Photovoltaic Climber Power

acoustic >> laser >>>>> solar power

This paper is about acoustic power as a superior alternative to photovoltaic power. Before we do so, we must clear away some misunderstandings about photovoltaic power.

The huge PV (photovoltaic) arrays depicted in the 2013 Assessment are far beyond current possibilities, and have components that violate geometry and physical law. Bypassing these show-stopping errors was the initial motivation for this paper.

The key error was the conflation of a photo of the 20x20 square meter Deutsches Zentrum für Luft- und Raumfahrt (DLR) solar SAIL with a solar CELL. The photo shows a small prototype sail spread out over a hangar floor; it cannot support itself in gravity.

A solar sail is a very thin sheet of aluminized plastic, designed to reflect sunlight, creating a tiny "light pressure" of up to 9 microPascals in Earth-radius sunlight. The "small" sail shown might generate a thrust of 2 milliNewtons (minus tilt and inefficiencies), enough to accelerate a 100 kg spacecraft by 600 m/s per year. The best application of solar sails is deep-space interplanetary missions launched down into the Sun's gravity well, where the higher light pressure can provide slingshot thrust to boost the package into outer planet trajectories.

Solar sails are too flimsy to survive in the Earth's gravity well, they generate no electricity.

The hypothetical PV arrays illustrated in the assessment will be heavy (much heavier than a light sail), and they will be under high lateral compressive force if built as shown, so they will need large cross-span spars to prevent buckling. As shown, they can turn less than 180 degrees to track the Sun, so even if they climb out of the Earth's shadow, and are turned 80 degrees from zenith, they collect no light from the Sun within 10 degrees of nadir, and only half power from the Sun within 40 degrees of nadir.

An electrostatic glider structure at the center cannot actually provide electrostatic thrust; the integral of the coulomb force is zero in the center of a conductive ring, and Coulomb forces are quite small at moderate voltages. High voltages will cause destructive arcing. Paschen's law describes the breakdown voltage in low density air, and the vacuum near the Earth is actually very thin, mostly ionized air. The ionosphere is quite conductive; it may conduct lightning to the space elevator tether from discharges on the same magnetic longitude, far to the north and south. Breakdown arcs limit the maximum voltage on photovoltaic arrays to less than 900 volts, below 10,000 kilometers altitude, and to less than 100 kV at GEO orbit. %% reference Fig 13.17 pg 632 Piscane

The main application for space solar /textbf{cells} is Earth satellites in orbital microgravity. Photovoltaic arrays for direct broadcast communication satellites in GEO orbit are long and heavy. Efficiency increases reduce launch weight or increase satellite power (usually the latter). Structural improvements can reduce weight and increase launch vibration survivability. The incentives to improve are strong, but the technology is mature.

Photovoltaic cells have an energy "bandgap", 1.1 eV (electron volts) for silicon. Less energetic photons (and half of sunlight is near infrared) are below the bandgap and produce no power at all. More energetic photons ( green is 2.3 eV ) can be captured, but the photon energy above the bandgap creates no extra power (though it can help with photon capture efficiency).

The best (and hugely expensive!) photovoltaic cells are triple-junction stacked cells, designed to capture three different photon energies and efficiently span more of the sun's spectrum. This expensive complexity increases PV efficiencies by less than a factor of 2; lower cost and lower vibration rocket launch systems may be cheaper in the long run.

Photovoltaic solar cells produce output voltages lower than their bandgap; their large area makes a highly conductive "parasitic diode", which shorts out the cell above the diode's turn-on voltage. For silicon cells at room temperature (300 Kelvin) with a theoretical maximum 1100 millivolt (mV) bandgap voltage, the diode limits output voltage to perhaps 650 mV. The 450 mV difference between bandgap and diode turn-on voltage is proportional to temperature; a cell at 400 K (127 °C) would have a 600 mV difference, and the solar cell output voltage drops from 650 to 500 mV, reducing theoretical sunlight efficiency from 23% to 17%.

