Intersteller Travel by Fission Power

[DonPMitchell]

How hard would it be to send a probe to a nearby star? I have yet to find a discussion of this problem that does not succumb to science fiction, antimatter, planet-sized lasers, etc. So let's try to tackle this practically, assuming we just have nuclear fission as a power source.

I. The Relativistic Rocket Equation

Edwin Taylor and John Archibald Wheeler derived a relativistic form of Tsiolkovsky's rocket equation in their 1963 book _Spacetime Physics_. The final velocity of a rocket is then given by:

(1) Boost = ExhaustVelocity * log( InitialMass / FinalMass )

(2) FinalVelocity = tanh( Boost )


II. Fission-Photon Drive

Let's start with an extremely simple propulsion system, the Fission Flashlight:

<fig 1>

Let's assume we take 100 kg of Uranium 235 and place it in a 2-meter spherical reactor. Let it achieve a temperature of 3100 kelvin (just below the melting point of UO2), and place this incandescent reactor at the focus of a light-weight parabolic reflector. This scheme converts mass into photons, so the Exhaust velocity is the speed of light. From the Stefan-Boltzmann law, we find the reactor core would radiate 70 megawatts for four years, giving a thrust of 0.23 Newtons (about 1/20 pounds).

The change is mass is 0.1 percent -- the amount of mass turned into energy by nuclear fission. From the rocket equation, the final spacecraft velocity would be about 0.1 percent of the speed of light. At that speed, it would take about 5000 years to reach a nearby star. Not very good.

<fig 2>

We can do a little better by carrying multiple reactor cores. Every four years, the spent core is ejected and a new one placed at the focus and activated. This is better, because we are losing the spent fission products instead of carrying them as payload. With this scheme, we can approach 0.7 percent light speed and reduce our trip time to about 700 years. Still, not really practical, and we've been calculating an upper bound, assuming the mass of the spacecraft's structure is zero, just pure uranium fuel.

III. Fission-Ion Drive

<fig 3>

Instead of using photons for exhaust, let's use the fission reactor to accelerate ions. Let's assume 100 Kg of Uranium-235 for power, and a mass M of extra propellent to be ionized and expelled at high speed. We can calculate a necessary exhaust speed by assuming that all of the fission energy is converted into kinetic energy, M * ( cosh( Boost) - 1 ). So

(3) ExhaustVelocity = tanh( acosh ( ( M + 0.001*Uranium)/M ) )

The final mass is just the uranium, minus the mass defect coverted to energy by fission. If we plug M=0, we get the same result as our Fission-Flashlight drive.

As we add mass, we get more final velocity from the log (M1/M2) term of the rocket equation, but we also reduce the exhaust velocity. There is an optimal amount of propellent in this case. With 100 Kg of Uranium and 390 Kg of propellant, we achive a final spacecraft velocity of 3.6 percent light speed. That's fast enough to reach the nearest star in only 140 years. Still a bit long.

Let's try a two-stage rocket. The first stage has 1000 Kg of uranium and 5800 Kg of propellant. It carries the second stage, which is the one described above. This combination can achieve a final spacecraft speed of 6.5 percent light speed. Now we've reduced our mission time for a flyby to 77 years, short enough that one generation could build it, and a next generation of scientists could receive the results it reports back.

I'll tinker a bit more and derive an optimal stage-size ratio. I'm sure a three stage spacecraft could reach something like 10 percent lightspeed.

[Johno]

Don, please forgive my lack of expertese on this subject.  You can treat me like a N00b . . !

At any rate, you're assuming a fission core.  This is reasonable since controlled fission reactions are a mature technology now.  Yet we are also in possession of uncontrolled fusion reactions (albeit triggered by fission).  Is it possible to use (for sake of argument) a series of H-Bombs as a propellant system?

