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Let's just take antimatter off the table right now. As I've learned recently, it's hard to make, expensive as hell and even more volatile, and you can never get more energy out of it than you put into making it, making it the Samsung Note 7 battery of future energy solutions.

With that out of the way, what do you think people will be using to fuel their interplanetary ships 200-300 years from now, assuming we're sticking to currently understood methods? I see two big contenders, and I'd like to know which you think is more likely to actually happen. Will they use fusion rockets and hydrogen scoops like the Bussard ramjet? Or will they stick to the much cruder but simpler (and probably more cost effective) method of nuclear pulse propulsion like Project Orion?

The way I see it, fusion power frees up more space for cargo and uses fuel that is essentially omnipresent and free throughout the universe, however containment failure in your fusion reactor is an ever present danger and a threat to the safety of the crew. Meanwhile, nuclear pulse propulsion isn't quite as green but can accelerate ships of a large mass (8000000 t) to significant percentages of lightspeed in under 10 days using bombs that, depending on their yield, can be considered relatively small. The technology involved is also simpler and much more foolproof than outfitting a spaceship with its own fusion reactor, and your propulsion system doubles as a weapon, meaning every ship could technically be considered a warship if the situation ever arises where it needs to defend itself.

What do you think?

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    $\begingroup$ I would think powering your ships with something that is designed to explode is much more dangerous than powering your ships with something that isn't designed to explode. Just a slight miss-timing of the nuclear bomb detonation and you are toast, while a magnetic confinement fusion reactor could be pretty easily designed to simply vent to space in the event of an emergency and thus posing minimal danger to the ship. $\endgroup$ – TheBlackCat Dec 8 '16 at 5:15
  • $\begingroup$ en.wikipedia.org/wiki/Alderson_drive This would be really cool. $\endgroup$ – Snowlockk Dec 8 '16 at 8:11
  • $\begingroup$ RF Resonant Cavity Thruster This would be really cool. $\endgroup$ – Anketam Dec 8 '16 at 11:18
  • $\begingroup$ Both the Alderson drive and RF resonant cavity thruster would be (if they actually worked) propulsion techniques, rather than energy sources. They would still need an energy source to be used. But even if they were, both violate the OP's "sticking to currently understood methods", since the Anderson drive is based on purely fictional physics and the RF resonant cavity thruster probably doesn't work at all, and if it does we have no idea how. $\endgroup$ – TheBlackCat Dec 8 '16 at 14:00
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    $\begingroup$ @TheBlackCat problem is that with currently understood methods, we would already be using them. $\endgroup$ – Snowlockk Dec 8 '16 at 15:50
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Fission power is much more feasible for the near future

Fission engines don't get much interest because nuclear materials are banned in space, and because they produce lots of bomb-making products as waste. However, fission engines have several advantages over other options:

  • Established industrial experience. Not only are there millions of hours of operator experience with power plants, but there is also extensive experience with small portable versions in submarines and ships. The submarine experience is particularly important, since there is 50 years of training on how to build and operate a smaller, safer fission reactor with a minimal crew.

  • Technologically feasible now. The system I will describe below already has had two prototypes built by NASA as part of the SAFE series, including a 30 KW end-to-end prototype where a fission-Sterling cycle generator powered an ion drive and a 400kW fission-Brayton cycle generator. There is no need to imagine theoretical solutions for these systems.

  • Space makes fission easier. The biggest problem with fission is radiation control, especially in submarines and ships. This problem largely disappears in space. Without heavy lead and water shielding, the weight to power ratio for fission engines can increase significantly, especially with a Brayton cycle electric generator. The 400 kW prototype delivered roughly 1 KW heat for every 1 kg of reactor; and a modern gas turbine can deliver 35 MW with 5250 kg at 39% thermal efficiency.

  • Materials to support fission reactors are available now. One of the big problems with fusion is the potential for neutron embrittlement from the very high energy neutrons being fired out of fusing D-T reactions. Fission reactors, on the other hand, have currently been in use for decades and the science of neutron damage to metallic structures is well known.

