Nuclear Photon Rockets: Flashlights to the Stars

[MatterBeam]

This is the most recent post on ToughSF: http://toughsf.blogspot.com/2020/11/nuclear-photon-rockets-flashlights-to.html

Nuclear Photon Rockets: Flashlights to the Stars

 

In this post, we will have a look at the concept of using a nuclear photon rocket for interstellar travel. They are an old concept that should theoretically be the ultimate form of relativistic propulsion.

However, today they are unknown or unpopular. Why might that be the case?

The image above is by David A. Hardy. 

The interstellar challenge
 

The Daedalus starship.

Interstellar travel is on a completely different level than interplanetary travel. The distances involved are orders of magnitudes greater. The shortest distance between stars is measured in trillions of kilometres. To face such distances, high velocities are required. 

The closest stars.

A robotic probe might not mind spending several centuries to reach a destination. A human crew would want the trip done in their lifetime. Taking longer than that means running into technical and ethical trouble. The closest star to our Sun is Alpha Centauri A, currently sitting  40 trillion kilometres away, or 4.2 light-years. It would take 4.2 years to reach it when travelling at the speed of light. If we want to complete the trip within 20 years, we would have to travel at 21% of the speed of light. We also want to slow down at the destination. This means that we need a way to accelerate up to 21% of the speed of light, and then slow down back to zero - the deltaV sum is 42% of the speed of light.

 

So how do we go that fast?

The Falcon 9's Merlin rocket engines.

Rockets are the space propulsion system we are most experienced with. There are many ways to measure a rocket’s performance, but only some are relevant to interstellar travel. Thrust, for example, is much less important when the trip will take many years; taking one month to accelerate instead of ten months is no longer a significant factor. Instead, let’s focus on exhaust velocity. Using the Tsiolkovsky rocket equation, we can work out the ratio between propellant and non-propellant masses of the rocket we are using.

• Mass Ratio = e^(DeltaV/Exhaust Velocity)

DeltaV in m/s

Exhaust Velocity in m/s

 

A chemical rocket consuming oxygen and hydrogen propellants has an exhaust velocity of 4,500m/s. We find that for a chemical rocket to achieve a deltaV of 42% of the speed of light, we would need e^28000 kilograms of fuel for each kilogram of equipment, structure, engines and payload. That is a number that lies between 10^8428 and 10^13359. For comparison, the entire mass of the Universe is estimated to be 10^53 kg. Chemical rockets for relativistic travel are beyond impractical. 

The needle array of Enpulsion's IFM nano thruster.

How about a rocket engine with a better exhaust velocity? Something like one of our most efficient ion thrusters? The Ultra-FEEP thruster that accelerates liquid indium to nearly 1,000 km/s is the best we can expect for now. It would still not be enough for relativistic velocities. To achieve a deltaV of 42% of the speed of light, we would need 6*10^55 kg of indium for each kilogram of dry mass. 

 

If you run the numbers yourself and lower the deltaV target, you would still find ridiculously high mass ratios being required. A deltaV target of just 2% of the speed of light, which would turn the trip to the nearest star an endeavour that spans about half a millennium, would still require a physics-breaking mass ratio of 10^579 from the chemical rocket, and a mass ratio of 453 from the Ultra-FEEP thruster. The lower value for the electric thruster seems much more reasonable, until you consider that indium is found at a concentration of 0.21 ppm in Earth’s crust. At our current output of 700 tons per year, a 1,000 ton dry mass craft would require at least seven centuries of indium production to fill its propellant tanks.

To get away from these extreme figures, a logical decision would be to increase the exhaust velocity all the way to the maximum. The maximum is the speed of light. 

 

Photon Propulsion

When your exhaust is light itself, the mass ratios required for relativistic velocities become decidedly modest. Light, more specifically photons, can be produced indefinitely ‘out of nothing’. In other words, if you heat up a surface, you can create a photon rocket that spontaneously produces and emits light without ‘running out’ of anything. All that is required is a power source. The more energetic the power source, the more photons that can be produced and the higher the photon rocket’s performance. The theory fits together neatly. 

 

The concept of using a nuclear reactor to heat up a surface so that it emits enough photons to produce appreciable thrust is at least 50 years old. Nuclear photon rockets could solve our problem of interstellar travel by harnessing the greatest sources of energy and utilizing the exhaust with the highest velocity. All the fuel they would ever need would be loaded up at departure, so they do not have to rely on the existence of any infrastructure at the destination or any assistance along the way. Perhaps they would have enough to return to us without having to refuel!

