Why fool around with dirty, obsolete, uncool, relatively weak, and dangerously radioactive nuclear fission when you can use clean, cutting edge, trendy, more powerful, and practically radiation-free nuclear fusion?

Because we can't figure out how to build a blasted fusion reactor, that's why.

Researchers have been promising us a workable fusion reaction "in the next ten years" for more than half a century now. To me they look like Lucy telling Charlie Brown to come kick the football just one more time. Methinks the problem is just a tad more difficult than they are willing to admit to their investors.

This is also one of two reasons why fans of mining Helium-3 on Luna are actually trying to sell you swamp land in Florida.

Magnetic confinement fusion tries to hold the frantically squirming fusion plasma in a complicated magnetic field. I've been told this is about as easy as using a web of rubber bands to hold a blob of gelatin or trying to nail Jell-O to the wall. Every time they figure out how to add more magnetic fields to deal with the latest fusion instability, the fusion plasma figures out three more new ways to wiggle out.

And inertial confinement fusion is shooting at a speck of fusion fuel with hundreds of lasers arranged like a three-dimensional circular firing squad, and hope that if you get lucky the resulting fusion explosion doesn't scrag the reactor.

But if they can ever get it to work, woo-boy, then we'll be cookin' with gas.

D-T fusion starts with deuterium and tritium and has a result of one helium-4 atom and a neutron. The starting mass is 2.013553 + 3.015500 = 5.029053. The ending mass is 4.001506 + 1.008665 = 5.010171. Subtracting the two, we find a mass defect of 0.018882. Multiply by 931.494028 to find an energy release of 17.58847 MeV. This is rounded up in the table below to 17.6 MeV.

Can we harness the most abundant fuel in the universe?

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Introduction

Nuclear fusion is often marketed as “star energy”, but this glosses over a fundamental difference between the fusion reactions that occur in stars and terrestrial fusion reactors. While stars are capable of fusing the lighter (and more abundant) isotope of hydrogen into helium, fusion reactors are limited to reactions that involve heavier (and rarer) isotopes of hydrogen, such as D-D, D-T, and D-He3. The reason for this is that reactor plasmas of practical density are optically thin and therefore lose energy by bremsstrahlung radiation (in contrast, magnetized plasmas of achievable density can efficiently absorb cyclotron radiation). The requirement that fusion power exceeds bremsstrahlung power rules out all but a small number of possible fusion reactions.

This issue represents a significant limitation on the ultimate fusion energy resources available to an advanced civilization. Fusing all the Deuterium in Earth’s oceans with maximum energy utilization would release 2.7 ·10³¹ Joules (8.5·10²³ watt-years), which could power a Type-I civilization (1.7·10¹⁷ watts) for 5 million years. In comparison, complete fusion of hydrogen would release 10³⁵ Joules (3·10²⁷ watt-years), which could power a Type-I civilization for 18 billion years.

The limitations of fusion reactors will be explored in more detail in the following sections. In addition, a speculative proposal for the practical utilization of hydrogen in fusion reactors will be discussed.

Fusion Reaction Types

Fusion reactions fall into three categories based on the fundamental force that mediates the reaction. The strong nuclear force, the strongest fundamental force, mediates fusion reactions with the highest cross sections (i.e. highest probability of occurring). These reactions typically involve two reactants forming two products, with momentum conserved by opposing motion of the products. A important example is the D-T reaction, which is used in nuclear bombs and fusion reactors:

Cross sections for these reactions tend to be on the order of 0.1–1 barns:

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While fusion reactors exclusively use strong force mediated reaction, stars incorporate them only as part of reaction chains that include slower reactions mediated by electromagnetic or weak forces. Because the slowest-step in a reaction chain determines the reaction rate, strong force reactions never set the reaction rate inside a star.

Fusion reactions mediated by the electromagnetic force typically involve two reactants forming one product, with momentum conserved by the emission of a gamma ray. These reactions tend to have intermediate cross sections and play a significant role in stellar energy production. An important example is the following reaction between carbon and hydrogen which forms the first step of the CNO-cycle, a hydrogen burning reaction chain:

The cross section of this reaction is much lower than the strong force mediated reactions, reaching 0.1 millibarns at 0.46 MeV.

Other CNO reactions display similarly low cross sections:

Finally, weak force mediated reactions typically involve two reactants forming one product, with momentum conserved by emission of leptons (and/or anti-leptons). These reactions tend to have the lowest cross sections. Unlike the previous two reaction types, weak force reactions do not conserve atomic number. The most important example in this category is the pp-reaction, which converts a proton to a neutron by positron emission:

A less common variant known as the pep-reaction converts a proton to a neutron by electron-capture:

Either reaction can form the first step of the Proton-Proton chain, a slow hydrogen burning reaction chain.

Bremsstrahlung

As mentioned previously, in order for a fusion reaction to be viable for use in reactors here on Earth, it must produce energy at a rate that exceeds bremsstrahlung emission. This is not a relevant constraint for stellar nuclear fusion because the stellar core is dense enough that it can reabsorb nearly all bremsstrahlung that is produced.

