I understand that the mathematicians' definition of "very" is that if a is a small number and b is a small number then a times b is a very small number.

There will be a small number of deuterium atoms in your friend's tube.

And they will probably get ionised and attracted to the cathode but they are vastly more likely to hit almost anything but another deuterium atom because the fraction of other atoms that are deuterium is small. So the likelihood of fusion is very small.

Unsurprisingly that's different from the state of affairs in a fusor where foreign gases are excluded as far as possible and deuterium is plentiful of the order of ten or a hundred microns of mercury pressure about 10^-4 atmospheres. You might want to compare that with about 10^-9 torr in a CRT (about 10^-12 atm). the difference is so vast it doesn't matter if I'm out by a couple of orders of magnitude here or there.

So previously you said "these various cold fusion scams have frequently been demonstrated to be false."

and I pointed out that 300,000,000K isn't cold.

You said "If producing fusion was only a matter of producing the required high temperature it would be easy peasy presumably it would be happening all the time within the CRT of my old TV."

and that was wrong too.

And you said"What is required is a product of temperature and density for a sufficient time."

so I pointed out that it has plenty of time (unlike an A bomb) and quite a high density.

So, the last thing to address is where you say

"but it is not what most people think of as nuclear fusion. "

Well, it does do nuclear fusion.

It's difficult to see why "most people" wouldn't think of that as nuclear fusion.