Beam-powered propulsion - keeping the beam focused

[schplade]

I've often read that beam-powered propulsion is the only basic interstellar propulsion concept without physics problems. To me, that doesn't seem far from the truth. However, for a long time I've felt that the biggest obstacle to overcome is the beam divergence problem. Most of the concepts I've read about use a single laser, or a laser array stationed at a single location. It seems to me that - unless your spacecraft can withstand enormous G-forces - you're going to need an acceleration path that's billions of kilometers long if you hope to reach 0.1 c or greater. Could you ever have that with a single laser? I've imagined that you would need many powerful space-based lasers along the acceleration path, but that would obviously introduce a lot of complication.

How small of a laser "spot size" could you realistically hope to achieve over a distance of a billion kilometers? Is there a theoretical best that you could shoot for?

 

[Simon Bridge]

I don't know what you mean by "without physics problems".

The idea is to make the laser tightly collimated rather than dynamically focussing it. ("focussing" usually refers to producing a clear image, or, in this context, making the beam converge to a waist at some specific location.)
The degree of collimation depends on things like the length of the laser cavity compared to it's diameter ... so you can, in principle, make it as collimated as you like. iirc the current best lasers divert from parallel to order of milliradians.

If you don't insist on a laser source - you can use sychrotron radiation for your beam.

Now - you wouldn't want to fly through the beam that is boosting something else...

 

[sophiecentaur]

How small of a laser "spot size" could you realistically hope to achieve over a distance of a billion kilometers? Is there a theoretical best that you could shoot for?

Why would you need such a good focus? A bit of beam spread would only produce a small amount of lateral momentum transfer (cancelling out for a symmetrical beam). It would only correspond to the Sin of the angle of spread, the main beam would only reduce as the Cos of the angle. Overall efficiency would presumably depend, not only on the beam spread but also on the efficiency of the projecting system. I have a feeling that would be lower for a narrow beam. Lasers are not that efficient, so they may not be the best way to produce your driving beam. This sort of Engineering has many facets.

 

[Filip Larsen]

If the beam can be modeled as a static, ideal Gaussian beam, then it seems that beam divergence [1] can be used to give estimate for the minimum expected reduction in beam power (equaling reduction in reflective force) as a function of range for a given beam waist (which relate to reflector size) and beam wavelength.

For instance, using microwaves λ ≈ 10^-2m and a waist of 100 km² the power received at the reflector is reduced to around 87% at 10 million km and around 14% at 1 AU relative to the power received when the reflector is in the waist [2].

[Edit: fixed wrong calculation, reworded example]

[1] https://en.wikipedia.org/wiki/Gaussian_beam#Beam_divergence
[2] https://en.wikipedia.org/wiki/Gaussian_beam#Power_through_an_aperture

 

[mfb]

Why would you need such a good focus?

You have to hit the spacecraft with as much power as possible. Over large distances the beam is wider than the spacecraft , so power received by the spacecraft is directly linked to the focusing quality.

iirc the current best lasers divert from parallel to order of milliradians.

A laser pointer achieves that (1 mm spread over 1 m distance = 1 millirad). Good lasers are diffraction limited, together with a telescope you can get microradians.

 

[sophiecentaur]

Ahh. I was assuming that the propulsion was by reaction from an on-board source. Would that not be better at great distances? The amount of wasted (spilled) energy, despite the apparent high quality of a beam would be enormous at a distance of a few AUs. Beam steering could also be a problem.
I guess there could be no real limit on the diameter of the receiving reflector, though. (many km, once deployed)

 

[mfb]

An on-board beam source needs an on-board power source, which makes the spacecraft heavier. Mass and energy are always limiting factors.

 

[sophiecentaur]

An on-board beam source needs an on-board power source, which makes the spacecraft heavier. Mass and energy are always limiting factors.

Yes. I realize that but there must be a limit to the range that a passive system can be expected to work. Beyond that range, an on board propulsion system would be essential. What sort of diameter would be reasonable for the sail, I wonder. It could be very flimsy in the benign conditions of deep space.
Also, when the craft gets to its destination, it cannot use a propelling beam to get it to manoeuvre to the intended destination - or even just to slow down. I suggest a hybrid system would probably be optimal.