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There are several conditions that must be met for fusion reaction viability. The first is that the reaction must have a sufficiently high cross section to maintain high power output. In practice, only strong force mediated reactions have sufficiently high cross sections to be considered viable. The second condition concerns the composition of reactants involved. Bremsstrahlung power scales quadratically with ion charge, so reactants with high atomic numbers are disfavored. Finally, the reaction itself must be highly exothermic to have the best chance of achieving ignition. The combination of all these conditions restricts the set of viable fusion reactions to D-T, D-D, and D-He3.

The “bremsstrahlung problem” is a significant constraint for futuristic applications of fusion energy. Robert Bussard proposed that instead of a starship carrying enough fuel to take it all the way to its destination, it could propel itself by fusing hydrogen collected from the interstellar medium en-route. Such spaceships are known as Bussard Ramjets

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The flaw with Bussard’s idea that the pp-reaction cross section is far too low to be useful. Daniel Whitmire’s proposed modification of the Bussard Ramjet replaces the pp-reaction with the CNO cycle for hydrogen burning:

Here we show that the problem of the slow PPI rate can be resolved in principle by exploiting a proton burning catalytic cycle similar to the well known CNO BiCycle occurring in sufficiently hot main sequence stars. The slowest links in the catalytic chains will be found to be 10¹⁸–10¹⁹ times faster than the PPI rate at an ion temperature of 86 keV and number density of 5 x 10¹⁹/cm³.

However, the paper mainly addresses the ability of reacting fusion plasma to accelerate itself at a rate comparable to 1 g. While the CNO cycle would certainly give better performance in this regard, Whitmire acknowledges that the CNO cycle is not capable of overcoming bremsstrahlung losses:

A straightforward calculation indicates that radiation energy losses at T(electron)=86.2 keV are greater than energy production for either catalytic cycle.

He goes on to propose that an optically thick plasma could resolve this problem:

At the reactor densities and dimensions considered here…some of the cyclotron and bremsstrahlung radiation will be reabsorbed. On the other hand, too much interaction between the radiation and matter will tend to bring the electron and ion temperatures into equilibrium and create a radiation pressure that must be taken into account.

Unfortunately, a closer analysis shows that this will not work. Equilibrium confinement of outgoing radiation at fusion temperatures requires plasma densities similar to those found in stellar cores. Such densities are inaccessible in a magnetic confinement reactor, but can be achieved briefly using inertial confinement.

In conventional ICF, high density is not strictly mandatory — there is a trade-off between density and pellet radius. The energy confinement time of an ICF plasma is approximately equal to the time needed for a thermal ion to traverse the radius of the plasma. Working through the math, the figure of merit for ICF fusion can be given as ρR, which is the minimum product of density and radius that an ICF plasma must attain in order to produce net energy. The reason why compression factors are so large is that the initial volume of fuel is quite small (NIF uses 40 MJ of fusion fuel per pulse). Thus, to get a good ρR, one must use a very high density and low radius. Note that this implies that the high density condition for conventional ICF could be relaxed by using a much larger pellet. Once the desired level of compression is achieved, methods for starting fusion in the pellet include volumetric ignition and hotspot ignition leading to a thermonuclear detonation wave.

If the plasma is required to be in equilibrium with its own radiation, the dimensions of the pellet are bounded below by the attenuation length for bemsstrahlung radiation, which is a function of plasma temperature and density. Very high plasma densities (comparable to NIF pellets) are needed to achieve reasonable attenuation lengths (on the order of meters). Plasma density also sets the ratio of photon energy to thermal energy in equilibrium, which once again requires very high densities (comparable to NIF pellets) for a reasonable ratio. For fusion reactions that produce orders of magnitude more bremsstrahlung than fusion power (such as electromagnetically mediated reactions), the pellet dimension may need to significantly exceed bremsstrahlung attenuation length in order to achieve a high degree of energy confinement. Development of high-efficiency drivers for high compression is essential for net-energy burning of advanced fusion fuels with ICF.

In addition to increasing pellet radius, energy confinement may be increased by using magnetic fields. Externally applied magnetic fields cannot achieve the strengths required to confine an ICF plasma, but external fields can be amplified into ultra-strong fields during the compression process itself, helping to improve energy confinement time and favorably alter other properties of plasma burning.

Electron degeneracy effects in ultra-dense plasmas and ultra high fields (on the order of 1 million Tesla) could directly suppress bremsstrahlung power. Bremsstrahlung may also be suppressed by operating at the low temperature, ultra high pressure regime (“pycnonuclear fusion”). Reaction rates may be enhanced in dense plasmas through plasma screening of the coulomb barrier.

The extreme conditions needed for burning advanced fusion fuels using ICF are a significant obstacle to realizing the “Caplan Thruster”, a Bussard Ramjet that uses the CNO and Triple Alpha cycles to power a stellar engine:

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Using ICF to run a hydrogen burning CNO cycle carries additional challenges. ICF cannot accommodate reaction chains that include radioactive decays, because decay times vastly exceed the confinement time of ICF plasmas. This is reflected in the proposal to only carry out the Hot-CNO cycle up to Oxygen-14. However, this is only a limitation for a “once through” system. Full hydrogen burning could be accomplished in multiple stages by capturing products, waiting for radioactive decay, and reinserting into a later stage.

