Fuel Types

RocketCat sez

Your atomic rocket's fuel is gonna be Uranium-233, Uranium-235, and/or Plutonium-239.

These are rare, so they will also use breeder reactors to turn worthless Uranium-238 into valuable Plutonium-239, and worthless Thorium-232 into valuable Uranium-233. Since the perversity of the universe tends towards a maximum, the ore has about a hundred times more of the worthless stuff than the good stuff. Good ol' O'Toole, you can count on him.

The propellant is gonna be liquid hydrogen, but you knew that already, right?

Plutonium-239 can also be used to make nuclear bombs. This is why atomic fuel gives the authorities sleepless nights. This is also the insane reason that "spent" reactor fuel rods are thrown away even though they contain 85% of their valuable uranium unburnt! Reprocessing the rod to recover the un-burnt uranium would also recover unwelcome freshly-made plutonium. The authorities figure it makes more sense to throw away the valuable uranium rather than being stuck with the job of guarding the plutonium. You never know if Somebody Evil might steal it in order to make atom bombs. Or Somebody Opportunistic might steal it in order to sell it on the black market to Somebody Evil.

For nuclear fission, the main fuel types are Uranium and Plutonium, specifically 235U, 233U, and 239Pu. Plutonium-239 is also used in nuclear weapons. In science fiction stories, these are often called "power metals."

Also very valuable are Thorium-232 and Uranium-238. They are worthless as fuel, but they are about a hundred times more plentiful and an application of neutrons transmutes them into useful fuels (the technical term is "fertile"). 238U transmutes into 239Pu, and 232Th transmutes into 233U. One generally sees these reactions used in a Breeder Reactor or a Thorium Fuel Cycle reactor.

In a breeder reactor, the worthless but fertile Thorium-232 captures a neutron, becoming Thorium-233. It does a beta-decay becoming Protactinium-233. It then does a second beta-decay, becoming valuable Uranium-233. In a breeder, worthless but fertile Uranium-238 does much the same thing, becoming Uranium-239, then Neptunium-239, and finally valuable Plutonium-239.

Currently most of the governments of the world are rather hostile to the idea of breeder reactors, due to fears of nuclear proliferation. It would be different if the breeders produced 235U, but the blasted things make plutonium (aka the sine qua non of nuclear weapons). The governments are also opposed to fuel reprocessing for the same reason. This puts the nuclear industry in the ridiculous position of trying to find ways of safely throwing away used reactor rods that still contain 85% of their valuable 235U un-burnt.

From a commercial power standpoint, it would have made more sense back in the 1940's to have developed thorium power reactors. Unfortunately for commercial power, back then the priority was creating large stockpiles of plutonium for the US military's nuclear weapon needs. Commercial power was only a secondary concern. So plutonium producing uranium reactors were developed instead.

Now that the cold war is over, commercial power is stuck with mature but inconvenient nuclear technology that creates unwanted plutonium. By comparison, thorium reactor technology is very immature. Lots of research money will have to be spent to bring it to maturity. Recently India announced that they were pursuing thorium reactor technology, due to that country's large thorium ore deposits.

Having said that, Luke Campbell points out thorium power reactors are not quite as weapon-proliferation free as the proponents like to think. For one thing it is quite possible to make a nuclear weapon out of 233U. There are some notes about proliferation risks of thorium reactors in this report.

Energy Content

RocketCat sez

So, how far can your ship go before it runs out of gasoline? Look at the table, find the fuel your ship uses, and look up the J/kg number (joules per kilogram, if you care). Divide the watts your engine produces by the J/kg and you'll see how many kilograms of uranium or plutonium you'll use up per second of thrust. It will probably be a tiny fraction of a gram, that stuff is potent.