  • Power density of the fuel is high. While the power density is not as high as, say, fusion, it is still much higher than any chemical reaction. Uranium is a relatively common element. As the SAFE series link above above points out, a coke can of uranium will release the same energy as 50 space shuttle external fuel tanks. Fuel mass will be small compared to reaction mass.

  • This technology has languished for lack of interest. Space fission engines are actually way behind simply because no one is funding them. The experiments I linked to before ran out of funding in 2004. That is a lot of time in which no development has been made. Putting some funding and research into these engines could probably make them even better than they look now.

Power source - Pebble Bed Fission Reactor.

The engine is a pebble bed reactor with low-enriched Uranium formed into Uranium Nitride ceramic pellets. The fuel would be expensive, because the 0.37% $^{15}$N isotope will be preferentially used over the normal $^{14}$N due to $^{15}$N's transparency to neutrons. However, if this became a common system for space power, industrialized processes would decrease the cost of fuel to reasonable levels.

Pebble bed reactors are inherently safe because of its fuel is split between U-238 and U-235. U-235 provides higher power density, while U-238 absorbs more fast neutrons at higher temperature in an effect called doppler broadening. This means that as temperatures go up, fission rate goes down. The net effect is that the reactor naturally regulates itself at a maximum upper temperature. As heat is removed by the working fluid, fission rate goes up to compensate. In a worst case accident, the reactor will go to max temperature, and stay there, continuing to produce power only a rate fast enough to maintain this temp.

Electrical power convertion - Brayton-cycle engine

The Brayton cycle engine is the gas turbine that powers airplanes. However, a spacecraft would use a closed cycle Brayton engine more similar to the gas turbines used on warships. The engine uses a three-stage process of forced compression, heat exchange, and expansion/exhaust through a turbine. The heat exchange would be with the pebble bed reactor, which would be kept at high temperature of about 1000 C. The exhaust section would have two turbines, the gas-generating turbine and the power turbine, as on marine applications. The gas generating turbine takes roughly 30% of extracted energy and uses it to drive the compressor section. The power turbine takes about 70% of energy and drives an electric generator. The working fluid, after passing through the two turbine sets, will then be sucked back around to the compression section. The compression section forces the gasses into the heat exchange areas at very high pressure to repeat the process.

The working fluid would have to be an inert gas. Helium and Xenon were both tested in the SAFE series. Argon and Krypton would be other options, as would diatomic nitrogen. None of those gasses would be reactive with metal engine components at nearly any temperatures. An alternate and more advanced solution would be to compress the working fluid directly through the pebble bed. This would significantly increase heat efficiency, but pose problems with some of those gasses as fluids due to their neutron absorption properties. Xenon is a powerful neutron poison, while diatomic nitrogen has undesirable properties as well. On the other hand, helium in particular is very unlikely to absorb a neutron being a 'perfect' 2$p$2$n$ nucleus.

Propulsion - Advanced magnetic engines

The last piece of the puzzle is what is actually providing propulsive power. If we are going with a fission-Brayton engine as stated, that only gets us as far as a few MW of electrical output. We still need something to power us. This table has lots of options.

The key is finding a technology that will have high specific impulse, and thus low fuel usage, and also be capable of thrust significantly higher than the fractional newtons available to currently in-use ion thrusters. Usually, those two requirements can only be met by a large power source, but our fission-Brayton reactor should have that covered. Lastly we need to identify a technology that is farther along than just the drawing board, so that some of the potential engineering problems have been encountered and, if not solved, at least identified.

Two technologies that seem most promising from the ability to provide a combination of high specific impulse and high thrust are magnetoplasmadynamic thrusters (MPD) and VASMIR. Both of these technologies have theoretical specific impulses in the 100+ km/s range, as well as the ability for a single thruster unit to scale up to the 100+ N thrust range. Aligning banks of these thrusters would allow a space ship to generate thrusts in the range of 10$^4$ N that are necessary for effective interplanetary flight with large (1000+ ton) spacecraft.

VASMIR works by using radio waves to heat a magnetically confined plasma of Argon propellant. It is currently under development today by Ad Astra Rocket Company of Houston.