Proton Burning

Avoiding large ICF pellet sizes requires a different approach to hydrogen burning. For practical hydrogen burning, we will need to consider a method of proton burning that improves on the CNO cycle. The main difficulties are that the cross section is too low and the rate of bremsstrahlung emission is too high. The cross section problem can be addressed by replacing the CNO cycle with a higher cross section reaction, and bremsstrahlung emission can be reduced by using a non-neutral plasma in which all electrons have been removed.

The main reason why hydrogen burning is hard is because of the role that the weak force must play in generating atomic number violation. The pp-chain requires that atomic number is violated at the exact moment of fusion, resulting in an exceedingly low cross section.

The CNO cycle achieves higher performance than the pp-chain by deferring atomic number violation until after the fusion reaction is complete. Each fusion reaction is mediated by a relatively high cross section electromagnetic interaction that requires no atomic number violation. Atomic number is only violated later by radioactive decay. A series of proton-capture reactions followed by radioactive decays eventually ends in a strong force mediated reaction that results in the emission of a helium nucleus, completing the cycle.

Thus, if we want to achieve further improvements in cross section, we will need to find hydrogen-consuming fusion reactions that are mediated by the strong interaction, generate atomic number violation by subsequent radioactive decay, and produce products that eventually match the inputs, resulting in a complete cycle.

A simple class of reactions that can satisfy these conditions are the (p,n) reactions, which involve a nucleus capturing a proton and subsequently emitting a neutron. Reactions which satisfy all three conditions are necessarily endothermic, but as part of a series of reactions that start with hydrogen and end with helium, the net energy release will still be positive. The basic idea is that we use these reactions to convert protons into neutrons, use the neutrons to produce deuterium, and then fuse deuterium by conventional methods into helium. These reactions can be divided into two sub-types:

The first type involves a product that decays by positron emission, lowering the atomic number by 1. These reactions tend to be more endothermic due to the production of a positron, but some of the energy can be recovered by annihilating the positron with an electron. In addition to their use for producing neutrons, these reactions would also make a great source of antimatter (positrons). An example of this reaction type involves the conversion of carbon-13 to nitrogen-13:

The reaction has a relatively high cross section at energies of a few MeV:

The second type involves a product that decays by electron capture, lowering the atomic number by 1. These reactions tend to be less endothermic than the positron emitting reactions, but also tend to require nuclei with higher-Z. In a fusion plasma, these reactions would lose more energy to bremsstrahlung as a result. An example of this reaction type is the conversion of chlorine-37 to argon-37:

This reaction also has a relatively high cross section at energies of a few MeV:

In either case, because the atomic numbers are significantly greater than one, bremsstrahlung losses will be high. One method of reducing radiation losses is by using a pure-ion plasma. Ions radiate far less intensely than electrons, which makes pure-ion plasmas ideal for low bremsstrahlung fusion.

In addition to radiating far less intensely, pure-ion plasmas are much easier to magnetically confine. However, a major obstacle to using pure-ion plasmas in fusion is the requirement that the magnetic field overcomes electrostatic repulsion on top of thermal pressure. The Brillouin Limit quantifies how dense a non-neutral plasma can be for a given confining magnetic field. For an all proton plasma confined by a 20 Tesla field, that density is only 10¹² ions/cm³.

Achieving plasma density of order 10¹⁴ ions/cm³ in a pure ion plasma— a comparable plasma density to the ITER reactor, would require a field strength of 200 Tesla. Such fields are beyond the capabilities of existing technology. The record field produced in a lab was 100 Tesla, and that field generated an outward pressure of 3.98 GPa on the coil structure. Increasing the field strength to 200 Tesla would require the ability to handle pressures of 16 GPa. By comparison, the tensile strength of commercially available carbon fibers can reach 7 GPa, while atomically engineered nanomaterials like Graphene are theoretically capable of achieving 130 GPa. Clearly, a 200 Tesla field would be extraordinarily challenging to realize without ultra-strong nanomaterials. Using only existing materials, we can take advantage of the fact that the stress in the confining structure will differ from the internal pressure depending on geometry. In particular, stress can be reduced arbitrarily in a thick shell.

More speculatively, the outward pressure produced by solenoid currents (in an internal layer) could be countered by the inward pressure generated by axial currents (in an outer layer) — removing mechanical strength as a relevant constraint. The solenoid layer only produces a non-zero B-field in its interior, while the axial layer only produces a non-zero B-field on its exterior layer. Thus, the magnetic fields will not interfere. This works in the infinite case; determining whether the concept can work in the finite or toroidal case is crucial to making this concept work in practice. Finding superconducting materials with a sufficiently high critical field would be necessary, as resistive electromagnets would dissipate too much power.

Lower fields may be usable in situations where volume is not an important constraint. Operating the reactor at 20 Tesla instead of 200 Tesla would require 10,000 times more volume for the same power output. Such large volumes are impractical for Earth-based reactors, but could be feasible in space.

