Re: Solar powered lasers in space

On Sep 14, 9:33 am, Ian Parker <ianpark...@xxxxxxxxx> wrote:

40% seems a very high efficiency for a laser, but even if this figure
is accepted there is one overiding problem. At noon in a desert you
have about 1kw/m^2 coming in through solar power anyway. The obvious
question to me is why not have solar power in the desrt and be done
with it. Lets generate power and split water into hydrogen and oxygen
in the desert using the energy that comes from the Sun anyway. Why
have a space laser as an intermediate stage?

Is it to get power 24/7? Well you have to be above LEO to effectively
extend the desert day.

You add the satellite to lower costs... that's the point. You lower
costs by increasing the capital utilization of the equipment.

BACKGROUND - SOLAR PANELS

PHYSICS
The sun is a thermal source emitting all colors. Silicon has a
specific bandgap energy at 1,108 nm which absorbs all wavelengths
shorter than that bandgap color, and converts each color with an
efficiency of the ratio of the wavelength absorbed relative to the
bandgap wavelength. So, 1,100 nm is almost perfectly absorbed. 550
nm is converted to electrical action at 50% efficiency 275 nm is
converted to electrical action at 25% efficiency - because the bandgap
energy is fixed. ALL the energy of wavelengths longer than 1108 nm
is lost - its converted with 0% efficiency. Summing across all the
wavelengths in a real system - you get about 180 watts electrical for
each 1000 watts solar put in.

UTILIZATION
Now in a desert region we have in North America the equivalanet of
1,600 hours of sunlight per year. That's because of seasonal
variation and cosine effects. The sun at dawn and dusk illuminates
the terrain at an angle. Its only at noon at certain times of the
year that you get peak power. All other times light comes in at an
angle and is lower intensity. So, you have an effective peak power
output of 1,600 hours.

OUTPUT AND COSTS
Energy is measured in kWh. So, each kW of panel from sunlight
produces in this scenario 1,600 kWh.

The cost of this system is lets say $1,000 per peak kilo-watt - and it
has a lifetime of 20 years. That means you're paying $50.00 a year
for the equipment. If you borrowed the money and paid it back over 20
years, you'd pay more like $100.00 a year for the equipment. Lets say
there are no other costs to keep it simple - since these are the main
costs. Then you're paying $100 for 1,600 kWh - that's 6.25 cents per
kWh.

BACKGROUND LASER POWER SAT

LASER POWER PHYSICS

Lets ADD a powersat that beam laser energy at 1,000 nm (1 um) onto
this same panel array. The laser energy is converted by the silicon
with nearly perfect efficiency. 1,0000 nm / 1,108 nm = 90.25% -
scattering in the air subtracts another 5% - So, for each 1,000
watts of laser you get 850 watts electrical.

INTENSITY
If we decide to emit the same 1,000 watts per square meter the sun
produces, using a solar pumped laser in space, then we obtain 850
watts electrical per square meter on the ground. This adds to the 180
watts electrical each square meter produces from sunlight.

COST OF PEAK WATT ON THE GROUND
This is the first advantage of a power sat. We said it cost $1 per
peak watt for the solar panel installation in our example above. This
is $180 per square meter of panels. Reusing the same installation for
a solar power receiver at the intensity described above means that
$180 per square meter is spread across 850 watts electrical output
from the satellite. So, the ground station costs are reduced from $1
per peak watt to ,

$180/850 = $0.212

21.2 cents per peak watt - for the ground statoin side - or $212 per
peak kW.

UTILIZATION

The solar pumped laser is at GEO - hovering stationary above the panel
array. The laser satellite illuminates the panels nearly all the time
and totals.nearly 8,766 hours per year - except for a few minutes when
Earth's shadow eclipses the satellite.

..
OUTPUT AND COSTS
Like the solar panels, the energy is kWh, so each kW of panels and
satellite produces a total of 8,766 hours of satellite power per
year.

Lets say that each kilowatt of solar laser power on orbit costs
$6,000. A satellite is mostly thin film highly reflective plastic
focusing sunlight onto a special device called a fabrey-perot cell -
filled with materials that lase at 1,000 nm. This laser beam passes
through a window of special adaptive optical window that adjusts the
beam in response to a controlling pilot beam from the panel array on
the ground so that the power safely and reliably falls on the panels
and nowhere else.

