Fission weapons (aka "atomic bombs") did bring an end to World War II, but nuclear scientists did not rest there. The second way to use nuclear physics to release vast quantities of energy is by nuclear fusion. By 1951 the first fusion weapon had been designed, the Teller-Ulam thermonuclear weapon (aka "H-bomb"). Fission was now old-hat, fusion was tapping the same source of power as the freaking sun. It was the energy of the future.
And as year overtakes year, fusion power remains the "energy of the future", it never becomes the energy of today. As with most things it is far more difficult to do something constructive than to do something destructive. Scientists all over the world have been trying to develop fusion power since the 1950's, and they are still far away from the "break-even" point (where they actually get more energy out of the fusion reactor than they put in to kick start it). They keep working on it, though, because the benefits are huge. You get more energy from a gram of fuel, there is no chance of a runaway reaction (it is hard enough just to keep the reaction running), no chance of large-scale releases of radioactivity, little or no atmospheric pollution, the fuel is mostly harmless light elements in small quantities, waste has only short-lived radioactivity, and it does not produce weapons grade plutonium as a by-product.
There are two basic operations possible in the universe, analysis and synthesis. That is, breaking one large object into smaller parts, or assembly smaller parts into one larger object. The ancients called this "solve et coagula." With fission, you take one large unstable atom and break it into fission fragments (aka "split the atom"). With fusion, you take two or more small atoms and fuse them into one larger atom.
In both cases, when you weigh the things you start with and weigh the result, you will find the result weighs less. This is know as the binding energy mass defect. It represents the amount of matter that is turned into energy. Everybody knows that e = mc2, but unless you've had a physics class you may not know that c (the speed of light in a vacuum) is a mind-boggling huge number, and squaring a mind-boggling huge number makes it astronomically huger. Bottom line is that microscopic amounts of matter create titanic amounts of energy.
The conversion is 1 atomic mass unit = 931.494028(±0.000023) MeV.
As a side note, fission and radioactive decay makes atoms become smaller atoms, until the atoms become atoms of lead, where they are stable (i.e., they do not decay or otherwise undergo fission). Fusion, on the other hand, releases energy as you fuse larger and larger atoms, until the atoms grow such that they are atoms of iron. After than, fusing heavier atoms actually consumes energy instead of releasing it.
Golden-aged science fiction authors E.E."Doc" Smith and John W. Campbell jr. noted this and postulated space-opera science that required elements in the middle of the periodic table for direct conversion of all the mass into energy. In Doc Smith's "Skylark" series the element was copper and in John Campbell's The Space Beyond the element was iron. But I digress.
|p||Proton, ionized Hydrogen||1.007276|
|1H||Hydrogen-1, common Hydrogen||1.00794|
|3He||The infamous Helium-3||3.014932|
|4He||Helium-4, common Helium||4.001506|
|7Li||Lithium-7, common Lithium|
|11B||Boron-11, common Boron||11.00931|
The Particles table gives the symbols of the various fusion fuels. The particle mass is given if you want to amuse yourself by calculating the binding energy mass defect of various reactions.
Jerry Pournelle is pretty sure tramp spacecraft owners will call Deuterium "Dee". For the same reason people call automobiles "cars."
Tritium is annoying since it has a fast half-life of only 12.32 years; e.g., after about twelve years half of your tritium has decayed into Helium-3. Use it or lose it. This is why there are no tritium mines. Most reactor designs that use tritium incorporate a tritium breeder. This usually takes the form of a tank of liquid lithium surrounding the reactor, sucking up the neutrons and transmuting the lithium into fresh tritium and helium-4.
The infamous Helium-3 is often touted as an economic motive for space industrialization, unfortunately it is not a very good one. There are no Helium-3 mines on Terra, so it is hard to obtain. Space enthusiasts trumpet the fact that there are helium-3 deposits on the moon that can be mined, but they don't mention that it is in a very low concentration. You have to process over 100 million tons of Lunar regolith to obtain one lousy ton of helium 3.
It is possible to manufacture the stuff, but it takes lots of neutrons. Basically you breed tritium and wait for it to decay. There is lots of helium-3 available in the atmosphere of Saturn and Uranus, if your space infrastructure is up to the task of traveling that far from Terra. Helium-3 concentration is estimated at about 10 parts per million, which beats the heck out of Luna. Jupiter has helium-3 as well, but its steep gravity well makes it uneconomical to harvest.