FuelMeV/fissionJ/kg1000 MW burn
6Li? MeV? J/kg? gram/sec
235U202.5 MeV83.14×1012 J/kg0.01208 gram/sec
233U197.9 MeV81.95×1012 J/kg0.01220 gram/sec
239Pu207.1 MeV83.61×1012 J/kg0.01196 gram/sec
245Cu5.623 MeV2.22×1012 J/kg0.450450 gram/sec

In the table, the column you probably will be most interested in is the "1000 MW burn" or "burn rate requred to generate 1000 megawatts." This is how much nuclear fuel must be totally burnt (fissioned) each second to produces 1000 megawatts of thermal energy. As you can see, nuclear energy has a power concentration that makes petroleum look pathetic. The table tells us that if you wanted to generate 1000 megawatts for an entire year (3.15×107 seconds), it would only take a measly 380 kilograms of uranium-235. That's concentrated, a coal-fired power plant typically burns closer to 4 million tons in a year. The equation is:

burnRate = powerReq / Jkg

where:

  • burnRate = nuclear fuel burn rate (kg/sec)
  • powerReq = power to be generated (watts)
  • Jkg = joules per kilogram for the fuel, from table (J/kg)
Example

Say your nuclear lightbulb engine runs on uranium-235 and produces 4,600 megawatts of thermal energy. What is its nuclear fuel burn rate? Remember that 4,600 megawatts = 4,600,000,000 watts

  • burnRate = powerReq / (Jkg)
  • burnRate = 4,600,000,000 / 83,140,000,000,000
  • burnRate = 0.000055 kilograms per second = 0.055 grams per second

Keep in mind that the reactor or engine is probably going to require 2 to 50 kilograms of nuclear fuel to create a critical mass. So even if your reactor only needs to burn a couple of grams a week, the reactor still needs several tens of kilograms of fuel to be present in order to allow the few grams to burn.

Also keep in mind that your fuel rods will become so choked with nuclear poisons that they will stop producing energy even though most of the fuel is un-burnt. See reprocessing below.

The Details

Now I'm going to go into the boring scientific details, so if you are not interested you'd best skip to the next section.

Each fuel type has a certain amount of energy given off when each of its atoms split (or "fission"). This is measured in units called "electron volts" or "eV". For nuclear physics, it is useful to use units of "millions of electron volts" or "MeV". Uranium-235 fissions produces 202.5 MeV per atom, Uranium-233 produces 197.9 MeV and Plutonium-239 produces 207.1 MeV. You can find these values in Wikipedia or any nuclear physics textbook. If you want to calculate the values yourself, the equations are here.

There are 1.602602214179×10-13 joules in 1 MeV, so Uranium-235 fissions produces 3.244×10-11 joules per atom, Uranium-233 produces 3.171×10-11 joules and Plutonium-239 produces 3.318×10-11 joules.

The question then becomes "how many atoms are in a gram?" The answer was told to you in chemistry class, when your eyes glazed over as the professor talked about "molar mass" and the "Avogadro constant". Avogadro constant is about 6.02214179×1023 mol-1. This means if you made a pile of 6.02214179×1023 Uranium-235 atoms it would weigh exactly 235 grams. A pile of that number (one "mole") of Plutonium-239 would weigh exactly 239 grams.

The point is, you can use this to convert between atomic mass units and grams. Basically you divide Avogadro constant by the atomic mass of the element to find the number of atoms of that element in one gram. So Uranium-235 contains 6.02214179×1023 / 235 = about 2.5626135×1021 atoms per gram.

Now simply multiply each element's joules per fissioned atom by the number of atoms per gram and you'll have the amount of joules produced by totally burning the entire gram of nuclear fuel. For example: Uranium-235 produces 3.244×10-11 joules per fission, times 2.5626135×1021 atoms per gram gives us 8.3131182×1010 joules per gram. Divide by 109 to obtain 83.14 terajoules per kilogram (109 means multiplying by 103to get joules per kilogram then dividing by 1012 to get terajoules per kilogram).

One watt is one joule per second. So if you want to produce 83.14 terawatts, you'll have to burn 1 kilogram per second.

