The assumption here is that the exhaust is in the form of a gas.
Once it passes through the constriction of the rocket nozzle, it expands (the effect is to turn thermal random motion of the particles of the exhaust into directed velocity).
Explain how "it expands" does not equate to expanding beyond the boundary of the shielding.
After leaving the bell, there are no more restrictions to expansion of the gas aside from the small amount of matter in space.
Again, explain how "it expands" does not equate to expanding beyond the boundary of the shielding.
And how it cools to background radiation levels BEFORE "it expands" hits the shield boundary.
Because THAT is the issue you've been skipping.
And again, so what?
Because "stealth" probably does not include "dying of old age 200 years before getting out of your own back yard".
Then use physics to make that argument not assertions that I brought up Voyager.
I already have. But you keep skipping over it. I just did it again at the beginning of this post.
Here it is again:
PHYSICS says that the exhaust will expand. Eventually the exhaust cloud will be larger than the area covered by the "shield". At which time the exhaust will be visible.
You claim that the exhaust will cool to the same level as the background radiation before that. Yet you do not explain HOW it will cool that much.
You keep confusing "cool" with "background radiation". Going from 3,000 K to 2,000 K is "cooling". But 2,000 K is not the same as "background radiation".
Stealth isn't perfect. It would be relatively hard against large, sensitive detectors.
Then it is not "stealth".
You are not "invisible" if you depend upon the enemy being blind.