The exact details of reactor operation would depend on the type of (p,n) reaction involved. If a reaction from the electron-capture category is used, we will have a choice between directly removing the fusion product from the plasma or injecting electrons into the plasma to permit the product to decay by an electron capture reaction. If a reaction from the positron-decay category is used, we will have a choice between direct removal of the product or permitting the product to decay in-situ and either removing the positrons or injecting electrons into the plasma to annihilate the positrons. Which ever technique is chosen, it will have to be done in a way that does not significantly degrade energy confinement time.

By using (p,n) reactions as a neutron source for the conversion of hydrogen into deuterium, followed by reaction chains that convert deuterium into helium, full conversion of hydrogen into helium would become possible.

The requirement to stringently minimize losses in the (p,n) reaction could be relaxed if an external source of high-energy protons can be obtained. A high energy proton source could directly “drive” the lossy (p,n) reactions, instead of relying on recirculating power to do this. The D-He3 reaction, an intermediate step in the process of fusing deuterium into helium, produces a highly energetic 14.7 MeV proton, making it an ideal source of high energy protons to “drive” an endothermic (p,n) reactor.

Conclusion

Precise calculations need to be done to confirm whether a (p,n) reaction can produce neutrons at sufficiently low energy cost to enable profitable hydrogen burning. Fusing 4 hydrogen atoms into helium requires the conversion of 2 protons into neutrons, yielding a net energy gain of 26.7 MeV. A (p,n) reactor can therefore afford to lose 13 MeV per neutron and still be profitable, a figure that compares favorably to the 1.5–3 MeV consumed by the endothermic reaction itself (though all loss channels will need to be accounted for to assess feasibility).

If determined to be feasible, a demonstration reactor using low-fields could be built today. Profitable operation of the (p,n) reaction will allow us to look forward to a future with thousands of times more fusion energy than we once thought available.

Of these reactions, the fusion of deuterium and tritium (D-T), has the lowest ignition temperature (40 million degrees K, or 5.2 keV). However, 80% of its energy output is in highly energetic neutral particles (neutrons) that cannot be contained by magnetic fields or directed for thrust.

In contrast, the ³He-D fusion reaction (ignition temperature = 30 keV) generates 77% of its energy in charged particles, resulting in substantial reduction of shielding and radiator mass. However, troublesome neutrons comprise a small part of its energy (4% at ion temperatures = 50 keV, due to a D-D side reaction), and moreover the energy density is 10 times less then D-T. Another disadvantage is that ³He is so rare that 240,000 tonnes of regolith scavenging would be needed to obtain a kilogram of it. (Alternatively, helium 3 can be scooped from the atmospheres of Jupiter or Saturn.)

Deuterium, in contrast, is abundant and cheap. The fusion of deuterium to itself (D-D) occurs at too high a temperature (45 keV) and has too many neutrons (60%) to be of interest. However, the neutron energy output can be reduced to 40% by catalyzing this reaction to affect a 100% burn-up of its tritium and ³He by-products with D.

The fusion of 10% hydrogen to 90% boron (using ¹¹B, the most common isotope of boron, obtained by processing seawater or borax) has an even higher ignition temperature (200 keV) than ³He-D, and the energy density is smaller. Its advantage is that is suffers no side reactions and emits no neutrons, and hence the reactor components do not become radioactive.

The ⁶Li-H reaction is similarly clean. However, both the H-B and ⁶Li-H reactions run hot, and thus ion-electron collisions in the plasma cause high bremsstrahllung x-ray losses to the reactor first wall.

(ed note: Luke Campbell is giving advice to somebody trying to design a torchship. So when he says that magnetic confinement fusion won't work, he means won't work in a torchship. It will work just fine in a weak low-powered fusion drive.)

For one thing, forget muon catalyzed fusion. The temperature of the exhaust will not be high enough for torch ship like performance.

You might use a heavy ion beam driven inertial confinement fusion pulse drive, or a Z-pinch fusion pulse drive.

I don't think magnetic confinement fusion will work — you are dealing with a such high power levels I don't think you want to try confining this inside your spacecraft because it would melt.

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D-T (deuterium-tritium) fusion is not very good for this purpose. You lose 80% of your energy to neutrons, which heat your spacecraft and don't provide propulsion. 80% of a terrawatt is an intensity of 800 gigawatts/(4 π r²) on your drive components at a distance of r from the fusion reaction zone. (see here for more about drive component spacing)

If we assume we need to keep the temperature of the drive machinery below 3000 K (to keep iron from melting, or diamond components from turning into graphite), you would need all non-expendable drive components to be located at least 120 meters away from the point where the fusion pulses go off.

(ed note: 120 meters = attunation 180,000. 800 gigawatts / 180,000 = 4.2 megawatts)

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D-D (deuterium-deuterium) fusion gives you only 66% of the energy in neutrons. However, at the optimum temperature, you get radiation of bremsstrahlung x-rays equal to at least 30% of the fusion output power.