Launch costs are approximately $10,000 per kg and construction costs
in the aerospace business are around $2,500 per kg. The costs of raw
materials are nil compared to these costs. The bulk of the weight of
the satellite is the thin film material - and so knowing the thickness
of this the efficiency of converting sunlight to laser light - we can
compute the area of the film and its weight - and add a correction to
estimate what the laser and controls would weigh - and multiply by the
figures above to get a preliminary estimate of satellite costs - and
see that $5 per watt is accurate.

Conversion efficiencies of sunlight to laser light at 1,000 nm can
exceed 22% The solar constant on orbit is 1,366 watts per sq m. So,
each kilowatt of laser energy requires;

1,000 / (1,366 x 0.22) = 3.33 sq m per kW laser

Now GBO (Giant birefringent Optical) material very efficiently
reflects light in thicknesses of 50 microns. The same material
without birefringent layering - is highly transparent. It is a thermo
plastic. So, it can be welded and formed quite easily. A reflective
disk bonded to a transparent front encircled by a transparent 'tire'
and inflated at low pressure - creates a large concave surface.

By controlling the thickness of the reflective surface, from 100
microns to 25 microns - with an average of 50 - the normally spherical
cavity - can be made parabolic.

The thermoplastic has a density of 1,200 kg per cubic meter. Two
sheets 50 microns thick, covering 3.33 sq m amounts to 199.8
milligrams!

The cost as we said above is $12,500 per kg to build something and put
it into space. So, each kilowatt is $2.50 -

Now, this is the cost to LEO - low earth orbit. To get the system up
to GEO doubles the mass on LEO - because we need a kick stage - and
that's where we get $5.00 per watt of laser energy.

Investing in reusable launchers to cut the cost of launch to $500 per
kg - and in production systems to reduc the cost of hardware to $500
per kg - would cut these costs to $1,000 per kg - and cost of laser
energy from space accordingly.

Now, the large film that concentrates the laser light is by far the
most massive part of the system. The laser and control window account
for no more than 10% of the mass on orbit... lets add another 10% for
hardware to help the system deploy - principally gases to inflate the
20,000 to 1 concentrator..

We're up to $6.00 per peak kilowatt now.

Wait a minute, we just showed how we could produce a powersat on orbit
for $6 per peak kilowatt - NOT $6,000 per peak kilowatt!!!! how
could that be? It could be because we are not constrained by the
safety concerns we are on Earth. We don't have environmental impact
around the satellite, and we can operate at very high power densities
- so, we can design an optimal system.

But to make my original point about the cost efficiency of powersats -
lets just arbitrarily multiply everything by 1,000 for the space
system... That makes our cost for the laser system equal to $6,212
per peak watt.

Lets say this system has the same 20 year lifespan as the receiver on
the ground. And lets say we have the same cost of capital - so we
take the $100 per year per kW and multiply it by the same factors as
in the solar panel case - and voila - we have $621.20 per year per kW.

But, we're getting 8,766 kWh out of each kW installed - so that means
our cost per kWh has become;

$621.20 / 8,766 = $0.07 per kWh

But since we're counting the ground system cost twice, we can subtract
this out to obtain;

$600 per year / 8,766 kWh per year = $0.0684 per kWh.

For the space based system.

If we use our original figures - we have

$27.20 / 8,766 = 0.31 cents per kWh

Reducing costs on the ground to $18 per square meter

$8.12 / 8,766 = 0.21 cents per kWh

Reducing launch and production costs of powersat and ground costs to
$18 per square meter

$2.65 / 8,766 = 0.03 cents per kWh

So, we can see that we can build low cost solar panels and then update
them with solar pumped laser sats in space - and even if the costs of
the space system are exorbitantly high, we'll produce power at a
competitive rate. Meeting the costs of existing systems will
dramatically reduce costs - and that will promote expansion - and
investment to cust costs of powersat construction launch and
deployment - and that will reduce costs further - and expand the use
of beamed energy from space.


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