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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 m^2^ unit cell), there are about 8E25 atoms exposed on a smooth surface, more on a rough surface. The tube plus rotor might have 1E26 atoms exposed. 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 plasma, and the rotor and track will disintegrate. 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 m^2^ 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.
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If the average velocity of the material in the gap is half of the rotor speed, and the thermal velocity variance around that average is also half of the rotor speed (WAG), then the thermal energy of a gas goes up as half the rotor velocity squared times the nuclear mass. For carbon, and a 14km/s rotor, the energy per nucleon is 0.5*12*7000^2^/6.0221E26 = 4.9E-19J = 3.05eV = 12000K. The bond energy of carbon is 3.6eV, and the ionization energy of carbon is 11.3eV, For carbon, and a 14km/s rotor, the energy per nucleon is 0.5*12*14000^2^/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 is 11.3eV. Assume the particles are knocked loose at relatively low energy, then are heated from multiple inelastic wall collisions.
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The gap will probably contain a mix of single carbon atoms and a few 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 [[ http://en.wikipedia.org/wiki/Saha_ionization_equation | 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 } $

|| Temp || equation RHS || <-4> number density /m^3^ ||
|| Kelvin || /m^3^ || @1E-7Pa || ions || @1E-10Pa || ions ||
|| 293.15 || 6.52E-169 || 2.47E+13 || 4.01E-78 || 2.47E+10 || 1.27E-79 ||
|| 500.0 || 1.75E-88 || 1.45E+13 || 5.03E-38 || 1.45E+10 || 1.59E-39 ||
|| 1000.0 || 2.75E-31 || 7.24E+12 || 1.41E-09 || 7.24E+09 || 4.46E-11 ||
|| 2000.0 || 1.83E-02 || 3.62E+12 || 2.58E+05 || 3.62E+09 || 8.15E+03 ||
|| 3000.0 || 9.65E+07 || 2.41E+12 || 1.52E+10 || 2.41E+09 || 4.37E+08 ||
|| 4000.0 || 7.96E+12 || 1.81E+12 || 1.52E+12 || 1.81E+09 || 1.81E+09 ||
|| 5000.0 || 7.64E+15 || 1.45E+12 || 1.45E+12 || 1.45E+09 || 1.45E+09 ||
|| 6000.0 || 7.83E+17 || 1.21E+12 || 1.21E+12 || 1.21E+09 || 1.21E+09 ||
 
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 will be relatively easy to manipulate with magnetic fields, and 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.

It will be interesting to see if the high rotor temperatures after a launch will anneal the graphite, or shake some loose!
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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 ejecta particle on the opposite surface can be treated independently.

For some interesting videos of simulated nanoparticle impacts, see the 11 mile/sec ( 17.7 km/sec ) impact movies at the bottom
of [[ http://www.thp.uni-duisburg.de/~kai/index_1.html | 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?

MORE LATER

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 getters and chemisorption.

MORE LATER

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.

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 is 11.3eV. Assume the particles are knocked loose at relatively low energy, then are heated from multiple inelastic wall collisions.

The gap will probably contain a mix of single carbon atoms and a few 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 }

Temp

equation RHS

<-4> number density /m3

Kelvin

/m3

@1E-7Pa

ions

@1E-10Pa

ions

293.15

6.52E-169

2.47E+13

4.01E-78

2.47E+10

1.27E-79

500.0

1.75E-88

1.45E+13

5.03E-38

1.45E+10

1.59E-39

1000.0

2.75E-31

7.24E+12

1.41E-09

7.24E+09

4.46E-11

2000.0

1.83E-02

3.62E+12

2.58E+05

3.62E+09

8.15E+03

3000.0

9.65E+07

2.41E+12

1.52E+10

2.41E+09

4.37E+08

4000.0

7.96E+12

1.81E+12

1.52E+12

1.81E+09

1.81E+09

5000.0

7.64E+15

1.45E+12

1.45E+12

1.45E+09

1.45E+09

6000.0

7.83E+17

1.21E+12

1.21E+12

1.21E+09

1.21E+09

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 will be relatively easy to manipulate with magnetic fields, and 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.

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

MORE LATER

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 ejecta particle on the opposite surface can be treated independently.

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?

MORE LATER

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 getters and chemisorption.

MORE LATER

Spalling (last edited 2011-06-14 15:27:32 by KeithLofstrom)