MPD works by using the magnetically confined high temperature plasma itself to conduct a large induced electrical current. Plasmas could be noble gasses, or also lithium. An MPD thruster was tested in space on the Japanese Space Flyer in 1995 and research is still ongoing at places such as the Princeton EPPDL.

Conclusion

The set of technologies I have described has no theoretical scientific hurdles to overcome. Each of them has a working prototype of some sort. With some applied engineering, demand, and cost reduction through mass production, these technologies could move humanity throughout the solar system on a time scale not unlike the old sailing voyages of Earth, allowing us to truly expand off this planet.

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It depends...

Depends on the technology used, how big is the fleet, what are distances of travel (inner solar system, Jupiter, outer gas giants, interstellar), methods of travel as o.m. noticed, velocities, desired ISP(and thus efficiency of reactive mass usage)

Mars-Earth-Venus-Mercury - Solar powered crafts make total sense.

Jupiter-Saturn-Uranus-Neptune - any kind of fission-fusion makes sense.

Interstellar - fusion, Bussard ramjet, beam-powered propulsion if one like fast travel, but solar powered etc also fine if time is not a problem but energy efficiency is(bulk transporting).

Mass drivers will be a good option for all Solar system for traveling between planets, space rings, and space lifts a good option for transporting to/from gravity wells.

Thus, until we invent something superior which can easy replace all those methods, and light robust fusion reactors are candidates for that, all those varieties may be used.

We struggle not to predict what can or may be used, but to predict the demands for particular needs as a function of time.

Amount of energy from fission fuel isn't bad actually - it is about 0.8MeV per nucleon(235U = 200MeV), for fusion it is about 3.8MeV per nucleon the most(2D + 3He = 18.3MeV).

0.01m/sec2 - for solar system it is not bad as an acceleration speed, 864 m/sec per day, or 17 days to gain 15 km/sec. 15km/s is enough to travel across the system, not fast but still. Same speed it not too much for mass drivers too(to launch a craft) and as result, we may actually expect a combination of approaches as mass drivers can be used to launch a craft and engines may be used for correction and slow down at the target orbit.

But is that combination viable depends on such things as for example travel between planets may be significantly faster and cheaper than travel from a planet to an asteroid, because mass drivers may be used and for launch and for slow down (this way we also would be able to transfer the energy between bases) As asteroids and small bases may have troubles(and definitely will have troubles) accepting high-velocity ships.

Mass driver launching needs infrastructure across Solar system, reactive propulsion does not need such infrastructure as it relays entirety on itself. However mass driver launch is way more energy efficient, mass efficient for the ship, allow to transfer energy between bases which may be important for remote bases(let's say at Jupiter) if no fusion is available. And because of those mass drivers alone may allow establishing bases on all significant bodies in the solar system, even without fusion.

So, what comes first orbital ring or a good fusion reactor-engine?
We just do not know, both allow to solve the problems(travel, energy) in a slightly different fashion, this way it just depends ... on people, on their interests.

Fusion will be used for sure, and it is superior, just because there it a lot of fuel for it in the universe, in the solar system, easy to get, easy to use(with technology for doing that).

But for a small fleet - 100-1000-10000-100000 ships in the solar system - fission is good enough. To deliver 1 cubic kilometer of liquid hydrogen, from Jupiter, it needs to spend 800 tons of fission fuel and 10% of that hydrogen as reactive mass. And this cubic km of hydrogen may be converted into 567 million tonnes of water (-10% already), and to produce 819 million tonnes of aluminum, or 1732.5 million tonnes of Iron as byproduct at almost 0 energy expenses - in fact it can be used to reduce all matter to its elemental form from an 950m diameter space rock(aka asteroid from inner parts of solar system with average density 3000kg/m3 of typical rock, a solid chunk, which they aren't, mostly)

All that Just at expenses of 800 tons of fission fuel, but we mine a bit more than that, 20 times more(at least) than that, and we do not get that many exciting results for our efforts to mine it, I mean energy wise. I would say spending 800 tons for the result it totally worth the spending.