Radiation

How much deadly radiation does the engine or reactor spew out? That is complicated, but Anthony Jackson has a quick-and-dirty first order approximation:

r = (0.5*kW) / (d2)

where:

  • r = radiation dose (Sieverts per second)
  • kW = thermal power of the engine/reactor. For a reactor this will be greater than the power output of the reactor due to reactor inefficiency (kilowatts)
  • d = distance from the engine/reactor (meters)

This equation assumes that a 1 kW reactor puts out an additional 1.26 kW in penetrating radiation (mostly neutrons) with an average penetration (1/e) of 20 g/cm2.

Example

Let's say that the previously mentioned 4,600 megawatt thermal energy nuclear lightbulb was mounted in a NASA resuable nuclear shuttle. That is 49 meters long, with the crew module as far as it possibly can be from the engine. Remember that 4,600 megawatts = 4,600,000 kilowatts

  • r = (0.5 * kW) / (d2)
  • r = (0.5 * 4,600,000) / (492)
  • r = 2,300,000 / 2,401
  • r = 958 Sieverts per second

80 Sieverts is enough to instantly put a person into a coma, with certain death in 24 hours. Since this is over ten times that amount, per second, this engine is going to need lots of radiation shielding.

Nuclear Fuel Cycle

Processing

Percent 235UTerm
0.7%Natural Uranium
0.9%-2%Slightly Enriched Uranium
2%-20%Low Enriched Uranium
20%-85%Highly Enriched Uranium
85%-100%Weapons-Grade Uranium

The life cycle of nuclear fuel is a complicated subject.

In nature, uranium is found as uranium-238 (99.2742%), uranium-235 (0.7204%), and a very small amount of uranium-234 (0.0054%). This means that only seven-tenths of one percent of a given lump of uranium is useful as fuel. Luckily the 238U can be turned into plutonium fuel by a breeder reactor.

Plutonium does not occur naturally at all.

Pretty much all naturally occurring Thorium is Thorium-232. Thorium is more plentiful than Uranium.

For lack of any better information, I'd assume that the above figures would hold true for uranium deposits on other planets, moons, and asteroids.

Separating the 235U from the 238U (the technical term is "enrichment") is a royal pain. This is because the two are isotopes of the same element, which means quick and easy chemical techniques will not work at all (or only with great difficulty). As far as chemistry is concerned, 235U and 238U are the same thing. Chemistry works on an atom's electron structure, and both isotopes have an identical 92 electrons, of which 6 are valence electrons. The only difference is inside the atomic nucleus, out of the reach of chemistry but vital to nuclear reactions.

There are several uranium enrichment methods, all of which require a very high technology base and are annoyingly expensive. When a rogue nation starts investing in such technology it is cause for alarm.

Some heavy-water nuclear power reactors can actually manage to run with the thin gruel of natural uranium, with only 0.7% 235U. Other require Slightly enriched uranium (SEU) with 235U concentration of 0.9% to 2%. Low-enriched uranium (LEU) has a concentration of 235U from 2% to 20%, and is used in light water reactors. Anything above 20% is Highly enriched uranium (HEU) (used in fast-neutron reactors) and above 85% is Weapons-grade uranium (used in nuclear weapons).

I'm still trying to find some solid figures on the levels of enrichment on the reactor elements in a nuclear thermal rocket. The only source I've found suggests it will be from 60% to 93% 235U!!

The opposite of enriching is downblending; surplus HEU can be downblended to LEU to make it suitable for use in a power reactor.

Reprocessing

RocketCat sez

As you burn your uranium fuel rods, the blasted things clog up with nuclear poison crap. Eventually they won't burn any more, even though they still got plenty of fuel in them. Too much clog. All you can do is replace the rods, and send the clogged rods to a fuel reprocessing plant. You better have some spare rods aboard, Captain Peter Peachfuzz, or your ship might be out of gas a long way from nowhere.