 

However, ‘photon starships’ are not a popular idea today. They are not featured in NASA’s NIAC programs, nor are aerospace engineers dreaming up modern designs for them. What ‘catch’ has them relegated to relics of the past?

 

Fission Photon Rocket

A nuclear photon rocket from Boeing's PARSECS study.

Let us start with the most familiar of nuclear energy sources: the fission reactor. 

 

A fission reaction produces about 80 TeraJoules for each kilogram of maximally enriched fuel. 95% of this energy is in the form of gamma rays or fission fragments; they can be blocked by a thick wall and converted into heat. About 5% leaks out in the form of neutrinos. This reduces the ‘useful’ energy density of fission fuel to 76 TJ/kg.

 

In a typical reactor, the fuel is in solid form. Only a fraction of its potential 76 TJ/kg can be extracted in one fuel cycle. The products of fission, such as xenon-135 and samarium-149, remain trapped next to the fuel. These isotopes have a high neutron cross-section, which means that they trap and absorb the neutrons needed to sustain a fission reaction. Nuclear engineers consider these products to be ‘poisons’. If enough poisons accumulate in the fuel, the fission reaction cannot be sustained. 

 

The result is that a single fuel cycle achieves very low burnup of the fuel, which is the percentage of fissile fuel that has undergone fission. Typically, this is 1% to 5% of the total fuel load inside a reactor. On Earth, nuclear engineers deal with this problem by shutting down a reactor, extracting the slightly used fuel and sending it off for reprocessing. This involves removing the poisons, mixing in a small quantity of fresh fuel, and then returning it all to the reactor. 

 

A spaceship does not have the luxury of regularly halting its reactor while also lugging around a nuclear fuel reprocessing facility. 

Instead, we need to use a type of reactor that grants high burnup with no reprocessing necessary. The best option seems to be a gas-core nuclear reactor. In this high temperature design, the fuel and poisons are in a gas phase. It becomes easy to filter out the poisons as they are chemically very different from the fuel. We can have the fuel  circulate within the core for as long as needed to achieve near 100% burnup.

 

With the burnup problem solved, we can convert those 76 TJ/kg into heat. 

 

From a physics perspective, only about 0.77 grams of matter in a kilogram of fissile fuel becomes energy. This leaves us with 999.23 grams of waste after consuming the fuel. With no further use for it, we eject it to lighten the spacecraft. 

 

Imagine a nuclear starship designed specifically to make our next calculations easier.

 

It consumes 1 kg of fuel per second. The average power output is 76 Terawatts. 

• Thrust = 2 * Power/ Exhaust Velocity

Thrust will be given in Newtons

Power is in Watts

Exhaust Velocity in m/s

 

Those 76 Terawatts should result in 506.6 kiloNewtons of thrust. With a 95% efficient photon emitter, we gain a real thrust of 481.3 kN. 

 

After producing this thrust, we eject 999.25 grams of waste. 

• Effective Exhaust Velocity = Thrust / Mass Rate

Effective Exhaust Velocity will be given in m/s

Thrust is in Newtons

Mass Rate is in kg/s

 

The ‘effective exhaust velocity’ based on this thrust and the amount of matter being ejected is actually 481.7 km/s. The critical point we make here is that while the thrust comes from photons travelling at the speed of light, exhaust velocity calculations must take into account all the masses being ejected.

 

So what can a fission photon rocket do with an effective exhaust velocity of 481.7 km/s?

 

It certainly cannot reach our desired deltaV. Achieving 42% of the speed of light would require a mass ratio of 10^113. Unless we have access to multiple Universes filled with highly enriched fissile fuel, this is impractical.

 

Even with an extraordinary feat of engineering so that we could load a starship with 100 kg of nuclear fuel for each 1 kg of dry mass (and not have it immediately go critical), the achievable deltaV is only 2,218 km/s or 0.74% of the speed of light.

 

Fusion Photon Rocket

What if we used the better nuclear rocket: the fusion rocket?

 

There are many different fusion reactions involving different fuels, but we are interested in those that provide the highest energy density.

 

Proton-proton fusion provides a whopping 664 TJ/kg. However, it is very slow, taking thousands of years to complete, and it is not realistic to ever expect to take place outside of stellar cores. Next down the list is Deuterium-Helium3. About 353 TJ/kg is on tap.

 

We won’t dive into the details of the various reactor designs that could be used, but suffice to say that near-complete burnup of fusion fuels is possible, and all the energy released can be converted into heat.

 

If we compare the mass of the Deuterium and Helium 3 before fusing, with the mass of the helium and proton particles after fusion, we notice that 0.39% of the mass is missing. That is the percentage of mass converted into pure energy. It is a much greater percentage than nuclear fissions’ 0.077%.

