If we make a hollow tube and create vacuum inside, than apply negative voltage on the wall - what will be the movement of electrons inside when we apply voltage at the ends of this tube? Is it not ideal superconductor?
It will not be an ideal conductor. For an Ideal conductor, the Ohms law should show linear characteristics. Whereas in the case of a vacuum tube there will be some breakdown voltage after which the current will increase rapidly as a function of voltage.
What I mean is that resistance R would be 0. Because there are not obstacles like atoms and their positive nucleus. There is no breakdown voltage because there are electrons injected in the tube and the voltage is AC. So they must oscillate with the voltage without R. The better term is superconductor.
A superconductor from a tube with a vacuum will not work. In a vacuum, there are electric and magnetic fields that disturb the movement of electrons. The fields are created by the atoms of the walls.
But does not the tube make a Faraday cage and block all fields inside. So the force on electrons inside must 0.
Notice also the negative voltage on the walls applied before the current starts to flow. I think it can serve as elastic media (electrostatic interaction is elastic) and so electrons would not loose energy when hitting the walls.
It's all about the scale. If we are talking about the ballistic transfer of electrons, then in an ideal vacuum it can be without resistance. However, any material object creates its own fields. Atoms in a metal have dangling bonds and surface states. Of course, if the pipe diameter is very large, so that the influence of the walls can be neglected, then the resistance associated with these fields can also be neglected. However, in contrast to real superconductivity, here the motion of an electron without resistance is possible only with rectilinear and uniform motion. Of course, this motion can be modulated by the charge on the pipe walls. But is it really going to be a movement without resistance? In fact, it will be the stimulated movement of the electron.
I'm not even talking about the fact that there is always a residual gas in the physical vacuum. It causes the signal to fade. And with real superconductivity, the signal never fades.
Of course you are right about the atoms of the walls and their fields. That's why I propose the walls to be conducting effectively shielding all fields through the Faraday's cage. Why do you think there would be fields inside when a Faraday cage is present? Also the negative field applied by the suggestion on the walls leads to prevent any contact with walls and the interaction of electrons with electric constant field is proved to be elastic (e.g. the Rutherford scattering) so their energy will not change when approaching the walls. They can never touch the walls.
I also can not understand why in case of AC voltage the real superconductor [SC] will not loose energy. Any acceleration leads to dissipation of Energy so the same is in real SC as in vacuum tube.
The attached link to a file could help your question, Dear prof. Ilian Peruhov. I almost answered 5000 questions in RG, I cannot find the paper with the Prof. explanation, you have to search for it, sorry, I don't feel well.
What I found in your link is: "A long copper tube --- two cylinders fell - second slowly -- Feynman says it's a magnet --the guy asked - if superconductor? -- end."
What can this help for interaction with the walls in a vacuum tube with negative voltage? Please explain.
A hollow tube filled with electrons is not superconductor, it is only a perfect conductor. The main difference between superconductor (SC) and perfect conductor: In a SC the kinetic energy of every charge carrier is quantized, so a supercurrent, once established, can be dissipated only by external energy excitations stronger than the kinetic energy quantum. In a perfect conductor the kinetic energy of every charge carrier can increase/decrease smoothly, by arbitrarily small values, so the current dissipates due to vanishingly weak energy fluctuations (thermal, electromagnetic etc.) The energy of free electrons in vacuum can vary by arbitrarily small values, so without external voltage a supercurrent vanishes, since an absolute absence of temperature and radiation is practically impossible.
Well really I see. Thank you. I must change my title to perfect conductor! In fact I imagined something like the optic cable OC but for electrons. The info in OC is transmitted with low losts. Maybe something similar is possible for carring energy with minimal lost based on vacuum tubes?