Rotor Surface Drag
Why to keep your launch loop pumped
Gas ions will hit the surface of the launch loop rotor and pick up speed, then lose it again when they bounce into the stationary walls of the sheath. In the narrow plenum between rotor and sheath, we can expect residual gasses to move at about half the rotor velocity v_r , with comparable thermal velocities. The exact modelling of the interaction requires a much better gas physicist than I, but I can make an estimate.
How many atoms hit the rotor? We can estimate the mass flux rate dot{M} ( Kg/s-m2) from the pressure P_r (Pa = N /m2 = Kg / m s2) and the average impact speed ( v_i , m/s ). Assuming this is a bounce, the momentum and pressure is doubled, so the pressure is half the mass flux rate times the impact speed, P_r ~=~ { 1 \over 2 } dot{m} \times v_i . If we know the pressure and and impact velocity ( presumably v_i ~=~ { 1 \over 2 } v_r we can estimate the mass flux rate dot{M} ~=~ P_r / 4 v_r .
A bouncing atom can bounce off the rotor over a range of velocities, but let's assume the average velocity before impact is half of rotor speed, and after impact is rotor speed. So the power expended by impact per area is Power/Area = { 3 \over 8 } dot{m} {v_r}^2 = { 3 \over 32 } P_r ~ v_r . For v_r = 14000 m/s, and P_r = 1 Pa, that is 1300 W/m2.
The area of a 5 cm diameter, 5200 km loop is π × 0.05 × 5.2E6 = 8.16E5 square meters, almost a square kilometer, and the drag power at 1 Pa would be 1 GW! 1 Pa is the pressure at 80 km, except that is a "cold" Pascal, gas with much lower thermal velocity and thus much higher atomic flux rate, far more than a gigawatt.
So - assume that we enclose the rotor in a vacuum sheath, and keep it pumped to a better vacuum, perhaps with the help of the rotor itself. If the pressure of our hot plasma is 1E-3 Pascal, on the borderline between medium and high vacuum, we can keep total drag loss below a megawatt. In actual fact, there will be breaches, and portions of the loop will be exposed to gas leaks, to be pumped out down the line until a robot can patch the hole. That, and not "typical" surface drag, will dominate drag losses in the launch loop.
Note: The above is a back-of-the-envelope estimate, and should be replaced by detailed calculations based on actual gas behavior and surface collision models. Assuming atomically smooth diamond coatings, such as those on modern hard drive platters, the surfaces will be strong and resistant to impact corrosion, but an impact will occasionally knock loose a carbon atom. The result could be a hypervelocity spalling cascade, and total destruction. Obviously, we will make lots of tests with lower speed PowerLoops before we deploy anything at 14 km/s. This will require years of research and operational experience.