The list of particles involved in fusion reactions, with their exact masses.

 

Let’s repeat the previous calculation for the effective exhaust velocity of a nuclear photon rocket.

 

1 kg/s of fusion fuels are consumed, for a power output of 353 TW. This produces 2,235.6 kN of thrust out of a 95% efficient emitter. We expel 996.1 grams per second of waste, so the effective exhaust velocity is 2,244.4 km/s.

 

This is nearly five times than a fission photon rocket’s effective exhaust velocity. However, this is still not enough. 

 

Our desired deltaV of 42% of the speed of light comes at the cost of a mass ratio of 2.4*10^24. While we could gather enough galaxies together to fuel our fusion photon rocket, we want something more practical.

 

The reality is that a plausible fusion photon rocket with a mass ratio of 100 would only have a deltaV of 10,335 km/s or 3.4% of the speed of light. Barely enough for a multi-century generation ship to cross the stars and certainly not enough for travel within a lifetime. Staging the fusion rocket will not help very much. 

 

Also notable is the fact that an effective exhaust velocity of 3.4% of the speed of light is actually lower than the exhaust velocity of direct drive fusion propulsion, where charged particles are directly released into space through a magnetic nozzle. DHe3 releases a 3.6 MeV helium ion and a 14.7 MeV proton. Their averaged velocity is 7% of the speed of light. A photon rocket is a very inefficient use of fusion energy.

 

Antimatter Photon Rocket

The ultimate fuel should give the ultimate performance. Nothing beats antimatter!

 

There are many types of antimatter. There are antielectrons, antiprotons, antineutrons and their combined form, anti-atoms like antihydrogen. Antielectrons annihilate with regular electrons in a ‘clean’ annihilation reaction that produces high energy gamma rays and nothing else. They are however the hardest type to store. Antiprotons are much easier to store, especially in the form of frozen antihydrogen ice. The downside is that their annihilation is ‘messy’, as it releases a plethora of products. With solid shielding, enough of the energy of those multiple products can be absorbed and converted into heat. We set the efficiency at 85%. 

 

Each kilogram of antimatter contains a potential for 90,000 Terajoules of energy. It must be matched by another kilogram of regular matter, so the average energy density is halved to 45,000 TJ/kg. As we only capture 85% of that amount, the useful energy density is 38,250 TJ/kg.

 

If we consume one kilogram of antimatter/matter mix per second, we would have a drive power of 38,250 TW. A realistic emitter would convert this into 242,250 kN of photon thrust. The effective exhaust velocity is 242,250 km/s or 81% of the speed of light.

 

With such a high exhaust velocity, an antimatter photon rocket would be able to achieve the relativistic velocities we desire. 

 

A deltaV of 42% of the speed of light would only require a mass ratio of 1.68. That’s 0.68 kg of antimatter/matter mix for each 1 kg of rocket dry mass. We might even be able to go much faster with high mass ratios; travel times to the stars in single-digit years seems possible.

 

However, antimatter is exceedingly difficult to collect or create. A mass ratio that seems acceptable for a conventional rocket would actually imply an unreasonable amount of antimatter. Existing accelerator facilities, if tasked with solely producing antimatter, would require about 3.6 ZettaJoules to produce 1 kilogram of antimatter. That’s 3,600,000,000 TeraJoules, equivalent to 286 times the total yield of all nuclear bombs today (1.25*10^19 J), or the total output of the United States’ electrical grid (1.5*10^19 J) for the next 240 years. 

If we were very serious about producing large quantities of antimatter, we could design a superbly optimized antimatter production facility, with very efficient antimatter capture mechanisms. Production efficiency can be increased to 0.025%. This means that 1 kg of antimatter would require ‘only’ 360,000 TJ to manufacture. An antimatter photon starship would ‘just’ need the combined output of all humanity (8*10^19 J/yr) for the next couple of millennia to fill it up.

An antimatter production facility.

In practice, the awesome performance of antimatter propulsion would be reserved for civilizations higher up the Kardashev Scale. 

 

Verdict and Consequences

All the calculations so far have assumed nearly perfect use of the energy released by fission, fusion or antimatter reactions. We have also ignored the massive complications that arise from trying to handle the power of those reactions. Despite this best case scenario, nuclear photon rockets do not seem to be up to the task of rapid interstellar travel. 

 

Fission and fusion power are just not energy dense enough. Antimatter is far too difficult to produce in huge quantities. The ‘catch’ is that physics is not kind to photon propulsion. For this reason, this sort of starship will remain a bottom-drawer concept for the foreseeable future. 

