Fission Stars

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gladiolas
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Fission Stars

Postby gladiolas » Wed Feb 25, 2015 7:39 pm UTC

Instead of a star using fusion, somebody with advanced technology creates a star which uses nuclear fission. To impress his/her/its boyfriend/girlfriend, I suppose; I can't think of a better reason. :D

But is this another one of my totally unworkable ideas? What would really happen if you put together a solar-mass amount of uranium and other materials in the right position and proportions?

I suppose the solar wind would be more radioactive and the nearby planets would be more radioactive, so life would evolve faster...that's all I can think of.

(Feel free to come up with other reasons for this...)

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Re: Fission Stars

Postby sevenperforce » Wed Feb 25, 2015 11:09 pm UTC

gladiolas wrote:What would really happen if you put together a solar-mass amount of uranium and other materials in the right position and proportions?

If all you were dealing with was a solar mass of uranium? It would blow itself apart instantly.

A solar mass of uranium would be approximately four times the diameter of Jupiter. You'd have to use some pretty spectacular magic to get it into that range, however, because a critical mass of enriched uranium is barely over half a foot across. For a gun-type assembly, where you're just smashing the critical masses together and waiting for the boom, we can do an order-of-magnitude estimate using the performance of the Little Boy device. In the Little Boy device, less than one thousandth of one percent of the uranium was ultimately converted into energy; using this ratio, we would expect one thousandth of one percent of a solar mass to be converted to energy as your "fission star" blew itself apart.

This is about 2e42 joules, or 430 billion trillion gigatons TNT equivalent. That's one hundred million times more than the annual energy output of the sun. Not quite supernova level -- this is about 2% of the energy of a supernova -- but definitely enough that you're not gonna have much left.

Now, if you want a sustained fission reaction, you'll probably need to mix a shit-ton of iron and other inert tampers in with your uranium to decrease the reaction rate. And you're going to end up with a HUGE neutron flux. The first electric nuclear power plant had a reactor vessel with a surface area of approximately 200 square meters; this means it would have endured a neutron flux of around 7e16 neutrons per second at its peak power output of 236 MW (2.36e6 W). The sun, in comparison, has a power output of 3.8e26 W. So the neutron flux from your fission star is going to be 1.1e37 neutrons per second.

At 1 AU, the neutron flux will be on the order of 3.8e13 neutrons per square meter per second, or 3.8e9 neutrons per cm2 per second. That means anyone at 1 AU will receive a dose of roughly 6 Sv per second, which will be instantly fatal.

Then again, if you increase your power output a bit and move the planet a little farther away, the neutrons won't be able to reach the planet before they decay. The decay of a free neutron takes about 882 seconds, meaning the mean decay radius will be around 1.7 AU. Moving the planet to a little past 1.7 AU will require 2.9x greater energy output for the fission star. When you work out the math, it turns out that the power released from the spherical neutron decay halo will be about 4 kilowatts per square meter. That's about three times greater than the power per square meter we get from the sun.

Of course, this means you can decrease the power output of your star by about a factor of 4, so that 25% of the energy is coming from visible solar radiation and 75% is coming from neutron decay. Unfortunately that 75% of the energy will mostly be in the form of very energetic electrons and a constant proton bombardment. I'm not sure what that would do to your planet.

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Re: Fission Stars

Postby PM 2Ring » Sat Feb 28, 2015 4:27 am UTC

I guess it's not totally impossible to have a star-sized fission reactor that runs for a long time - the more modestly-sized natural Oklo reactor ran for a few hundred thousand years. Still, constructing one would be somewhat challenging. :) And then there's the issue of where you'd source the required materials, both fissionable & non-fissionable. Most of the matter in a typical stellar system is hydrogen and helium. You'd have to harvest around a thousand stellar systems to get a stellar mass of iron. I'm not going to try & estimate how many systems you'd have to strip to get the amount of fissionable material you'd need, but I suppose it could be approximated using the data from Wikipedia's Abundance of elements in the universe.