For a terawatt torch, this means you need to deal with 960 gigawatts of radiation. You need a 130 meter radius bell for your drive system to keep the temperature down.

(ed note: 130 meters = attunation 210,000. 960 gigawatts / 210,000 = 4.5 megawatts)

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D-³He (deuterium-helium-3) fusion gives off maybe 5% of its energy as neutrons. A bigger worry is bremsstrahlung x-rays are also radiated accounting for at least 20% of the fusion output power. This lets you get away with a 66 meter radius bell for a terawatt torch.

(ed note: 66 meters = attunation 55,000. 250 gigawatts / 55,000 = 4.5 megawatts. I guess 4.5 megawatts is the level that will keep the drive machinery below 3000 k)

To minimize the amount of x-rays emitted, you need to run the reaction at 100 keV per particle, or 1.16 × 10⁹ K. If it is hotter or colder, you get more x-rays radiated and more heat to deal with.

This puts your maximum exhaust velocity at 7,600,000 m/s, giving you a mass flow of propellant of 34.6 grams per second at 1 terawatt output, and a thrust of 263,000 Newtons per terawatt.

This could provide 1 G of acceleration to a spacecraft with a mass of at most 26,300 kg, or 26.3 metric tons. If we say we have a payload of 20 metric tons and the rest is propellant, you have 50 hours of acceleration at maximum thrust. Note that this is insufficient to run a 1 G brachistochrone. Burn at the beginning for a transfer orbit, then burn at the end to brake at your destination.

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Note that thrust and rate of propellant flow scales linearly with drive power, while the required bell radius scales as the square root of the drive power. If you use active cooling, with fluid filled heat pipes pumping the heat away to radiators, you could reduce the size of the drive bell somewhat, maybe by a factor of two or three. Also note that the propellant mass flow is quite insufficient for open cycle cooling as you proposed in an earlier post in this thread.

Due to the nature of fusion torch drives, your small ships may be sitting on the end of a large volume drive assembly. The drive does not have to be solid — it could be a filigree of magnetic coils and beam directing machinery for the heavy ion beams, plus a fuel pellet gun. The ion beams zap the pellet from far away when it has drifted to the center of the drive assembly, and the magnetic fields direct the hot fusion plasma out the back for thrust.

It seems like the main question is how much energy you get from burning 1 kg of deuterium—helium-3 mixture.

If you are just burning it without worrying about using the reactants as a rocket, you will get 350 TJ/kg. Assuming 100% efficiency, complete burnup. and the ability to collect all the emitted energy (including neutrons).

If you are using it for a rocket, however, it will be difficult to just find a way to only emit the reaction products without also letting the fusion fuel leak out. After all, you're producing the exhaust stuff in the middle of your fuel. Instead, what you probably do is heat the fusion fuel with the fusion reaction until it is at 100 keV of energy, and let the hot plasma escape as your rocket plume. This will produce 29 TJ of useful work for each kg of fuel/propellant expended. Since you're losing about 25% of your energy to neutral particle radiation, your actual fusion reaction will be producing more like 39 TJ/kg. But you can't use the latter figure in any of your thrust equations because the bremsstrahlung and x-rays won't be doing you any good.

For the question about the contribution of visible, infrared, and ultraviolet light to the heating, it will be negligible. Actually, it should already be included in the bremsstrahlung losses, but the spectrum of the bremsstrahlung at 100 keV is so heavily peaked toward the x-ray spectral region that lower frequency stuff will be tiny in comparison. You will get some minor corrections to the spectrum when the fusion exhaust fuel/propellant is optically dense (that is, light produced inside it has difficulty getting out) leading to a black body spectrum over the optically dense spectral regions — but any practical fusion fuel will be optically thin to x-rays so this will not make much of a difference.

I think you (Winchell) already have a good description of the likely appearance of a torch drive nozzle on your site, with diagrams of magnetic nozzles and blade shields.

If I missed something, or there are other questions, let me know.

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SHOW YOUR WORK SECTION:

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If you are just burning it without worrying about using the reactants as a rocket

From Wikipedia Nuclear Fusion the energy of the He-4 particle from D - He-3 fusion is 3.6 MeV, and the energy of the proton is 14.7 MeV. 1 MeV is 1,000,000 times 1.602×10^-19 J (1.602×10^-13 J). This gives the energy of the reaction products of a singe D - He-3 fusion.

(ed note: 3.6 MeV + 14.7 MeV = 18.3 MeV = energy of reaction products in MeV
1.602×10^-13 * 18.3 = 2.932×10^-12 Joules = energy of reaction products in Joules)

The mass of a He-3 atom is 3.016 AMU (atomic mass unit, also sometimes denoted u), the mass of a deuteron is 2.014 AMU. One AMU is 1.66E-27 kg. This lets you find the mass of all the reactants going in to the fusion reaction.

(ed note: 3.016 AMU + 2.014 AMU = 5.03 AMU = mass of all reactants in AMU
1.66×10^-27 * 5.03 = 8.35×10^-27 kg = mass of all reactants in kilograms)

Divide the one by the other and you get the specific energy (energy per unit mass) of the fusion reaction.

