the intrinsic energy in the waves where the waves exist is stored
in the transmission line, and nothing happens to energy where waves don't
exist. The waves in question don't convey energy from the source to the
load ...

Of course not because they are destroyed at the cancellation point. But
the energy in the canceled waves is indeed conveyed to the load.

The rate of flow of energy has to be 100 joules/sec since the energy
in those two waves cannot stand still and cannot be destroyed.

The rate of flow of energy "in" those two waves is not 100 Joules per
second.

Of course it is. We know that 50W of reflected power from a mismatched
load has not been re-reflected and tried to continue to flow toward the
source. We know it never gets past the impedance discontinuity. There's
only one thing that can stop a wave in its tracks without dissipation of
energy. That's another wave traveling in the same direction with equal
amplitude and opposite phase as explained on the Melles-Griot web page.
We are therefore forced to deduce that the other wave exists and indeed
it is predicted by Pfwd(|rho|^2) and the s-parameter term, s11*a1. It
doesn't last very long because it is instantaneously canceled as it
is reflected but we know it has to exist and indeed Pfwd1(|rho|^2)
equals 50W, the exact amount of energy we need to accomplish the
wave cancellation process.

The energy does travel forward, but not by way of those two waves.

If it doesn't come from the two canceled waves, where does it come from?
Besides the two canceled waves, only Pfwd1(1-|rho|^2) and Pref2(|rho|^2)
exist and there is not enough energy in those two other wave components
to account for the magnitude of Pfwd2. Hecht, in _Optics_ says the
constructive interference energy (flowing toward the load) comes from
the destructive interference event (toward the source). If the canceled
waves contain no energy then there is no destructive interference energy -
without which constructive interference is not possible.
--
73, Cecil, W5DXP