@sevenperforce

I haven't checked the rest of your arithmetic, but it appears that you're giving the emitted neutrons a speed close to c. That's not correct. According to the World Nuclear Association's article Physics of Uranium and Nuclear Energy the speed of freshly-emitted fission neutrons is around 7% of c. That's pretty fast, but not fast enough for relativistic effects to be significant ((1-.07**2)**0.5~= 0.99755). However, for a sustained fission reaction, the neutrons have to be moderated to a much slower speed, around 1000 m/s for 235U.

Also, you mention that neutrons have a lifetime of about 882 seconds. But that's a mean lifetime, corresponding to a half-life of about 611 seconds; mean_lifetime = loge(2) x half-life. See Free neutron decay.

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Re: Fission Stars

Postby FancyHat » Sat Feb 28, 2015 4:35 pm UTC

sevenperforce wrote:If all you were dealing with was a solar mass of uranium? It would blow itself apart instantly.

A solar mass of uranium would be approximately four times the diameter of Jupiter. You'd have to use some pretty spectacular magic to get it into that range, however, because a critical mass of enriched uranium is barely over half a foot across.

Are you sure about this?

Why would you need to have the uranium star so dense, when it would be critical at much lower densities?

Could a uranium star sit at, or oscillate around, some sort of equilibrium point, where the energy released by fission holds the star up in a similar way to the way in which energy released by fusion holds the sun up?

A sufficiently rarefied cloud of uranium vapour or dust would have most of the neutrons released by fission (both spontaneous and induced) decay into protons before inducing any more fissions. You'd have a subcritical uranium cloud, able to coalesce under its own gravity.

At some point, if the cloud is massive enough and the pressure of radiation, neutron flux, and so on, doesn't stop it contracting first, it will contract to the point of criticality. What then? I don't know if it would be stable, or stably oscillating, or if it would be unstable, possibly blowing itself apart. Could it, perhaps, be unstable in such a way that it has chaotic bursts of fission?

But if pressure from radiation, neutron flux, and so on, is enough to stop chain reactions from dominating, you'd still have some sort of uranium star, still held up by released nuclear energy, just without induced fission being the dominant mechanism. I'd imagine there'd still be some induced fission, though. Could that make the uranium star unstable enough to destroy itself? I guess it depends on how massive the uranium star is, and on how much of a contribution induced fission makes to the rate of release of nuclear energy.

There's also the question of breeding and other consequences of neutron absorption. How much of the uranium would end up as fissile plutonium? What other isotopes would be produced, and what would their effects be on such a star? But I suppose those are questions for after the basic question of what the basic statistics of a young uranium star would need to be like.
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Re: Fission Stars

Postby sevenperforce » Sat Feb 28, 2015 5:37 pm UTC

PM 2Ring wrote:I haven't checked the rest of your arithmetic, but it appears that you're giving the emitted neutrons a speed close to c. That's not correct. According to the World Nuclear Association's article Physics of Uranium and Nuclear Energy the speed of freshly-emitted fission neutrons is around 7% of c. That's pretty fast, but not fast enough for relativistic effects to be significant ((1-.07**2)**0.5~= 0.99755). However, for a sustained fission reaction, the neutrons have to be moderated to a much slower speed, around 1000 m/s for 235U.

Ah, whoops. I guess the neutrons wouldn't come anywhere close to the planet, then. They would, however, decay at a (mean) radius of about one light-minute, which could make for a very interesting-looking star (depending primarily on whether the decay of free neutrons in a vacuum produces ANY visible-spectrum effects).

FancyHat wrote:
sevenperforce wrote:If all you were dealing with was a solar mass of uranium? It would blow itself apart instantly.

A solar mass of uranium would be approximately four times the diameter of Jupiter. You'd have to use some pretty spectacular magic to get it into that range, however, because a critical mass of enriched uranium is barely over half a foot across.

Are you sure about this?

Why would you need to have the uranium star so dense, when it would be critical at much lower densities?

I was assuming he was talking about a solar mass of solid uranium.

A sufficiently rarefied cloud of uranium vapour or dust would have most of the neutrons released by fission (both spontaneous and induced) decay into protons before inducing any more fissions. You'd have a subcritical uranium cloud, able to coalesce under its own gravity.