(ed note: 2.932×10^-12 Joules / 8.35×10^-27 kg = 3.511×10¹⁴ J/kg = 350 TJ/kg if you are just burning it without worrying about using the reactants as a rocket)

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If you are using it for a rocket with reaction at 100 keV of energy

A temperature can be shown to be the average energy per degree of freedom of the particles making up a system. So with a temperature of 100 keV, we find that we get 100 keV of energy per degree of freedom of the plasma. 1 keV is 1000 times 1.602E-19 J (1.602E-16 J).

(ed note: 100 * 1.602×10^-16 = 1.602×10^-14 J)

For an equal mixture of D and He-3, each ion has three degrees of freedom (it can move up-and-down, right-or-left, and forwards-or-backwards … or if you are more mathematically inclined one degree of freedom for each dimension on your Cartesian grid. Rotational degrees of freedom are probably not important).

Each electron also has three degrees of freedom (for the same reason). If we take as our system of analysis one D atom and one He-3 atom, we have two ions (the D and the He-3) and three electrons (one for the D and two for the He-3).

So our system has 15 degrees of freedom.

Multiply this by the energy per degree of freedom and you get the thermal energy of the system.

(ed note: 15 * 1.602×10^-14 = 2.403×10^-13 J)

You already found out the mass of a D and He-3 atom, so divide by that to get the energy per unit mass.

(ed note: 2.403×10^-13 Joules / 8.35×10^-27 kg = 2.878×10¹³ J/kg = 29 TJ of useful work for each kg of fuel/propellant expended)

However, there is a major flaw in the Traveller ship system which Marc Miller apparently does not realize and the implications of which are not reflected in other aspects of the game. The smallest power plant that can be mounted on a spaceship is an A-rating plant. An A-plant consumes 20 tons of hydrogen in the course of a standard one-week interstellar jump. Now, starships do not in Traveller carry liquid oxygen, so it is clear that the hydrogen is not being burned to create energy. Instead, the power plant must be operating as a fusion device. Further, Miller does not permit ships to separate out the deuterium (heavy hydrogen, the easiest atom to fuse) and use only that to generate power. If he did, ships could carry vastly less fuel and would thus have much more space available for cargo. So the energy must be created by proton-proton fusion of raw hydrogen, tons of which are consumed each week — the same fusion reaction which produces most of the sun's energy. (Actually, considering the energetics of proton-proton reactions, Imperial technology must be extremely advanced, since even at temperatures of millions of degrees, proton-proton fusion occurs very rarely. The Imperium must have some mechanism for catalyzing such reactions, something beyond the slightest glimmer of our comprehension at the moment.)

In proton-proton fusion, through a series of three reactions, four protons fuse to produce a single helium atom plus about 25Mev (million electron-volts), plus some stray gamma rays, neutrinos, and positrons. H¹ weights 1.008 g/mole, so 1 kilogram contains about 992 moles of hydrogen, or 5.97 x 10²⁶ atoms. Fusing these atoms produces 3.73 x 10²⁷ Mev. There are 1.60 x 10^-19 J/ev, so this is about equivalent to 5.97 x 10¹⁴ Joules, or about 19 MW-years. So there are about 19 MW-years of energy per kilogram of hydrogen.

The smallest power plant which may be installed on a ship in Traveller is a standard "A" power plan. The A-plant can consume 20 tons of hydrogen over a period of a week, convert it to energy, and feed it to an "A" FTL drive. (This is how much energy is needed by the smallest FTL drive to make a jump of 1 parsec if installed in a 200 ton ship.) If we assume Miller is using metric tons (1 ton = 1,000 kg), an A power plant then can deliver 380,000 MW-years of energy over a period of one week. Over a year, it could deliver 19,800,000 MW-years. Thus, a single A power plant produces about 86 times as much energy in a year as all of the electrical generating plants in the United States. A single jump in Traveller uses about 160% of the energy the US produces in a single year.

A "Jump 1" in Traveller corresponds to a travel distance of one parsec, about 3 1/3 light-years. Let us be generous and say a ship can travel 5 light-years at Jump 1, consuming 380,000 MW-years in the process. A Free Trader carries 82 tons of cargo, so the cost in energy to transport a kilogram is 380,000 divided by 82,000, or roughly 4.6 MW-years. This is about 5,000 times as good as the Boardman anti-matter drive, so that there is no doubt that interstellar trade in the Traveller universe is a good deal cheaper than in an Einsteinian one.

It still takes 6.7 million KW-hours of energy to transport a kilogram, however. That is a lot of energy. Now it is true that energy is very cheap (in terms of Imperial credits) in Traveller — it has to be, given the cost of owning and operation an "A" power plant — but the cheapness of energy means that other manufactured goods must be very cheap. So there still will be few goods worth trading in Traveller. What goods will be worth trading is debatable, since it is very difficult to estimate costs of production. However, certainly trade in bulk goods like metal ores, pig iron, or grains can be ruled out. The Traveller trading system does make it possible to make a profit trading such goods, but that is a peculiarity of the system. I think we can say with some assurance that in Traveller the primary items of trade will be 1.) luxuries, 2.) extremely rare resources such as superheavy metals and — possibly — radioactives, and 3.) high-tech goods to be sold on planets where they cannot easily be produced locally.