 

[Filip Larsen]

Also, when the craft gets to its destination, it cannot use a propelling beam to get it to manoeuvre to the intended destination - or even just to slow down.

There exists light sail propulsion designs [1] that allows breaking maneuvers. Of course, the engineering challenges for such systems are presumably orders higher than for a simple "acceleration-only" light sail, but should still be within what is physical possible.

[1] Roundtrip Interstellar Travel Using Laser-Pushed Lightsails, R. L. Forward, Journal of Spacecraft and Rockets, Vol. 21, No. 2 (1984), pp. 187-195, http://www.lunarsail.com/LightSail/rit-1.pdf

 

[sophiecentaur]

There exists light sail propulsion designs [1] that allows breaking maneuvers.

That's a clever idea. Just a few practical problems to overcome, though! I would think that the propulsion source would be better placed away from the Earth but then there would be the problem of getting power to it. But all this stuff sort of assumes the existence of fusion power so that problem would not be so great.
The low efficiency of lasers is surely relevant here. Using lower frequencies would make it possible to use more efficient sources, would it not? Achievable beam width would be traded off against efficiency.

 

[Cutter Ketch]

Beam quality for laser beams is essentially the same as the diffraction limit for optics. The minimum possible beam divergence is inversely proportional to the aperture size.

Half angle >= wavelength / (pi * beam radius at waist)

However you don't have to completely fill the aperture to get close to the diffraction limit. A few small apertures around the edges of a large virtual aperture can achieve nearly the same divergence if the beams are coherent. A visible laser with an Earth diameter sized virtual aperture could achieve a 2e-14 divergence and so increase diameter by less than 1000x at Alpha Centauri.

 

[GTOM]

You have to hit the spacecraft with as much power as possible. Over large distances the beam is wider than the spacecraft , so power received by the spacecraft is directly linked to the focusing quality.A laser pointer achieves that (1 mm spread over 1 m distance = 1 millirad). Good lasers are diffraction limited, together with a telescope you can get microradians.

Could it become much better?
http://iopscience.iop.org/article/10.1088/1742-6596/425/5/052034
It talked about a nanoradian, but probably i missed something.

 

[sophiecentaur]

I would appreciate some (informed and numerical) comment about my comments about the efficiency of lasers compared with alternative sources. There seems to be a lot of information but I can't seem to find a source that will say what efficiency you could expect for a continuously running laser with many kW output - at any frequency. The 'wall plug' efficiency and the mean power are both very important factors in a project like this. We do know that, already, there are microwave sources that can produce several kW of continuous power. This link indicates that 750kW of continuous power can be achieved from a 'Gyroklystron' and, at 300kW, the efficiency is around 32%. Is there any laser source with the equivalent power? The disadvantage of a microwave source is the need for an eye wateringly large aperture for the beamwidths needed but the limit to achievable aperture would be enormous. The beauty of microwave devices is that they can be used in synchronised sets, to achieve as much power as you want.
I know that lasers are flavour of the month (decade) but the alternatives are always there. I wondered about a massive fresnel lens, used to direct the Sun's radiation in a useful direction. It would, I guess, need to be held on station somehow to avoid it being blown away by some of the same radiation pressure that it is directing.

 

[mfb]

Could it become much better?
http://iopscience.iop.org/article/10.1088/1742-6596/425/5/052034
It talked about a nanoradian, but probably i missed something.

That is the precision of the central position, the beam width doesn't seem to be given anywhere. Diffraction limits it to more than a nanoradian for realistic optical element sizes. X-ray lasers are not very efficient, however.

The wall plug efficiency of CO2 lasers can be as high as http://www.sematech.org/meetings/archives/litho/7739/presentations/23%20High%20Pwr%20CO2%20Lasers-Soumagne.pdf, fiber lasers reach http://www.messer-cs.com/de/us/processes/laser-cutting/vertical-cutting-laser/faser-laser/ but with a worse beam quality.

 

[sophiecentaur]

That is the precision of the central position, the beam width doesn't seem to be given anywhere. Diffraction limits it to more than a nanoradian for realistic optical element sizes. X-ray lasers are not very efficient, however.