Helium-4 is also called an alpha particle. It is a charged particle. This means that any fusion reaction that produces alpha particles can be used to generate electricity. The particles are directed by magnetic fields and trappped to extract electrical current. This can be useful if you wish to use that reaction for both propulsion and ship's electricity.
|D + D||⇒||T|
|p + 11B||⇒||3×4He||8.7||69.97||100%|
|D + T||⇒||4He|
|D + 3He||⇒||4He|
|n + 6Li||⇒||T|
|n + 7Li||⇒||T|
- Reaction: Input fusion fuels ⇒ reaction products (for example the fourth row shows that fusing one nuclei of deuterium with one nuclei of tritium results in one helium-4 nuclei, one neutron, and 17.6 MeV of energy)
- MeV / fusion: mega-electron-volts of energy from each individual fusion event (as per the equation above)
- TJ/kg: Terajoules of energy from one kilogram of fusion fuel (I calculated this, use at your own risk)
- % Thermal / %Neutrons / % Radiation: Breakdown of energy released into thermal energy, neutron energy, and Bremsstrahlung radiation energy
- 1000 MW burn g/s: grams per second of fusion fuel requred to burn at a rate of 1000 megawatts (I calculated this as well, treat this also as suspect)
- L-C: Lawson criterion, how hard it is to start and maintain the reaction
- A-N: Aneuronic, does the reaction produce neutrons? Please note that even if there is no n symbol in the results column neutrons can still be produced by side-reactions
- Exhaust velocity: Exhaust velocity for a pure fusion engine
The Reaction table displays the various fusion reactions that look promising for power plants and spacecraft. Note that the Deuterium + Deuterium reaction has two possible outcomes and thus two rows in the table. Each outcome has about a 50% chance of occurring. The two lithium reactions are not power or rocket reactions, they are the tritium breeding methods mentioned above.
There are many fusion reactions, but only a few are suitable for use as power sources or rocket fuels. There are lots of limitations that you can read about here. Of the candidates, you want to use those with low Lawson criterion, which measures how hard it is to start and maintain the reaction. It is a plus if the reaction only produces charged particles, since these can be turned into elecctricity directly, instead of having to be converted into heat first.
Finally it is a plus if the reaction does not release neutrons, because they are not only dangerous radiation, but they have the nasty habit of weakening engine parts ("Neutron embrittlement"), and transmuting engine parts into radioactive elements ("Neutron activation"). Unless you are using the neutrons to breed tritium.
The D + 3He reaction is of particular interest for rocket propulsion, since all the products are charged particles. This means the they can be directed by a magnetic field exhaust nozzle. Having said that, while D-3He is aneuronic, if you mix a bunch of deuterium and helium-3, some of the deuterium is going to be wayward and insist upon fusing with other deuterium instead of helium-3 like you want. Sadly D-D fusion reactions do produce neutrons. In theory it is possible to use spin-polarized 3He in the fusion fuel to absorb the neutrons. You will get less energy out of each gram of fusion fuel, but with the advantage of a lot less deadly neutron radiation.
The p + 11B reaction is the celebrated Hydrogen-Boron fusion, sometimes called "thermonuclear fission" as opposed to the more common "thermonuclear fusion". It too is aneuronic, but it does have two nasty side reactions. One makes a Carbon-12 atom and a gamma ray, the other makes a Nitrogen-14 atom and a neutron. The first side reaction is quite a bit less likely than the desired reaction, but gamma rays are harmful and quite penetrating. The second side reaction occurs with secondary alpha particles before they are thermalized. However the main draw-back is a truely ugly Lawson criterion. D+3He only has a Lawson of 16, Hydrogen-Boron has an overwhelming 500. On the plus side, in theory the Lawson criterion can be lowered by using antiprotons as a catalyst. Recently (2015) one study suggested that using picosecond laser pulses instead of microsecond could make things easier.
The Deuterium-Tritium reaction is easy to ignite (low Lawson criterion), but it uses that pesky decaying tritium. Hydrogen-Boron (a proton is an ionized hydrogen atom) has the advantage of being aneutronic, but is very difficult to ignite, with a whopping Lawson criterion of 500! Helium-3+Helium-3 is also aneutronic, but helium-3 is hard to come by. Which is probably why I could not find any source quoting its Lawson criterion.
Proton-proton fusion is what the Sun uses, and what Bussard Ramjets would like to use. Four protons fuse to create an atom of helium-4 and 26.73 MeV of energy. Trouble is that the Lawson criterion is off the top of the chart. Trying to get four protons to simultaneously fuse is almost impossible, short of using an actual star.
To make the fusion reactor into a fusion rocket, the fusion energy has to be used to accelerate reaction mass. The method will determine the exhaust velocity/specfic impulse, which is the critical variable in the delta V equation.
Pure fusion rockets use the fusion products themselves as reaction mass. Fusion afterburners and fusion dual-mode engines use the fusion energy (plasma thermal energy, neutron energy, and bremsstrahlung radiation energy) to heat additional reaction mass. So afterburners and dual-mode reduce the exhaust velocity in order to increase thrust.
- Pure fusion rockets use just the plasma thermal energy, and just the fusion products as reaction mass
- Fusion afterburners use just the plasma thermal energy, but adds extra reaction mass to the fusion products
- Dual-mode use the neutron and bremsstrahlung radiation energy, and adds extra reaction mass to the fusion products. In addition a Dual-mode can switch into Pure Fusion mode.
The advantage is incredibly high exhaust velocity (though sometimes it can be too high).
The disadvantage it the absurdly small thrust.
