Space elevator: up and down cars

Power the space elevator by having at least two tracks, preferably many tracks for redundancy, with up-cars powered by regenerative braking of down-cars. This requires more weight going down than going up, which should be no trouble once we start mining the moon and asteroids. Cars could cycle up then down then up etc.

Cars need to be slow in the atmosphere, but outside the atmosphere the faster they go the less weight they add to the elevator and the less food passengers need to bring along, so faster is better. Escape velocity and beyond would be great if you can do it. Cars should use electromagnetic propulsion, like a railgun, rather than actually touching the elevator. Cars would be very sensitive to fast oscillations.

The space elevator needs to damp fast oscillations. Have the elevator be a rigid cylindrical shell, like bamboo, tens of meters across, with fins sticking out as tracks, and with a heavier cable running down the middle. Each part of it needs to be super-strong self-supporting space elevator stuff, but the central cable can have fast oscillations while the outer shell and tracks have to stay steady for the cars. Fast oscillations in the outer shell and tracks can be dumped into the central cable by pushing and pulling. The outer shell can have oscillations too, but only low enough frequency ones that the cars experience them as gradual movements rather than jolts.