Most of the light hitting the solar cell turns into heat. On the ground, the heat conducts into the environment. In space, it must be disposed of by black body radiation, a challenging problem with a 5700 K Sun on one side. Hot is bad. Is there a way around this?

Monochromatic light, tuned to a photon energy perhaps 200 mV above the bandgap, is efficiently absorbed by a PV cell. A semiconductor material like gallium nitride (GaN) has a 3.4 eV bandgap, and 3.6 eV photons would be efficiently absorbed. The diode turn-on voltage for a GaN cell would be 2.95 V at 300 K, and 2.8 V at 400 K. Much less high temperature efficiency drop, though high temperatures exponentially accelerate aging and wearout. So, 3.6 eV photons might produce power with in a GaN PV array with better than 70% efficiency. Increased efficiency means less heat to radiate, higher temperature greatly increases black body radiation.

Assuming 80% black body emissivity, a 400K PV cell can radiate 2300 watts per square meter from both sides, and produce 7/3 times that more output power, 5400 watts per square meter, illuminated by 7700 watts per square meter of 3.6 eV ( 340 nm ) monochromatic UVA light. An 8 MW array, capable of lifting a 20 tonne climber at 40 meters per second in a 1 gee gravity field, requires (with inefficiencies) a 1200 m², 20 meter radius PV array; large, but 250 times smaller than the 29 hectare array in the assessment.

The only way to deliver such power levels is with lasers. PLURAL. One big laser with a narrow beam is impractical, inefficient, dangerous, and easily blocked by clouds, as appendix E-2 of the space elevator assessment correctly observes. But that is the wrong way to do it. 40 lower power large aperture lasers, spread far from the base station and converged and focused on the climber, can reduce power intensities above and below the climber to less than 400 W/m² . The beams converge on the climber, and spread out above and below it.

This is a key point not considered in the assessment. Total power levels need only be moderately high for climbers (briefly) at lower altitudes, and power densities must be limited, for heat dissipation reasons. Laser beams need not be blinding pencil beams. If they are tuned to slightly different wavelengths, they can be added together from multiple sources without interference. The high power is needed only for the first few hours of initial climb.

Delivering approximately uniform illumination to a 20 m radius climber PV array below 6400 km altitude (50% of total climb energy, highest climb power) will require a source imaging mirror more than 4 times larger than diffraction limit, perhaps 10 meters radius. Many large telescopes, probably floating on well stabilized platforms. Perhaps an insuperable challenge, but not nearly the challenge implied by large gossamer PV arrays.

LEO satellites in a 400 km altitude orbit pass over the equator twice every 90 minutes; the chance of passing through one of the 40 beams per orbit is ( 2 * 40*40 m / 2π 6.8e6 m ) or 75 parts per million; they will hit a beam about once every 27 months. At an orbital speed of 7.7 km/s, they will go though it in 5 milliseconds, and it will deposit 10 joules of UV energy per square meter in that brief time. Space sunlight is 8% UV, 110 watts per square meter, so the laser deposits the same energy as 90 milliseconds of sunlight. If sensitive optics are involved, don't point them at the Sun, and don't point them at the laser. That leaves 99.999% of the sky to point them at.

Of course, if a satellite is in a known orbit, we can simply turn off a laser beam for 5 milliseconds to allow the satellite to pass through without the 10 J/m² energy bump. A tiny jolt to the climber; we can briefly increase the power of the other beams by 2.6% to compensate.

Indeed, a much larger threat to the satellites would be fragments of large area climbers breaking up above 30,000 km; minimizing climber mass and area is far more important than the possibility of laser damage.

These laser-powered PV cells are not shaded by night, nor do they need to track the Sun, only lasers near nadir; if the lasers are spaced far apart, clouds will not obscure all of them. In the long term, staged climbers at higher altitudes, which need far less power to operate, can be powered from by lasers in geosynchronous orbit. As that capability grows, the space power may extend all the way from GEO to the cloud tops.

Again, the purpose of this digression is to suggest the best possible alternative to acoustic climbers, which can easily do better than both (practically impossible) solar PV arrays, and much smaller and more efficient laser powered PV arrays.