[Satanic Mechanic]

Johno,
You are talking about Dyson's Project Orion which used low yield nuclear bombs as propulsion.  I believe Dyson's design used many small 1 to 5 kilotonne bombs.  There is a lot of literature out there about Project Orion and I believe there is a film on youtube about his designs.
Hydrogen bomb use- I don't think the spacecraft would survive if you used hydrogen bombs.  A hydrogen bomb is essentially an atomic bomb with tritium, lithium deuteride or some other chemicals with deuterium.  The yields are in the 100's of kts to the Mts.   You could have the spacecraft fly further away but you are wasting all that extra energy in my opinion.
The bomb explosion goes in all directions, you are trying to get close enough to get that energy without destroying the spacecraft and frying the crew.

SM

[Satanic Mechanic]

About a month ago I read this IAA White Paper: Nuclear Thermal Rocket Propulsion Systems, written by Lt.Col. Timothy J. Lawrence of the U.S. Air Force Academy.  It is a pretty good read and a nice comparison of the NERVA, Particle-Bed and CERMET propulsion systems.  Even though the Particle-Bed and CERMET has never been built, both have potential.  The CERMET has high thrust and the Particle-Bed has a high Engine thrust to weight ratio.

SM

[DonPMitchell]

Fusion power would be cool in terms of cheapness of fuel.  Hydrogen is way more abundant than heavy metals.  H-Bombs are more powerful than A-Bombs, just because you can scale up fusion, while it is hard to build a fission bomb with more than one critical mass.  Here's a photo of the kilometer wide fireball from the Soviet 50 megaton test, the biggest nuclear explosion ever made:



That said, fission and fusion both yield about the same mass fraction converted to energy, about 0.1 percent, so they are equally good for space travel.  I calculated energy yields for several reactions:

  D+D -> T + P: Defect = -0.00432925,  Fraction = 0.00107503
  D+D -> He3 + N: Defect = -0.00296079,  Fraction = 0.000735215
  U235 -> Ba141 + Kr92 + 2N: Defect = -0.186033,  Fraction = 0.000791482


Nerva and Orion are better suited to interplanetary travel.  Neither of these drives have high enough exhaust velocity for practical intersteller travel.  High-energy ion drive is what you need, to get specific impulse of around 2 percent light speed.  That's something like 100 KeV ions, easy to do.

[jdbenner]

Don, How about a rocket that ionizes and expels reaction products.  I know how unreliable Wikipedia is, but I found a reference to a reactor that allows online removal of fission products, this is called a molten salt reactor.  The fissile material and contaminants are dissolved in a fluoride salt, and the solution can be constantly chemically processed.

http://en.wikipedia.org/wiki/Molten_salt_reactor

Of course, the propellant does not have to be limited to fission products, it can be supplemented.

And, spent conventional reactors or  fuel rods, could be used as propellant.

Another Idea, would be to make solar sails out of alloys containing fissile or fissionable materials.

The solar sail would act as the first stage.  And could be recycled as fuel and propellant for the second stage.   

[ijuin]

You might be interested in Project Daedalus

[DonPMitchell]

Using parts of the spacecraft structure as fuel is a good idea.  Fridrikh Tsander, in the 1920s, suggested doing that with chemical rockets, building a spacecraft from magnesium and using parts of its structure as chemical fuel.  Using spent fission products as ion propellent is a good idea too.  The only problems may just be engineering issues, like the equipment needed to do that processing and manipulation of the materials might add too much weight to the spacecraft.

Project Daedalus sounds interesting, but is based on unproven technology (efficient electron-beam fusion).  People have done inertial confinement fusion with lasers, but so far it has been very inefficient.  Fusion is just SO hard.  Even in the core of the Sun, fusion just barely occurs.

I haven't considered practical efficiency issues either.  A fission power plant is only 50% efficient, and I don't know how efficient ion accelerators are. 

[jdbenner]

Your ion thrust boost phase will take years, that is plenty of time for even small equipment to cut up large equipment.

On a manned spacecraft an astronaut could use a saw or chisel to cut up scrap (assuming that it is not too radioactive).

On a robotic probe with a molten salt reactor, a small chemical processing plant is all that will be required to retrieve the fission fragments and add new fuel.  By the way this is a slow breeder reactor design, so the fuel, in storage will not reach critical mass.  Thorium is much cheaper than Plutonium or enriched Uranium any way.

What percentage of the energy can be recovered if the radiators are pointed to the rear?