The Carbon-Catalyzed Fusion Drive

Mass drivers can get materials into space and beanstalks can get people into orbit, but to move around the solar system a drive of some kind is necessary. Fusion drives are a staple of science fiction for the simple reason that chemical fuels simpy lack the energy content required to make an interplanetary, let alone interstellar, civilization possible. However, the reality is that controlled fusion has proven a tremendously difficult genie to get out of its bottle even for simple power generation, an easier problem to solve than a space drive. The first serious attempt at developing a fusion drive was Project Orion, which envisioned propelling a ship through the simple mechanism of kicking a nuclear bomb out the back and detonating it, repeating as necessary. This is hardly a graceful technique, but despite its seeming insanity it is not, a priori, unworkable. Caculation and experiment showed that a large “pusher plate” close to a nuclear explosion would experience a considerable acceleration——hardly surprising. More surprising is the fact that, given a thin protective layer of ablatable graphite, both the plate and a spacecraft on the other side of it could survive the detonation unscathed, could travel in a reasonably predictable direction and that a not-impossibly-large system of shock absorbers could make the ride survivable by people. Project Orion envisioned putting payloads measuring thousands of tons into orbit and saw a manned trip to Mars by 1965 and a trip to Saturn by 1970. However a bomb-powered spacecraft would inevitably generate a tremendous amount of radioactive fallout, and the accident risk involved with a ship carrying several thousand nuclear “pulse units” into orbit needs no elaboration. After the investment of several million dollars the project was shelved with the surface test-ban treaty. More advanced concepts have been put forward, including the British Interplanetary Society’s project Daedelus which proposed laser-imploded microfusion capsules as the drive source NASA’s Variable Specific Impulse Magnetoplasma Rocket (VASIMR) plasma drive uses many of the techniques relevant to a fusion drive and the Gas Dynamic Mirror (GDM) project (currently shelved to pay for shuttle refurbishment) was aimed at creating a true fusion drive. A primary stumbling block to the GDM drive is the availability of sufficiently strong magnetic fields. Beyond this problems to be solved are not small, given that even fusion power production still has large technological hurdles to clear. Fission power plants are now a fifty-year-old technology, but fission rockets require too much shielding and operate at too low a temperature to be practical, even ignoring the specter of accident and widespread radiological contamination. The same concerns have left atomic cars and airplanes on 19505 drawing boards. Fission fuel contains millions of times more energy, kilo for kilo, than chemical fuel, but the realities of harnessing it confine its use to large power plants.

Fusion happens whenever atomic nuclei get close enough together that the short range but powerful attraction of the strong nuclear force can overcome the weaker but longer-ranged electrostatic repulsion of the positive protons in the nucleus. Fused nuclei are more stable together than apart, and the stability difference shows up as energy that can then be put to work. The key variables are temperature and pressure-—the nuclei have to be moving fast and be close enough together to make them fuse, and it takes a lot of both. Fusion bombs use no less a force than a fission bomb to heat and compress their fuel, but power generation and space drives (Project Orion excepted) require less violent methods. Adding to the headaches, the easiest fusion reaction to ignite is the deuterium-tritium reaction, and this gives off a lot of neutrons which require a lot of shielding, and which generate a tremendous waste disposal problem by slowly rendering the reactor itself radioactive. In addition tritium, also radioactive, must be made in a nuclear reactor at tremendous expense, generating more waste in the process (tritium is roughly eighty times the cost of plutonium, weight for weight). Current reactor concepts cleverly use the neutron flux from the fusion reactor itself to make more tritium, solving some of the neutron contamination problem at the same time, but it would be nice if we could tap into fusion power without having to deal with radioactive waste at all, and preferably without using exotic and expensive isotopes either.

The primary fusion pathways in the sun (the proton- proton chain, which burns normal light hydrogen and the carbon-nitrogen-oxygen catalysis cycle, or CNO cycle, which burns light hydrogen using carbon-12 as a catalyst) are aneutronic—fortunately for us, as any large-scale neutron flux from the sun would certainly bake our planet sterile. The sun uses nothing more than gravity to produce a stable, long-lived,‘ high-flux fusion output without too many nasty side effects. In a star temperatures of ten. million degrees and densities of 100 gm/cm³ are required for the p-p chain and sixteen million degrees and densities of over 150 gm/cm³ for the CNO cycle.