The wall plug efficiency of CO2 lasers can be as high as http://www.sematech.org/meetings/archives/litho/7739/presentations/23%20High%20Pwr%20CO2%20Lasers-Soumagne.pdf, fiber lasers reach http://www.messer-cs.com/de/us/processes/laser-cutting/vertical-cutting-laser/faser-laser/ but with a worse beam quality.

What mean Power would a CO₂ laser be capable of?

 

[mfb]

Depends on the application. I have seen lasers up to tens of kW, I don't know about applications even higher powers could have.

 

[sophiecentaur]

Is that a continuous Power rating or short burst?

 

[mfb]

Average power of course. Peak power would be irrelevant.

 

[sophiecentaur]

I was just checking that meant continuous for a long time. The project would need to be powered for a long time (years) and without interrupted service. I guess a hot reserve would be called fur, whatever system were used.

 

[mfb]

Short breaks shouldn't harm, especially if with the current laser sizes, as you need a huge number of lasers in parallel anyway.

 

[GTOM]

That is the precision of the central position, the beam width doesn't seem to be given anywhere. Diffraction limits it to more than a nanoradian for realistic optical element sizes. X-ray lasers are not very efficient, however.

The wall plug efficiency of CO2 lasers can be as high as http://www.sematech.org/meetings/archives/litho/7739/presentations/23%20High%20Pwr%20CO2%20Lasers-Soumagne.pdf, fiber lasers reach http://www.messer-cs.com/de/us/processes/laser-cutting/vertical-cutting-laser/faser-laser/ but with a worse beam quality.

Thanks, but i would like to make other things clear.

https://en.wikipedia.org/wiki/Angul...tion_limit_diameter_vs_angular_resolution.svg

According to this one, angular resolution of miliarcsec is reachable. That is closer to nrad than microrad. Could we focus the laser this precisely if we know exact distance of rocket?

How inefficient are xasers? I read that an X-Fel needs to accelerate electrons to 0.998c. Does that mean, that due to relativistic mass, you get J output (beam power) from KJ input?

 

[mfb]

In principle you can use a telescope in reverse, but they are designed for low power (starlight) - making them efficient reflectors of high-powered laser beams might need some adjustments. On the positive side, you have a single wavelength, so the mirrors can be made much more reflective.

Electron acceleration is quite efficient, not sure about the conversion process afterwards. This article claims that 10% might be possible.

 

[schplade]

In this paper James Benford argues that microwaves are the most cost-effective for propelling a sailcraft, although they might be at a disadvantage for missions that require long acceleration times.
https://arxiv.org/ftp/arxiv/papers/1112/1112.3016.pdf

I guess this shows you where I got the "without physics problems" phrase from. He's definitely not the only physicist that describes it that way though. It's an oversimplification, but I can see some validity in it. Beamed energy propulsion allows you to leave the fuel behind.

With the speeds required for interstellar missions, carrying the fuel along in the spacecraft just isn't a good option. The propellant mass ratio becomes such a crippling problem that the idea is almost dead on arrival. Antimatter might offer the energy density you need, but that presents its own massive engineering challenges. At least, that's the impression I've had so far from reading about it.

 

[Cutter Ketch]

I would appreciate some (informed and numerical) comment about my comments about the efficiency of lasers compared with alternative sources. There seems to be a lot of information but I can't seem to find a source that will say what efficiency you could expect for a continuously running laser with many kW output - at any frequency. The 'wall plug' efficiency and the mean power are both very important factors in a project like this. We do know that, already, there are microwave sources that can produce several kW of continuous power. This link indicates that 750kW of continuous power can be achieved from a 'Gyroklystron' and, at 300kW, the efficiency is around 32%. Is there any laser source with the equivalent power? The disadvantage of a microwave source is the need for an eye wateringly large aperture for the beamwidths needed but the limit to achievable aperture would be enormous. The beauty of microwave devices is that they can be used in synchronised sets, to achieve as much power as you want.
I know that lasers are flavour of the month (decade) but the alternatives are always there. I wondered about a massive fresnel lens, used to direct the Sun's radiation in a useful direction. It would, I guess, need to be held on station somehow to avoid it being blown away by some of the same radiation pressure that it is directing.

Different lasers different answers, but they can be more efficient than you might think. Another issue in trying to find the information is that there are several stages to the efficiency and people will hide inefficiency by only quoting part of the efficiency.