The plant will melt 'em down, filter out the crap, and make new rods. Which is a royal pain in the posterior, see Processing above.

The experts ain't gonna tell us how much is "too clogged with poisons" is. Best guess I've read is at 15% fuel burnt (85% unburnt) for standard rods, 50% fuel burnt for rods made out of weapons-grade uranium salted with burnable poisons.

As a fuel rod undergoes a chain reaction, it gradually fills up with nuclear poisons. Eventually it is so full of poisons that it will no longer react. There is still plenty of fuel left in the rod (only about 15% of the fuel has been burnt), but it is too clogged with poison. The rod has to be removed and sent to a fuel reprocessing plant. The plant filters out the poisons and can recover 55 to 95% of the un-burnt fuel, to be made into a new fuel rod.

With reprocessing, in the long term each totally consumed kilogram of plutonium or highly enriched uranium (HEU) will yield ~1 × 1010 newton-seconds of impulse at a specific impulse of ~1000 seconds. Dr. John Schilling also warns that there is a minimum amount of fissionable material for a viable reactor. Figure a minimum of 50 kilograms of HEU.

The higher the level of enrichment, the longer the fuel rod can burn until it becomes clogged with nuclear poisons. That's why the nuclear thermal rocket uses HEU (or even weapons-grade) instead of LEU.

Dr. Schilling figures that as an order of magnitude guess, about one day of full power operation would result in enough fuel burnup to require reprocessing.

Another source (a certain Mr. Wilde) suggested that if your rods are weapons grade but salted with "burnable poisons", you could get 10,000 to 20,000 effective full power hours out of your rods. Your rods will become clogged after 50% of the fuel has been burnt, instead of only 15%. At this point, the principal concern starts becoming neutron embrittlement of the reactor vessel rather than fuel burnout. He goes on to say that the purpose of burnable poisons is to allow you to use very highly enriched uranium as fuel during early core life. The highly enriched 235U would generate far too much positive reactivity at BOL (beginning of life) to work with, and this is dampened with elements that absorb neutrons and then decay to or become an isotope of something that which does not (the burnable part), over core life so that the average positive reactivity add of the uranium is relatively even throughout core life.

As another data point, there are some indications that US Navy nuclear submarines use fuel rods that are above 90% 235U. Their reactors are designed to run for 30 years, but the reactors are NOT designed to be re-fueled. The exact details are classified.

One must always keep in mind that all this life-cycle and reprocessing stuff only applies to solid-core rockets (and nuclear-lightbulb close-cycle gas core). Liquid-core and (open-cycle) gas-core nuclear thermal rockets eventually blow all their nuclear fuel out their exhaust nozzles into the vast depths of space, so there is no way to take the expended fuel back to a reprocessing plant. This is why such propulsion systems put a premium on keeping the nuclear fuel inside the reaction chamber as long as humanly possible, if the unburnt nuclear fuel loss is too high such propulsion systems are too uneconomical to be used.

Extraterrestrial Sources

One theory of solar system formation is that there are more metals in the inner solar system. That would mean most of the uranium can be found at Mars, Mercury, Earth, Luna, Venus and asteroid belt.

In 2009, the Japanese Kaguya spacecraft detected uranium with a gamma-ray spectrometer as it orbited the Moon. Unfortunately it detected that uranium was in short supply on the Moon, less than the concentration in terrestrial granite. Lunar maria regolith is about 2 to 6 ppm uranium.

The asteroid Vesta is what astronomers call an "evolved object" or "protoplanet." This means it has a distinct core, mantle, and crust; unlike common asteroids that are more homogeneous. Objects become evolved if they are formed with enough radioactive material inside to melt the rock. I am unsure if this implies that Vesta has deposits of uranium large enough to be worth mining, but it's a start (some of my reading suggests that asteroid melting is caused by the decay of Aluminum-26, which is worthless as atomic fuel).

Other known protoplanets are Ceres, Pallas, and Kuiper Belt dwarf planets.

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