Back to OP premise, side note about antimatter production

A note about antimatter and energy of its production, if the technology exists, it can be used the same way as fission can be used - basically, it is ultimate type of energy accumulation, spaceship rechargeable battery. Even if total efficiency is 0.01% (production, storage, use, conversion to propulsion) it can be used. 1000x1000 km mirror foil at earth orbit may help to produce 4765.44 kg (at 0.01% efficiency of production) of antimatter per year. It is not big energy production facility(1000x1000km is not a lot in space), and it is pretty a lot of antimatter because 1 kg of antimatter is equivalent to about 1 metric ton of fission fuel (energy of fission fuel 235U is about 0.00091mc2), this way same 800 metric ton for fission fuel is equivalent to 800kg of antimatter and such station may produce fuel to transfer 6 cubic km of hydrogen per year, which equivalent to refining of a lot of matter, and possibly those materials are enough to build 5-20 new stations. Therefore despite difficulties of antimatter production it may outweigh the fission and maybe even fusion since you do not need to search and extract those fuels, but instead, you can create antimatter from nothing using the energy of the sun, which at the moment is just dumped into the space void, and which is plenty of available for cheap.

The 23rd-24th century - we may or may not use all Sun energy for other purposes, therefore, production of antimatter may be not a problem energy wise, despite the efficiency of the process, and may be well above of all our needs at the time. But if you choose it, it may be a good idea to place production farther away to increase efficiency of the production, Gas giant shadows, or near Neptune(or planet X maybe(?)) and beam energy needed for the production from inner solar system, because at farther distances you can recuperate energy you loose during the production and increase efficiency of the process.

At Neptune orbit solar irradiation is about 1.5W/m2 it is equivalent to 71 K temperature(black body) and if you loose 99.99% of energy during the production of antimatter, and waste heat is at 1000 K, you can recuperate the 92.9% of waste heat during each cycle and overall efficiency of the process of this imaginary antimatter production facility will be 0.14% instead of 0.01%. And that is worth of travel actually, worth of a "trade" ship.

Back to OP problem

As you may see already, the problem is not what we already know, because indeed our current knowledge probably allows us to look at a bit distant future then we could do 100 year ago, and they were damn good at it (Nikola Tesla, Jules Verne - we are just not enough in the future to fulfill some of their ideas. As I have discovered recently, Nikola Tesla proposed Orbital Ring more than 100 years ago, Jules Verne with his indestructible(at earth depths) fast moving submarine just a prophet(I know how to build it:) ) and cannon mass driver(also good enough for looking in the future of maglev mass drivers))

But the topic is broad, for different situations for different demands and activities there are their own best solutions.

Fission is good enough for star systems.

Fusion is ok almost everywhere even with interstellar, but it does not shine with interstellar, except Bussard ramjet, but very good for a star system.

Bussard ramjet is relatively good for interstellar travel but inside star systems not good at all.

Antimatter is ok for a star system, and ok for interstellar if the efficiency of production is good enough, but it does not shine with interstellar travel.

Beam propulsion is ok for a star system and good for interstellar travel - if combined with some of reactive propulsion or infrastructures in destination point, interstellar variant need a bit more advanced infrastructure (I keep forcing that technology even if no one seems to like it, it is ok to be used at destination point to catch those beam(or mass driver in this case) accelerated crafts, some use case applied to disassemble planets is here)

Recommendation

I would recommend sticking with mass drivers, they are always handy to lift things from gravity wells and to be used upon all massive bodies - in form of tracks, launch loops, orbital rings, not only to launch but also to give a surplus delta-v kick for those crafts, consider it as advanced version of gravity slingshot maneuver.

As the energy production for reactive propulsion to fission, solar powered(not necessary solar cells), fusion.

As for reactive mass to Hydrogen from Jupiter.

I would avoid solar sails as not an energy efficient solution as for travel in the star system, but an acceptable solution for interstellar travel as it is more mass efficient than other solutions with reactive propulsion, but it is demanding for infrastructure in both cases.