 

What effect does that conclusion have?

 

If we want to use rockets, we must accept that interstellar travel will be slow. Other techniques or technologies have to be employed to make crossings that last centuries. Cryogenic hibernation, life extension or digitizing the mind can enable the original crew to survive that long; generation ships or embryo seeding can allow another group of people to arrive at the destination. 

Robert L. Forward's Laser-propelled lightsails.

If we instead want interstellar travel done quickly, we cannot rely on rockets. All the popular methods for interstellar travel depend on non-rocket propulsion, such as Robert L. Forward’s massive laser-propelled sails or the ‘bomb-tracks’ discussed in a previous post. The energy cost of relativistic travel is no longer derived from a fuel carried onboard a starship, but from an external source. This external source takes the form of large infrastructure projects and preparations that require many years to complete; we trade away the flexibility and autonomy of rockets to gain huge speed, efficiency and cost advantages. 

 

A consequence of non-rocket propulsion is that interstellar travel cannot be a whimsical affair. It has to be planned a long time in advance (which has implications for the stability of the civilization organizing it all) and it would be evident to all observers at the departure and destination what is going on. No ‘secret’ missions to other stars!

 

Of course, a scifi writer might not like the sound of that. Their options lie in more exotic types of rockets, more advanced civilizations or speculative science. 

 

Examples of exotic rockets include a starship powered by a rotating black hole, where matter is converted into energy at 42% efficiency (an effective exhaust velocity of up to 252,000 km/s or 84% of the speed of light) or a Ram-Augmented Interstellar Ramjet, where the thin interstellar medium is added to the exhaust of a fusion reactor for a greatly improved effective exhaust velocity. More advanced civilizations handle enough energy to be able to produce large quantities of antimatter, overcoming the main difficulty with this fantastic fuel. 

Speculative science opens up the possibility of using ‘quark nuggets’ to rapidly and easily create antimatter, as well as wormholes and Alcubierre warp drives. 

 

 

Though, we must warn you, that these different options might be more troublesome than photon rockets!

[KSK]

Very nice post. Should be stickied in the KSP2 forum as a reality check for everyone going gaga over interstellar travel.

 

[wumpus]

I have to admit that I'm a big fan of photon propulsion, largely because of effectively infinite Isp.  On the other hand I'm certainly skeptical that there exists any realistic level where photon propulsion beats ion propulsion.  Note that this probably doesn't include "standard" ion propulsion, but exotic cyclotron-based ion accelerators.  Because blue LEDs aren't the only thing that can create momentum out of pure electricity: you can add all the momentum you want to an ion by accelerating it into relatavistic speeds.

When you realize that it will be extremely important to have your heatsinks "white" (minimal blackbody radiation) on one side and "black" (maximum blackbody radiation) on the other for additional photon propulsion, you might realize just how inefficient photon emission can be.  On the other hand, if your nukes are still producing power and you've long gone through both your Argon and Xenon, you might as well fire up your LEDs for all your remaining delta-v.

Just don't plan on decelerating and orbiting any star system that way.  I'd expect a rather weak last stage.

 

[cubinator]

5 hours ago, MatterBeam said:

We have also ignored the massive complications that arise from trying to handle the power of those reactions.

Heh. Yeah, trying to get any appreciable thrust out of a photon rocket by heating something will melt it.

[MatterBeam]

3 hours ago, wumpus said:

I have to admit that I'm a big fan of photon propulsion, largely because of effectively infinite Isp.  On the other hand I'm certainly skeptical that there exists any realistic level where photon propulsion beats ion propulsion.  Note that this probably doesn't include "standard" ion propulsion, but exotic cyclotron-based ion accelerators.  Because blue LEDs aren't the only thing that can create momentum out of pure electricity: you can add all the momentum you want to an ion by accelerating it into relatavistic speeds.

When you realize that it will be extremely important to have your heatsinks "white" (minimal blackbody radiation) on one side and "black" (maximum blackbody radiation) on the other for additional photon propulsion, you might realize just how inefficient photon emission can be.  On the other hand, if your nukes are still producing power and you've long gone through both your Argon and Xenon, you might as well fire up your LEDs for all your remaining delta-v.

Just don't plan on decelerating and orbiting any star system that way.  I'd expect a rather weak last stage.

 

Technically, it is infinite propellant and not infinite Isp. Antimatter definitely beats ion propulsion, but anything with less energy density than that cannot do so...

1 hour ago, cubinator said:

Heh. Yeah, trying to get any appreciable thrust out of a photon rocket by heating something will melt it.

The photon rocket will likely look like a solar sail, except glowing hot at 3000K+ on one side.