At some point, if the cloud is massive enough and the pressure of radiation, neutron flux, and so on, doesn't stop it contracting first, it will contract to the point of criticality. What then? I don't know if it would be stable, or stably oscillating, or if it would be unstable, possibly blowing itself apart. Could it, perhaps, be unstable in such a way that it has chaotic bursts of fission?

But if pressure from radiation, neutron flux, and so on, is enough to stop chain reactions from dominating, you'd still have some sort of uranium star, still held up by released nuclear energy, just without induced fission being the dominant mechanism. I'd imagine there'd still be some induced fission, though. Could that make the uranium star unstable enough to destroy itself? I guess it depends on how massive the uranium star is, and on how much of a contribution induced fission makes to the rate of release of nuclear energy.

Hmm, a very interesting conjecture. If we were going to go with pure uranium, there would probably be an optimal dust particle size, something where the cross-section would be ideal for reflecting radiation pressure.

We could go with a "repeated fizzle" model, where a critical mass is momentarily attained, blowing the star apart, but then collapses again to repeat the cycle. Intuitively I would expect a central core with sustained fission, but then again the shell theorem would imply that this is not necessarily the case. It may maintain a near-constant density gradient. Of course, fission/fizzle in the outer layers might produce sufficient radiation pressure to compress the center into a core anyway.

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Re: Fission Stars

Postby gmalivuk » Sat Feb 28, 2015 10:49 pm UTC

sevenperforce wrote:I was assuming he was talking about a solar mass of solid uranium.
The OP said "right position and proportions", which doesn't necessarily mean it's a solid block.

Given that the solar mass of hydrogen we've got at the center of our own orbit doesn't blow itself completely apart, surely there must be some suitable arrangement of fissile materials that can manage the same sort of equilibrium?
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Re: Fission Stars

Postby sevenperforce » Sun Mar 01, 2015 3:16 am UTC

gmalivuk wrote:
sevenperforce wrote:I was assuming he was talking about a solar mass of solid uranium.
The OP said "right position and proportions", which doesn't necessarily mean it's a solid block.

Given that the solar mass of hydrogen we've got at the center of our own orbit doesn't blow itself completely apart, surely there must be some suitable arrangement of fissile materials that can manage the same sort of equilibrium?

I imagine so.

Calculating that, though? Hmmm...maybe there's a paper here somewhere.

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Re: Fission Stars

Postby gladiolas » Sun Mar 15, 2015 2:24 am UTC

Thanks, everybody.

Yes, I meant a star made of several elements, not just uranium. I didn't know how doable it would be.

Pu-244 has a half-life of 80 million years. And a really massive fusion star could last that long. It would be interesting to try a plutonium star.

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Re: Fission Stars

Postby sevenperforce » Sun Mar 15, 2015 7:08 am UTC

gladiolas wrote:Thanks, everybody.

Yes, I meant a star made of several elements, not just uranium. I didn't know how doable it would be.

Pu-244 has a half-life of 80 million years. And a really massive fusion star could last that long. It would be interesting to try a plutonium star.

FYI, the half-life of an element has very little to do with its critical mass and so forth. A critical nuclear fission reaction functions by chain reaction, not by half-life decay.

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Re: Fission Stars

Postby PM 2Ring » Mon Mar 16, 2015 10:10 am UTC

sevenperforce wrote:FYI, the half-life of an element has very little to do with its critical mass and so forth. A critical nuclear fission reaction functions by chain reaction, not by half-life decay.

Sure, but to get a decent lifetime for your fission star then you need to use a fuel with a long half-life so that it doesn't decay before it gets into the reaction core.

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Re: Fission Stars

Postby sevenperforce » Mon Mar 16, 2015 4:09 pm UTC

PM 2Ring wrote:
sevenperforce wrote:FYI, the half-life of an element has very little to do with its critical mass and so forth. A critical nuclear fission reaction functions by chain reaction, not by half-life decay.

Sure, but to get a decent lifetime for your fission star then you need to use a fuel with a long half-life so that it doesn't decay before it gets into the reaction core.

Ah, good point.

