Could you replace a laser cutter with a focused-sunlight cutter?
I mean obviously you can burn through things with focused sunlight — I’ve been doing it since I was a kid — but I’m asking if you can match the performance of off-the-shelf low-power laser cutters.
The laser cutter I’ve been using to cut MDF cuts a 100-μm kerf positioned with 60-μm precision using a 60W laser through 3-mm MDF at 24 mm/sec, although it can handle up to I think 12 mm at lower speeds. If we figure that the divergence of the beam can’t be more than about 50 μm over those 3 mm, that’s about a sixtieth of a radian, 16.7 mrad, almost twice the visible width of the sun, which is about 9.3 mrad.
So there are two problems here: one is to focus, say, 100 W of sunlight in an area that’s less than 100 μm across, and the other is to keep the divergence of that focused beam down below, say, 10 mrad.
The very direct approach is to use a single movable parabolic reflector at a sufficiently large distance. But this will not work very well. 100 W is about 0.1 m² of sunlight at the surface, a mirror of 357 mm diameter; this is 10 mrad at a distance of 35.7 m. A geometrically-perfect image of the sun at that distance would be 9.3 mrad, which would make a 332-mm-wide image of the sun, which is substantially larger than the 0.1 mm we are shooting for.
This amounts to a spot that is 3½ orders of magnitude too wide and is 7 orders of magnitude too dim.
Getting a smaller and thus brighter image from an imaging-optics system involves shortening the focal length, as all photographers know. The desired power density here is 10 GW/m², which is (not totally coincidentally) 7 orders of magnitude brighter than sunlight.
This is somewhat problematic because the illuminance limit imposed by thermodynamic reversibility is for the focal spot to be entirely surrounded by (reflected or refracted) sun surface, that is, 4π steradians of sun. A 9.3 milliradian cone has a solid angle of about 0.27 millisteradians (2π(1 - cos(9.3 mrad))), and so the theoretical maximum is only about 46000 suns, with 23000 suns being the limit for a point on a flat surface only being illuminated from outside the surface. This is still three orders of magnitude dimmer than the laser — and without even being pulsed!
Therefore even non-imaging optics can’t help us here. We need stronger stuff than mere optics.
One possibility is to concentrate the light optically as far as possible, then use some other approach to deliver the power to a small area. We don’t actually have to violate any laws of thermodynamics to do this; the MDF doesn’t have to get hotter than the surface of the sun (5500°), and we don’t have to deliver all of the energy to it, but can waste some in pumping heat around. One obviously feasible approach is to use photovoltaic panels to power the existing electric CO₂ laser, but are there more direct routes, maybe more efficient ones?
One obvious (to me) example is to use the sunlight to heat a fluid to a sufficiently high temperature and then cause the fluid to flow through the MDF. Air is one possibility, although it might tend to catch the MDF on fire even more than the laser does. Lead, which doesn’t dissolve much iron and doesn’t boil until 1749°, is another possibility; at higher temperatures, copper, which doesn’t melt until 1084° but doesn’t boil until 2562°, or silver, which melts at 962° and boils at 2162°, might resist oxidation better. (Molten silver, however, has a tendency to attack steel.)
How fast could air deliver power? Suppose the hot air stream is limited to 1600° in order to be able to use ordinary ceramics to control it; air’s specific heat is 29.2 J/K/mol, and it weighs about 30 g/mol. Let’s suppose that the MDF cools the hot air down to about 500°, so we have 1100 K to play with. Delivering 60 W then requires a flow of about 1.9 millimoles per second, which works out to about 56 mg/s, which would be 56 mℓ/s at normal temperatures — but at 1600° it’s more like 360 mℓ/s. Dividing that by the area of a 50-μm-radius circle, we get the utterly implausible air speed of 46 km/s, roughly Mach 138.
(I would have liked to use metals, but even superalloys are limited to about 1000°.)
If we relax the requirements considerably, we can get into a feasible range; suppose that we make our air nozzle out of white-hot quicklime instead of regular ceramics, so that we can use air at 2600° (reducing the flow rate to 290 mℓ/s), and make the air stream 1 mm in diameter instead of 100 μm. Then we can get the air speed down to 370 m/s, Mach 1.1, which is probably feasible. (Turbulence in the nozzle just transforms into more heat in the air!) A slightly wider nozzle of 1.35 mm diameter can get your gas stream speeds down to 200 m/s, which is quite clearly feasible. But if you’re blowing white-hot air on it, it’s going to be really difficult to keep the MDF from catching on fire; you probably need an inert-gas atmosphere, nitrogen at least, which probably means you need to filter and recirculate it.
Molten metal is probably a much more feasible approach; even at room temperature, it’s about ten thousand times as dense as air, and that advantage increases with temperature rather than decreasing.
Lead’s vapor pressure is a still-relatively-safe 10 Pa at 814° (an atmosphere is 101 kPa). Tin is a more expensive but nontoxic alternative with an even lower melting point (232°), an even higher boiling point (2602°), and an even lower vapor pressure; I think it is more vulnerable than lead to oxidation in air. The eutectic 63%-tin mixture of the two melts even lower.
If we figure that we can work from 900° down to lead’s freezing point of 327°, then take advantage of its 4.8 kJ/mol heat of fusion, how much lead flow do we need? Its molar mass is 207.2 g/mol, so that’s 23 kJ/kg of latent heat of fusion. Engineering Toolbox says molten lead’s heat capacity is 140 J/kg/K, and we have 573 K here, so that’s 80 kJ/kg of sensible heat. Together, they’re 103 kJ/kg, so our flow rate is only 580 mg/s; with molten lead’s density of about 10.7 g/cc, that’s only 58 microliters per second of lead.
Through a 100-micron-diameter circle, that’s still 7.4 meters per second, which is some pretty healthy metal pumping action; I don’t know what molten lead’s viscosity is, but that won’t be easy. But it’s surely feasible.
Hmm, this IAEA document on nuclear reactor design says lead’s dynamic viscosity is about 1 mPa·s in the temperature range considered. A Poise is 100 mPa·s. Water’s viscosity at 20° is 1.002 mPa·s, so we can treat lead as especially dense water in this temperature range. This document also describes in some detail the physical properties of the lead-bismuth eutectic coolant used in many Soviet reactors. Some random engineering calculator site claims that 1 mm of 0.1 mm-diameter pipe at 58 μℓ/s should result in about 13 MPa of head loss; this is a straightforward pressure to achieve, and it amounts to a force of about 0.1 N across the area of the nozzle, and a hydraulic power of 750 milliwatts.
These numbers are all easily feasible.
Another possibility is to use the sunlight directly to pump a lasing medium, such as a doped fiber; this is called a “solar-pumped laser”, and there are apparently a number of them around, mostly Nd:YAG, including a megawatt one in Uzbekistan (!).