Wall plug efficiency: the whole enchilada

But that includes the inefficiency of the electronics: power conversion, pulse forming, unavoidable poor efficiency when the current is high and the voltage is low. So to avoid talking about that inefficiency you will see

Electrical to optical efficiency: the optical power out over the electrical power delivered to the pump head.

But that includes the inefficiency of the first step. Particularly with diode lasers which are 10 - 60% efficient depending on the pump wavelength, that can be a big step. So to avoid talking about that people publish

Optical to optical efficiency: the optical power out divided by the optical power delivered to the pump head.

But that includes the energy used creating a population inversion and getting to threshold. Particularly in three level laser systems especially when they are pulses that can be a very large inefficiency, so people talk about

Slope efficiency: optical energy out divided by the optical energy delivered to the pump head over and above the threshold energy

Universally everybody ignores the often very large amount of power it takes to run cooling systems, which can often dominate the power consumption.

I know you didn't ask about any of that, but I just wanted to highlight why it can be tough to get a straight answer. The easiest way to get a real answer is not by looking at articles, but rather by looking at spec sheets of lasers you can buy.

Now for some answers.

Diode lasers around 800nm and in the 9xx range typically have > 50% electrical to optical. It varies with temperature and they can be 65% efficient in Alaska in the dead of winter and fall to 50% in Death Valley in summer. At room temperature running CW with a good power supply you can get close to 50% wall plug efficiency. Diode lasers at other wavelength vary in efficiency (different materials). 25% around 1.5um. 10-15% for blue, etc. One off champion results have achieved > 70%, but you can't actually buy that. The efficiency of diodes make them the perfect first step for other lasers.

Diode pumped solid state lasers (DPSSL) are pretty good at converting the diode light. Nd:YAG can achieve 30-40% O-O and so 15-20% E-O. For high power this often involves very high current circuits which are hard to make brilliantly efficient so the wall plug efficiency might only be 10. However that is for a single resonator. Amplifier stages can be more efficient and if you work hard you can push that up. Northrop Grumman's 100kW class directed energy weapon achieved 17% wall plug efficiency (not including the substantial and power hungry cooling system) with diffraction limited beam quality.

Gas lasers like CO2 can also achieve about 20% wall plug efficiency.

So for futuristic beam riding discussions 20% is a safe starting point, and you can imagine figuring out how to scale the diode laser efficiency up to high power and top 50%

On the other hand, for a beam rider who cares how efficient the ground laser is?

 

[GTOM]

In principle you can use a telescope in reverse, but they are designed for low power (starlight) - making them efficient reflectors of high-powered laser beams might need some adjustments. On the positive side, you have a single wavelength, so the mirrors can be made much more reflective.

Electron acceleration is quite efficient, not sure about the conversion process afterwards. This article claims that 10% might be possible.

Also X-Rays can be only focused efficiently with diffraction with perfect lenses. Which gives me the speculation, that if we want to reach Alpha Centaury, first send a lots of lenses, that keep refocusing the beam.

 

[sophiecentaur]

Any propulsion beam will need to be generated in a spacecraft and the Energy requirement will be another massive problem to deal with. A football field (or greater) size PV array would be called for and the efficiency of that would also be relevant. Hence my question / comment about using sunlight, direct, with a focussing mirror or lens to produce the beam. There would be a danger of such a beam, however generated, slicing its way through anyone who strayed into it. It would need to be marked on the 'charts' just like bridges, cables and wrecks on marine charts. Any source would also be occluded occasionally by other orbiting bodies and that would need to be dealt with.
It's so easy to get drawn into these sorts of projects without considering all sides of the problem. It reminds me of the Space Elevator idea, which is also very attractive - but also poses some possibly unsolvable snags.

 

[mfb]

You cannot focus sunlight in any realistic way. Its angular spread is just too large.

Any source would also be occluded occasionally by other orbiting bodies and that would need to be dealt with.

Completely negligible.
For an Earth-based beam, you would certainly check if there are crossing satellite orbits, but even that is unlikely.

 

[sophiecentaur]

You cannot focus sunlight in any realistic way. Its angular spread is just too large.
Completely negligible.
For an Earth-based beam, you would certainly check if there are crossing satellite orbits, but even that is unlikely.