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Re: Fission Stars

Postby FancyHat » Mon Mar 16, 2015 4:48 pm UTC

How viable might a thorium cycle fission star be?
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Re: Fission Stars

Postby Tass » Sun Mar 22, 2015 10:08 pm UTC

I think a big problem might be to make the chain reaction self-regulating. In certain reactor types (such as FLIBE) this an be achieved because thermal expansion of the fissioning material gives larger surface area that loses more neutrons. In ordinary fusion stars it works because the reaction rate depends on temperature and pressure. But if you mix a fissile material with a moderator such that a star sized object is right on criticallity throughout, then the surface area is inconsequential, and you are likely to either have it die down or explode.

Maybe if you use thermal neutrons (which at the temperatures in the core are still rather fast), and find the right nucleus with a greatly temperature dependent cross section, it could work. But side reactions may be a problem, and we are limited by half-life as well. Don't want all the fissile material to have alpha-decayed after a few measly thousands of years. We may need an actual nuclear physicist to look at the possibilities.

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Re: Fission Stars

Postby sevenperforce » Mon Mar 23, 2015 4:22 am UTC

Simply-put: on the one hand you have nuclear detonation; on the other hand you have fizzle. A self-sustained nuclear-fission star must ride the balance between these two states for several billion years at minimum.

Good luck.

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Re: Fission Stars

Postby peregrine_crow » Mon Mar 23, 2015 10:04 am UTC

sevenperforce wrote:Simply-put: on the one hand you have nuclear detonation; on the other hand you have fizzle. A self-sustained nuclear-fission star must ride the balance between these two states for several billion years at minimum.


What is the difference between fusion and fission such that this isn't an issue for regular stars?
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Re: Fission Stars

Postby Xenomortis » Mon Mar 23, 2015 10:33 am UTC

A fusion event doesn't cause other fusion events.
A fission event can cause further fission events.

Thought:
There may be stabilising mechanisms; as the fission rate increases the "star" expands due to the increase thermal pressure - would that reduce the reaction rate (the star becomes less dense, so the mean time for a neutron to encounter another fissile particle goes up), allowing gravity to exert its influence and shrink the star again.
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Re: Fission Stars

Postby Tass » Mon Mar 23, 2015 12:27 pm UTC

Xenomortis wrote:A fusion event doesn't cause other fusion events.
A fission event can cause further fission events.

Thought:
There may be stabilising mechanisms; as the fission rate increases the "star" expands due to the increase thermal pressure - would that reduce the reaction rate (the star becomes less dense, so the mean time for a neutron to encounter another fissile particle goes up), allowing gravity to exert its influence and shrink the star again.


If the neutrons actually bounce around on the order of fifteen minutes before succeeding it reacting with a nucleus, then yes, that could work. Bigger less dense star would mean enough neutrons decay before reacting, so it becomes sub critical, as it collapses it goes critical an the heat stops the collapse.

You' need a LOT of inert material which cannot absorb neutrons, and a fissile isotope with a VERY little fission cross section and no side reactions.

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Re: Fission Stars

Postby Neil_Boekend » Mon Mar 23, 2015 12:57 pm UTC

In effect we have a decreasing fission rate with a decreasing density. Combined with the radiation pressure I foresee a self stabilizing system.
Density is too high -> less neutrons decay before they encounter a fissile core-> fission rate increases -> radiation pressure increases -> star expands -> density decreases -> more neutrons decay without causing fission -> fission rate drops etc.
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Re: Fission Stars

Postby Tass » Mon Mar 23, 2015 1:05 pm UTC

Neil_Boekend wrote:In effect we have a decreasing fission rate with a decreasing density. Combined with the radiation pressure I foresee a self stabilizing system.
Density is too high -> less neutrons decay before they encounter a fissile core-> fission rate increases -> radiation pressure increases -> star expands -> density decreases -> more neutrons decay without causing fission -> fission rate drops etc.


Exactly

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Re: Fission Stars

Postby sevenperforce » Mon Mar 23, 2015 1:47 pm UTC

I suppose the chances of fizzle aren't really all that important after all; the star's gravity is going to hold it together regardless. So we really just have to worry about avoiding the big boom.