To calculate the exhaust velocity of a Pure Fusion Rocket:
Ve = sqrt( (2 * E) / m )
- Ve = exhaust velocity (m/s)
- E = energy (j)
- m = mass of fuel (kg)
Remember Einstein's famous e = mc2? For our thermal calculations, we will use the percentage of the fuel mass that is transformed into energy for E. This will make m into 1, and turn the equation into:
Ve = sqrt(2 * Ep)
- Ep = fraction of fuel that is transformed into energy
- Ve = exhaust velocity (percentage of the speed of light)
Multiply Ve 299,792,458 to convert it into meters per second.
This is based on information from physicist Luke Campbell.
For a given mission with a given delta V requirement, it is possible to calculate the optimum exhaust velocity. In many cases a fusion engine has thrust too low to be practical, but the exhaust velocity is way above optimal. It is possible to increase the thrust at the expense of the exhaust velocity (and vice versa) by shifting gears. An afterburner for a fusion engine is a way to shift gears.
A pure fusion engine just uses the hot spent fusion products as the reaction mass. An afterburner fusion engine has a second plasma chamber (the afterburner) constantly filled with some cold propellant (generally hydrogen or water, but you can use anything that the spend fusion plasma can vaporize). The hot spent fusion products are vented into the afterburner, heating up the cold propellant. The average temperature goes down (decreasing the exhaust velocity) while the propellant mass flow goes up (increasing the thrust). The propellant mass flow increases naturally because instead of just sending the fusion products out the exhaust nozzle, you are sending out the fusion products plus the cold propellant. The contents of the afterburner are sent out the exhaust nozzle and Newton's Third Law creates thrust.
In the equations below, a nozzle with an efficiency of 100% would have a efficiency factor of 2.0. But in practice the efficiency maxes out at about 85%, which has an efficiency factor of 1.7
eq.1 Ptherm = F2 / (1.7 * (F / Ve))
eq.2 mDot = F2 / (1.7 * Ptherm)
eq.3 Ptherm = F2 / (1.7 * mDot)
eq.4 F = sqrt[ 1.7 * Ptherm * mDot ]
eq.5 Ve = F / mDot
eq.6 mDot = F / Ve
F = thrust (newtons)
Ptherm = Thermal power (watts)
mDot = propellant mass flow (kg/s) spent fusion product propellant + cold reaction mass
Ve = Exhaust Velocity (m/s)
1.7 = efficiency factor
sqrt[ x ] = square root of x
The thermal power is obtained from the fusion fuel table, using the % Thermal value. For instance, if you were using D + T fuel, 21% of the power from the burning fuel is what you use for Ptherm. That is, if the engine is burning 0.001 kilograms of D+T per second, it is outputting 339.72×1012 * 1×10-3 = 339.72×109 watts of energy, so Ptherm equals 339.72×109 * 0.21 = 7.1341×1010 watts.
The amount of mDot contributed by spent fusion products can also be obtained from the fusion fuel table by using the TJ/kg column. For instance, with D+T fusion, if the rocket needs Ptherm of 2 terawatts, the total energy needed is 2 / 0.21 = 9.52 terawatts. The spent fusion products mDot is 9.52 / 339.72 = 0.028 kg/s. Usually the spent fusion product mass will be miniscule compared to the cold propellant mass. That is the reason the thrust was so miserably low to start with.
The equation you use depends upon which value you are trying to figure out.
- When you have decided on the thrust and exhaust velocity, and want to know how much Thermal Power you need.
- When you have decided on the thrust and thermal power, and want to know how much propellant mass flow you need.
- When you have decided on the thrust and propellant mass flow, and want to know how much Thermal Power you need.
- When you have decided on the thermal power and the propellant mass flow, and want to know how much thrust you will get.
- When you have decided on the thrust and propellant mass flow, and want to know how much exhaust velocity you will get.
- When you have decided on the thrust and exhaust velocity, and want to know how much propellant mass flow you will need.
This is based on information from physicist Luke Campbell.
The neutron and bremsstrahlung energy produced by the fusion reaction is basically wasted energy when it comes to rocket propulsion. A dual-mode engine can switch from pure fusion mode into harvesting mode. This means additional cold propellant mass is moved around the fusion reaction chamber to be heated by the neutrons and bremsstrahlung radiation. This augments the thrust, at the expense of increasing the propellant usage rate.
If the additional exhaust nozzles have an efficiency of 70%, and the additional propellant has an exhaust velocity of 10,000 m/s, the harvesting mode engine will create thrust of 1 newton per 7,000 watts of neutron + bremsstrahlung power, and consume 0.0001 kilograms of propellant per newton of thrust per second.
There are some designs that try to harvest the wasted neutron and bremsstrahlung energy by attempting to turn it into electricity instead of thrust. But sometimes it is not worth it. To avoid excessive radiators the power generator typically have a maximum efficiency of 25% or less. So a maximum of 25% of the combined neutron+bremsstrahlung energy can be turned into electricity. This requires a turbine and electrical generator, which cuts into the payload mass.