Spalling and Sputtering Cascades

The gap between the rotor and the containment tube will be evacuated, but the vacuum will not be perfect. A 5600km long, 7 cm diameter tube has an inner surface of 1.23 square kilometers, and the 5 cm rotor has an outer surface of 0.88 square kilometers. If that vast surface is graphite (layered-graphene hexagonal grid structured carbon, .142nm bonds, 3.8E-17 m² unit cell), there are about 8E25 atoms exposed on a smooth surface, more on a rough surface. It is very unlikely that all those atoms are strongly attached - some will break loose, travel across the 1 cm gap, and impact the opposite side at rotor speed. If that process breaks loose even more atoms, then the population of the gap can grow exponentially. The gap will fill with hot carbon gas, and the rotor and track will disintegrate.

Single Atom Collisions - Plasma, Gas, or Independent Atoms?

For carbon, and a 14km/s rotor, the energy per nucleon is 0.5*12*14000²/6.0221E26 = 1.96E-18J = 12.2eV = 48000K. The sublimation temperature of carbon is 3900K, the bond energy is 3.6eV, and the ionization energy E_i is 11.3eV. Assume the particles are knocked loose at relatively low energy, then are heated from multiple inelastic wall collisions.

The gap may contain a plasma of carbon ions, moving at half of the rotor speed (7000m/s). We can estimate that the mean thermal velocity and energy is on the order of 7000m/s and 3.05eV, for a thermal temperature of 12000K . From the Saha ionization equation we can estimate the density of ionized atoms:

\LARGE { { {n_i}^2 } \over { n_0 - n_i } } = 2 \left( { { 2 \pi m_e k_B T } \over { h^2 } } \right)^{1.5} ~ e^{ -E_i / k_B T }

Here is the estimated energy, thermal speed, ion density, and mean free path as a function of temperature. 1E-7 Pascal is a good lab vacuum, 1E-10 may be possible if the rotor acts as a turbomolecular pump to expelling pumps along the track.

At 1E-7 Pa, the gas is entirely ionized at 5000K. At 1E-10Pa, the gas is entirely ionized at 4000K. These temperatures are far less than the thermal/velocity temperatures associated with 14000 m/s . The ionized atoms have a very long mean free path, and will be relatively easy to manipulate with magnetic fields. When they collide with the walls, they will couple with the electrons in the carbon target surfaces long before they displace any nuclei. They may end up as near-surface interstitials, or just bouncing off the surface; they are unlikely to yield any sputtered secondaries.

However: using the Saha equation may not be valid, given the calculated long mean free path for ions, and the much larger mean free path (smaller cross section) for neutral atoms. The atoms may not have time to thermalize and have electrons removed.

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It will be interesting to see if the high rotor temperatures after a launch will anneal the graphite, or strip outer layers loose!

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Nanoparticle Collisions

Multi-atom nanoparticle collisions will resemble nanometeorite collisions. A large enough collision at a steep enough angle will eject more material than the original hit, but the ejecta will be much smaller particles, and spray out to hit a large area (many square centimeters) of the opposite surface. Chances are this will spread the energy and arrival time such that the collision of each ejected particle on the opposite surface can be treated independently, as above.

For some interesting videos of simulated nanoparticle impacts, see the 11 mile/sec ( 17.7 km/sec ) impact movies at the bottom of this page. The impactors and targets are iron, AMU=56 rather than carbon, AMU=12 . So, the energy carried by the 418 iron atom nanoparticle with a 90 degree impact might be similar to a 10,000 carbon nanoparticle at 14 km/s and a 30 degree impact - the same perpendicular energy. The simulations on Dr. Kadau's webpage were performed with a large supercomputer; it would be interesting to see how much could be accomplished using an nVidia coprocessor and the CUDA programming environment. Would anyone like to try?

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Pumping Systems

There will be diverter chambers along the sides and bottom of the acceleration tube, and on all sides of the incline tube. Hopefully, most atoms and particles will scatter into the diverters, to be absorbed by pumps, getters and chemisorption.

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Wall Breaches and High Volume Air Leaks

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