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Re: Fission Stars

Postby Neil_Boekend » Mon Mar 23, 2015 3:10 pm UTC

Just like normal stars are formed: start with a cloud of fission fuel instead of a solid object. As the cloud contracts gravitationally the fission speed increases.
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Re: Fission Stars

Postby FancyHat » Mon Mar 23, 2015 5:45 pm UTC

I'm reminded of the demon core, and the accidents with it. Did the demon core qualify as a fission star during those accidents?

That article led me to articles on prompt criticality and delayed neutrons. Prompt neutrons are those emitted pretty much immediately when a nucleus fissions, while delayed neutrons are released later by fission products. A core can be subcritical when it comes to prompt neutrons while critical or supercritical when it comes to prompt and delayed neutrons combined. That seems to be how fission reactors are kept controllable.

But even with prompt criticality, as with the demon core, there do seem to be some effects that lean towards self-stabilization. I gather part of the difficulty in getting a high yield from a fission weapon is that you have to be able to sufficiently overcome such effects.

So, sustained fizzling (if I can use that term that way) does seem not only plausible, but something that's already happened, at least briefly, without even being intended.
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Re: Fission Stars

Postby PM 2Ring » Wed Mar 25, 2015 11:52 am UTC

As well as the basic expansion-contraction cycle, we can also have a convection cycle affecting moderator concentration, like what happened at Oklo. However, to qualify as a star, this thing has to be white-hot, so its structure has to be fairly simple.

We want to restrict the fission reaction to the very core of our star. That means we need a lot of fission-inhibiting moderator mixed with the fuel through most of the star, and some way to reduce the inhibitor concentration when the fuel is taken up by the reaction core. I suppose convection would be useful for that, but we may also need some way of reducing the effectiveness of the moderator as the fuel + moderator mixture goes into the core so that we don't end up reducing the concentration of the remaining fuel too much. Perhaps we can use a moderator that gets converted into a non-moderator when it gets hit by fast neutrons produced in the core. Also, we could use breeder reactions that increase the effectiveness of the remaining fuel mix as our star ages.

If this fission star has a mass and temperature comparable to our Sun its reaction rate per unit volume needs to be very low: much lower than a typical terrestrial fission reactor.
Wikipedia wrote:The energy production per unit time (power) of fusion in the core varies with distance from the solar center. At the center of the Sun, fusion power is estimated by models to be about 276.5 watts/m3.[3]

Despite its intense temperature, the peak power production density of the core overall is similar to an active compost heap, and is lower than the power density produced by the metabolism of an adult human. The Sun is much hotter than a compost heap due to the Sun's enormous volume.[4]

The low power outputs occurring inside the fusion core of the Sun may also be surprising, considering the large power which might be predicted by a simple application of the Stefan–Boltzmann law for temperatures of 10 to 15 million kelvin. However, layers of the Sun are radiating to outer layers only slightly lower in temperature, and it is this difference in radiation powers between layers which determines net power production and transfer in the solar core.

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Re: Fission Stars

Postby Neil_Boekend » Wed Mar 25, 2015 1:39 pm UTC

Note: this post is based on a quick wikipedia check and may not be a sign of sentience. I am not an expert on this subject, I just have a casual interest and wikipedia.

I'd restrict fission to the core by means of a neutron absorber in the top layers. A neutron moderator is quite a different beast.

The fission star is going to be a plasma if there is similar energy conversion rate as the sun.
In a plasma you simply need a neutron absorber with a lower atomic mass than the fission fuel. That neutron absorber will "float" on the top and suppress fission there.
Boron-10 should do. It is a light neutron absorber that doesn't get radioactive when it absorbs a neutron and becomes boron-11. If it absorbs another neutron it'll become boron-12 which is radioactive: β decay mostly to Carbon-12. Carbon-12 is stable. If it absorbes 2 neutrons it becomes carbon-14 which β decays to nitrogen-14, stable again. After that captures 2 neutrons the Nitrogen 16 βdecays to oxygen 16. That can absorb 3 neutrons to turn into Oxygen 19 which βdecays to fluorine 19. That can absorb a neutron to turn into fluorine 20 which βdecays to Neon 20. Then I get too bored to check what happens. Our boron-10 has now absorbed 10 neutrons and emitted only electrons and antneutrinos, neither helps fission. And the neutron absorbtion/βdecay chain may not have ended.
Boron really rocks as a neutron absorber and is light enough to float on the fission fuel, with only convection mixing it with the fuel.
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Re: Fission Stars