What do you mean by "angular spread"? If it were a distant Point Source then it could be focussed on an Airy Disc, with angular spread according to the aperture. I agree that some sort of Relay Optics would be needed to achieve this for a large source like the Sun. Overall efficiency would not suffer from two energy conversion processes that an electrical device would involve.
The Earth is spinning so could the source be steered in a practical way? ( mirrors, perhaps) Also, you would need a number of sources to avoid a long daily break in transmission. How could you keep the relevant bit of sky clear at all times?
Have you ever observed the number of satellites up there on a clear night? It's like Piccadilly Circus up there and they are mostly in trans polar orbits, covering the whole of the sky, eventually and they are not all recorded and tracked. There is loads of junk up there which would be dangerously reflective, too. You could never eliminate the risk of damage to orbiting objects or to Earth by reflection. This beam would not be pencil thin, but metres wide (same requirements as for a Very Large Telescope).

 

[mfb]

The sun is not a distant point source, it has an angular diameter of about half a degree at 1 AU, and correspondingly your beam has the same minimal spread. Sunlight reflected by a 100 meter mirror will diverge notably after 10 kilometers. Do you want to place another huge mirror every 10 kilometers? Going to 2 AU reduces the spread by a factor 2, but then you need four times the mirror size for the same power. The same scaling applies to every other distance.

 

[schplade]

I used the Gaussian equation for evolving beam width to figure out how wide the beam would need to be for a given distance and wavelength.
https://en.wikipedia.org/wiki/Gaussian_beam#Evolving_beam_width

Hopefully I'm not misusing the equation. All of this assumes an ideal Gaussian beam.

For example, if you want to use the laser over a range of a billion kilometers, and you're using a visible violet wavelength (400 nm), then the following is the calculation if you assume a beam waist size of 253 meters at the midpoint along the beam. The beam diameter shown is the maximum over that range - this is the beam diameter at the source and at the 1 billion km mark:

Total Range: 1,000,000,000,000 m
Distance from focus: 500,000,000,000 m
Wavelength: 0.0000004 m (visible violet)
Waist Size: 253 m

Rayleigh range = (π * 253²) / 0.0000004 = 502,725,510,409.07

Spot size = 253 * √(1 + (500,000,000,000 / 502,725,510,409.07)²) = 356.83 m

I believe the spot size is the beam radius, so beam diameter = 713.65 m

So I presume this means you would have to run the laser through a 713.65-meter telescope?

I plugged the equation into a spreadsheet and fiddled with the numbers until I got what looked to be the narrowest possible beam for a few different wavelengths. All of these are for a total distance of a billion kilometers. The spot sizes and beam diameters shown describe the beam at its widest points over that range:

 

[sophiecentaur]

The sun is not a distant point source, it has an angular diameter of about half a degree at 1 AU, and correspondingly your beam has the same minimal spread. Sunlight reflected by a 100 meter mirror will diverge notably after 10 kilometers. Do you want to place another huge mirror every 10 kilometers? Going to 2 AU reduces the spread by a factor 2, but then you need four times the mirror size for the same power. The same scaling applies to every other distance.

Is that true? I'm assuming a concave mirror, probably with some other optics. I realize that optics tends not to be intuitive so can you help me with some basics about this?

 

[mfb]

Is that true?

Yes. It does not matter what you use as optics, you cannot reduce the size in phase space. For the same reason, a solar oven cannot exceed the temperature of the surface of sun: you cannot focus sunlight better.

What you can do: make a small hole in an absorber, then use only light shining through that pinhole, and focus that. You can focus it better, but only because you reduced the light with the pinhole. The intensity reaching the spacecraft doesn't go up from that process.

 

[sophiecentaur]

you cannot reduce the size in phase space.

Thanks. That makes sense.

 

[schplade]

Am I using the evolving beam width equation correctly? I have no idea if it's reasonable to assume something close to an ideal Gaussian beam in this case. If the math is right, then it suggests to me that you would need to focus the laser through a telescope with a 713.65-meter aperture to produce a beam with those characteristics.

 

[mfb]

The scaling looks right, the order of magnitude looks right, factors of 2 will depend on the precise engineering solution anyway.