The rotor moves at 14000 meters per second. The track moves at 0 meters per second. They are separated by 1cm of vacuum, with spacing actively controlled by a magnetic field. Sounds like a formula for disaster, right?
One way to characterize the small spacing versus high velocity problem is as a ratio of these two numbers, space/velocity. For the launch loop, this is 1cm/14000m/s or 720 nanoseconds. That seems like a tiny number.
However, the platter of a 3.5 inch hard drive is moving at 14 meters per second, and the spacing between the head and the platter is 10 nanometers. A running hard drive can be subjected to many gees due to unpredictable impact forces, or unexpected power removal. 10nm divided by 14m/s is 720 picoseconds, a thousand times smaller. The head spacing on a hard drive is maintained by airflow, this is called a "flying head". However, there is no other active control, beyond the servo that moves the head laterally across the surface, and removes it very rapidly when the disk shuts down. If power is removed unexpectedly, the energy stored in the spinning platter is used to write buffered data, then move the head to a safe track. A disk drive manages all of this for years of operation without breaking the very fragile head or magnetic platter surface.
In reality, the problem is NOT relative velocities, it is relative energies. The issue in a launch loop is hypervelocity spalling cascades. A sufficiently large particle either rotor or track at 14000 meters per second will have enough energy to kick loose more mass, which may impact the opposing surface and kick loose more.
This is potentially problematic over a range of particle sizes. At the smallest, atoms will strike the side, and trigger spalling. This problem can probably be dealt with by boron plating the interior components, boron tends to absorb atoms below a certain number of electron volts of energy.
At larger sizes, dust will strike the side and vapourise/turn into plasma. This plasma will take up volume and will press on the rotor. However, the high speed is on our side here, the total mass of rotor that will be pressed is large, both because it's moving and because it's multiple kilograms per metre, and hence it will move little and the plasma shoulld eventually be taken out by the vacuum system.
At the gram-sizes it's more iffy, particularly on the turnaround sections which are high g. If you're lucky the fragment will skim along on a layer of plasma until it slows or evaporates. The worse case would be if it ran headlong into an obstruction and explodes the sheath.
Boron is a good possibility. Perhaps a more appropriate coating would be small carbon nanotubes (finally, a use for them!), possibly unrolled as graphene, which would be stronger and less likely to tear loose. The sheath will not be uniform along its entire length, but would have diverter/deflector ridges along the upper surface and capture pockets and vacuum pumps along the lower surface, at frequent intervals. The magnetic field will cause ionized particles to follow curved paths, and this may be useful for moving them out of the gap between the rotor and the sheath.
The turnarounds are easy - there is no weight limit on the complexity of systems to remove or capture debris, and the entire outer side of the turnarounds are available for this. If necessary, a meter of capture system can be located radially outwards from the rotor inside the inner wall vacuum sheath.
I doubt we will be able to theorize optimum spalling mitigation techniques without years of practical experience.
Launch loop is unlikely to be the first use of high velocity energy and momentum storage. Power storage loops, first on land and then along the continental shelf, will scale from small to large and slow to fast, over time. This allows incremental evolution of techniques and a gradual scale-up of velocity. In automated production systems, quality improves with quantity, and launch loop should not be attempted until we are building large scale power loops running at the same (or faster!) speeds, with years of operating experience. First motorcars, then airplanes, then jets, then rockets.
It is unlikely that gram-weight projectiles will appear in the plenum between rotor and sheath unless something is seriously broken and shedding chunks already. There is no place for the gram weight materials to appear from. Again, we will need years of manufacturing experience (including a well-developed quality control program) before we can build launch loops where all the pieces stay put mechanically (electronic failures will be more common but less drastic). The quality levels needed are about the same as a electronic manufacturing can produce now.