Postby sevenperforce » Wed Mar 25, 2015 3:44 pm UTC

Neil_Boekend wrote:Boron-10 should do. It is a light neutron absorber that doesn't get radioactive when it absorbs a neutron and becomes boron-11. If it absorbs another neutron it'll become boron-12 which is radioactive: β decay mostly to Carbon-12. Carbon-12 is stable. If it absorbes 2 neutrons it becomes carbon-14 which β decays to nitrogen-14, stable again. After that captures 2 neutrons the Nitrogen 16 βdecays to oxygen 16. That can absorb 3 neutrons to turn into Oxygen 19 which βdecays to fluorine 19. That can absorb a neutron to turn into fluorine 20 which β decays to Neon 20. Then I get too bored to check what happens.

Let's see here.
Spoiler:
  • Neon-20 + 3 neutrons will β decay into Sodium-23.
  • Sodium-23 + 1 neutron will β decay into Magnesium-24.
  • Magnesium-24 + 3 neutrons will β decay into Aluminum-27.
  • Aluminum-27 + 1 neutron will β decay into Silicon-28.
  • Silicon-28 + 3 neutrons will β decay into Phosphorus-31.
  • Phosophorus-31 + 1 neutron will β decay into Sulphur-32.
  • Sulphur-32 + 3 neutrons will β decay into Chlorine-35.
  • Chlorine-35 + 3 neutrons will β decay into Argon-38.
  • Argon-38 will, through various routes, pick up 4 neutrons on the way to Potassium-42, which β decays to Calcium-42.
  • Calcium-42 will pick up a glorious 5 neutrons before β decaying to Scandium-47.
  • Scandium-47 isn't entirely stable but will either β decay to Titanium-47 or absorb a neutron and then β decay to Titanium-48. Either way, Titanium is stable up to Titanium-51, which β decays to Vanadium-51, having absorbed 4 neutrons on the way there.
  • Vanadium-51 + 1 neutron β decays to Chromium-52.
  • Chromium-52 + 3 neutrons β decays to Manganese-55.
  • Manganese-55 + 1 neutron β decays to Iron-56.
  • Iron-56 + 3 neutrons β decays to Cobalt-59.
  • Cobalt-59 absorbs 6 neutrons and passes through various isotopes of nickel before reaching Copper-65.
  • Copper-65 will pick up 11 neutrons going through gallium to Germanium-76.
  • Germanium-76 will pick up 8 neutrons going through various elements to Krypton-84.
From there it goes rubidium, strontium, yttrium, zirconium, niobium, molybdenum, ruthenium, rhodium, palladium, silver, cadmium, and indium.

Cadmium and Indium have a tendency to bounce back and forth between various isotopes of each other in β and β+ decay, but will eventually reach tin. From there, it will go antimony, tellurium, iodine, xenon, barium, lanthanum, cerium, praseodymium, neodymium, and up past promethium. At this point, we're getting into majority fission decay products, which means things are going to become much messier.
This is going to be one weird-ass star.

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Re: Fission Stars

Postby FancyHat » Wed Mar 25, 2015 8:35 pm UTC

If it's a sufficiently huge (in terms of volume) and rarefied star, could induced fission be limited by the outer parts of the star simply being too rarefied to be critical? The more rarefied it is, the more neutrons will decay before inducing further fissions. Could that provide a (fuzzy) boundary between the core and the rest of the star?
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Re: Fission Stars

Postby Neil_Boekend » Thu Mar 26, 2015 7:26 am UTC

Since the plasma will have a density gradient anyway that might just work. A light neutron absorber would make the boundary less fuzzy though.
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