For the sun, which is held together by gravity and isn’t going anywhere in a hurry, temperature and pressure are the end of the story, but for an artificial fusion reactor a third critical variable enters the picture—confinement time. This is the length of time the system can hold the fusing plasma together against the expansion caused by the fusion energy. This expansion lowers the pressure and temperature and eventually stops the reaction. In order for fusion to occur efficiently at a given temperature the plasma particles have to be held together long enough for a significant number of fusion events to occur. Lawson’s criterion, the product of particle density and confinement time, serves as a figure of merit for fusion reactors, and successive generations of research machines have striven to come ever closer to the magic point of breakeven, where the reactor produces as much power as it consumes, and ignition, where the plasma burn becomes self-sustaining, requiring no further energy input from outside. (The third magic point, profitability, the point where a fusion reactor produces power for something like a nickel per kilowatt hour, is nowhere on the horizon.) The oldest and best-explored fusion scheme, the toroidial magnetic tokamak, uses low pressures (a few atmospheres), long confinement times (a few seconds to half an hour) and temperatures of hundreds of millions of degrees to achieve fusion. The more recent inertial confinement fusion approach uses intersecting laser beams to compress a tiny fuel pellet to pressures more than ten million times higher. Fusion occurs so quickly in this regime that the fuel pellet’s own inertia holds it together for the nanoseconds necessary for the reaction to complete. A third fairly recent development is magnetic target fusion, which magnetically implodes a thin-walled aluminum cylinder to achieve a fusion regime intermediate between these two. MTF achieves, for a few microseconds, magnetic field strengths of 500 Tesla.

Given that all of these techniques are barely capable of generating fusion with deuterium-tritium it may seem needlessly ambitious to plan a drive around the CNO cycle. Even granted that we want aneutronic fusion, the proton-proton chain is available at much lower pressures and temperatures. However, the CNO cycle’s reaction rate goes up no less than 350 percent for every 10 percent increase in temperature, rising as the sixteenth power of temperature, compared to the proton-proton chain’s reaction rate which goes up as the fourth power of temperature. This means that, given the ability to reach this extreme regime, it should be possible to reach a point where the CNO cycle will become very efficient.

The trick of course is reaching the CNO operating point at all, and whether this is possible is an open question—even buckytube supermagnets might not do the job. However if they do, the system might work like this.

Imagine a hollow tube ringed with magnetic coils. A small stream of hydrogen and carbon plasma is fed in at one end, and a current is run through it to generate its own magnetic field. A magnetic wave is sent down the tube by successively energizing rings of magnets. This wave accelerates the ionized gases down the tube, and the wave amplitude is made to increase down the tube while the wavelength decreases, the gases will also be compressed and heated as they travel. At some point, possibly with further energy inputs, the plasma begins to fuse. This tremendously increases its energy content——temperature and pressure soar and it begins to expand, still fusing. Forward and outward expansion are limited by the incoming magnetic wave, still increasing in amplitude, and the reaction forces of fusion particles moving against this wave provide thrust for the ship. Wave amplitude decreases and wavelength increases past the fusion point, allowing the plasma to expand and stop fusing in that direction, focusing it into a coherent jet. Finally the plasma exits the rear of the tube through another magnetic field which uses the stream of charged particles to generate electrical power to run the system. Behind the tube is a reaction chamber into which water can be sprayed to trade exhaust velocity for thrust for planetary launch. Once in orbit we turn off the water and use the jet by itself to accelerate.

Exploring the detailed physics of this system is far beyond the scope of this discussion. In a story it’seasy to gloss over details like plasma disruption and wall interactions, but these are critical problems for real-world reactors. This may be the drive of the future; it may, like Project Orion and the atomic airplane, be possible but impractical; or it may be simply impossible. Assuming it is possible then the magnetic wave system means the thrust would be continuous and very controllable. This is the fusion equivalent of a jet engine with constant, or nearly constant, combustion, as opposed to a pulsed fusion drive (Project Orion being the extreme example) which, like a piston engine, produces power in discrete bursts. This steady, throttled power is exactly what we’re looking for, and this drive is easily adaptable to the fusion ramjet concept which gathers its fuel from the interstellar medium as it travels. It should be noted though that the fusion ramjet requires solving even larger problems than a “simple” fusion drive, including the generation and control of a magnetic funnel about the size of Iupiter. Even buckytube supermagnets are probably inadequate to this task, but a field too small to serve as an interstellar fuel scoop could still serve Well as an unconfined magnetic particle shield. As discussed above, some sort of particle shield is absolutely essential for manned interplanetary flight, with or without a fusion drive system, and supermagnets like this are a primary enabling technology. Solving the shield problem like this would open up the solar system to large-scale exploration and completely revolutionize the commercialization of space. Even if we don’t want to colonize Mars or set up an asteroid-mining industry the scientific benefits alone would be incalculable.

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What is the theoretical limit of the amount of energy that can be extracted from a fusion reaction? I am not talking about the practical efficiency of a reactor, but rather what fraction of the mass-energy can be released.

Of the theoretically possible fusion reactions, combining 56 free nucleons into ⁵⁶Fe would release 9.1538 MeV per nucleon. Combining 28 free protons and 34 neutrons into ⁶²Ni would give a slightly tighter binding per nucleon. This seems to represent an empirical limit to fusion, converting 0.00935605478 (iron) and 0.0096783439 (nickel) of the nuclear mass into energy.

So this limit seems to be ≈0.97% (0.0097). By comparison, the proton-proton chain leading to ⁴He is 0.7% efficient (0.007).