I would avoid using Project Orion as a good example for a space ship, as very inefficient design. It is not good at multiple levels. I salute all those people who spend their time for the project, as it is very useful in moving us forward in understanding what is good and what isn't so great, and at that time of the project, it was the great spirit which I would like to see today and applied to our current technologies. Basically, it was great at that time, but its intent wasn't to foresee the future but apply known technologies to the problem of interstellar propulsion at that time.

Also, I recommend defining which kind of "trading" will it be in your setting, because everything isn't so easy and you may take look at some space based economy questions [economy][space-colonization] and [economy][space]

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    $\begingroup$ You surprised me suggesting Bussard ramjets for interstellar travel. This hypothetical propulsion system has been thoroughly debunked. The first papers doing so appeared in the mid-1970s. Apart from that one caveat, as usual, another of your good well-researched answers. Plus one from me. $\endgroup$ – a4android Dec 9 '16 at 12:30
  • $\begingroup$ has been thoroughly debunked. - may I have link, or something? There a lot of problems with Bussard ramjet, and I refer rather to a principle - "There is sparse source of energy and mass and it can be used for propulsion" than to an particular implementation of it. It is rather my bad that I call this principle "Bussard Ramjet" but it is only well know conception which I'm aware of which tries to implement the principle. I have my version of BJ, it shoud work so if no one will figure out how to deal with it, we will use my version with active matter, lol. $\endgroup$ – MolbOrg Dec 9 '16 at 13:28
  • $\begingroup$ The relevant papers are Bond (1974) and Heppenheimer (1978). No links. For a good account see research.omicsgroup.org/index.php/Bussard_ramjet and en.wikipedia.org/wiki/Bussard_ramjet which is less technical but cites Alan Bond's 1974 paper. I think it was Bond's paper that made me realize Bussard ramjets wouldn't work. They required ramjet intake diameters of one million kilometres per ton of vehicle. The concept is lovely, but infeasible. $\endgroup$ – a4android Dec 26 '16 at 11:42
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As Jay mentioned, there is the option that something entirely new will be on the table. But scientists today believe that they have a much more systematic grasp of physics than those 18th century scientists. So:

Check out Atomic Rockets.

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I'm going to bypass the technical aspects entirely (Atomic Rockets has a huge engine list filled with possible choices), and focus on "why" you'd chose a particular system.

The true issue for transport is cost, and in space costs are determined by the amount of energy needed to change orbits and reach your destination (deltaV). Obviously getting to some places will require more deltaV than others, and you can get places faster (even much faster) by using more deltaV, but in general, you want to pay the minimum energy cost, so will tend to choose the lowest deltaV transfer orbits you can get away with.

For freight, this could mean decades long journeys by the equivalent of ISO containers boosted into transfer orbits by a mass driver. There is no additional energy cost, no costs for life support or almost any other system cost (maybe a transponder and small engine for fine course corrections as you approach the target).

People are not too inclined to be stuck in an ISO container for any length of time if they can help it, much less several decades, so passenger ships will have to go for far more expensive drives which provide high thrust or high ISP and can get you to your destination in a matter of months to years. These are generally quite energetic, and impose lots of secondary costs (engineering, radiation protection, making ships large enough to carry all the required equipment and shielding, then extra fuel for carrying all the stuff....)

So in the future, space travel will likely be divided between low cost, low energy freight transport and high energy, high cost passenger transport.

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I think a fusion type generator would work, especially if it wasn't cold fusion. I know a lot of people don't go for that, but here's my thought process:

Fusion, by and large, generates a lot of energy, but it has heat as a 'waste' product. But what if it was coupled to a thermoelectric generator? http://physicsworld.com/cws/article/news/2013/dec/09/new-generator-creates-electricity-directly-from-heat

https://en.wikipedia.org/wiki/Thermoelectric_generator

So you have your giant boost fusion engine, and the heat is used to power the thermoelectric generator, which, while more ineffecient, could still be used for say, smaller or slower movements, or areas that don't take/need much power. This might also help with the containment problem, because the heat is going somewhere where it's more safely siphoned off.

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