what would happen to flowing electrons in a vacuum if they are not giving any exit point? Lets say theoretically electron flow is captured in a vacuum and not allowed to exit then where would they go? I do not want to know the practical impossibilities of it. And also what would happen if that vacuum was in a glass container?
 A: That's essentially what particle accelerators are doing (even a symple cyclotron). You need magnetic field to curve the path of a moving electron into a circle.
Of course, once the electron is allowed to touch the surface, it's over. So you need to keep it in there. Yes, electrons feel repulsive forces, but moving electron beams also produce magnetic fields and self-focus (they attract laterally) - this is called plasma pinch and is what makes the lightning bolt so narrow and concentrated. When you have a lot of electrons stored in a vacuum ring (or a Tokamak, if you're building a fusion reactor -- although, plasma also contains positive ions, so at least repulsive forces aren't that big of a problem), they themselves are creating a lot of complex electrogmanetic field, and adaptive control is a good idea to keep things confined.
A: The old style tv tubes with an electron gun and a phosphorescent screen had to have a conducting path from the screen to earth to prevent the build up of negative charge on the screen.  If this was not done a reduction of picture brightness would result. Even with this return path for the electrons charges did accumulate on the screen with the result that dust particles were attracted to the outside of the screen.
