How can the neutron star factory make heavy elements?

Question

My Primordial galactic empire is facing a huge deficit of heavy elements. So I decided to make a neutron-star factory to make heavy elements like gold and lead

See that purplish thing in the center of of the shell? That's a neutron star. When stuff falls onto it, that stuff gets heated up to ridiculously high temperatures, and is blasted out in jets. Sometimes, this can get so hot, that nuclear fusion can occur. Although, my advisers, the Golems, tell me that the temperature will be too low in the accretion disk, to generate anything past carbon. So, I dropped my proposal.

My industry in question is located near the center of the galaxy, a few light-years away, so that I can get energy from my Supermassive Black Hole Power Plant. I recently got a lot of funding from interested parties in this project. I have just proposed this design to my investors:

• A thick shell of iron and beryllium is installed outside the neutron star, about 10 meters thick. Since this is a compact and small neutron star, and not a giant star, we can afford to make the shell thicker, as we need lesser materials to envelop it. The shell is about a few hundred miles away from the neutron star.

• Once I input hydrogen and helium into my "starshell reactor", I begin bombarding the neutron star with relativistic projectiles, to blow off massive chunks off the crust of the neutron star. On leaving the gravity field of the neutron star, the chunks of neutron-rich matter begin to explosively decompress outwards, disassociating into free neutrons, protons and electrons. That is exactly what I want.

• These free neutrons are then captured by the hydrogen/helium nuclei, which decay and form heavy metals, as the neutrons decay into protons. This process is known as Rapid Neutron Capture and actually occurs in real life during supernovas. This means that a lot of heavy elements, from iron straight up to even uranium, will be synthesized.

• The resulting heavy elements will be extracted from the jets of the star. I don't have a deficit of iron in my galaxy, it is dirt common. It is the rarity of the heavier elements like gold and lead that is a pain for my empire. So screw iron, I am sending it back to the neutron star to be further bombarded by neutrons to make heavy elements.

• There is not just one reactor here. The industry uses multiple neutron stars and therefore multiple factories to make heavy elements. There are about 500 factories operating in this industry, each with their individual neutron star.

The plan is to turn my industry, called Hekaton into the cheapest source of heavy elements in the entire galaxy. Do not comply and no gold for you, do not comply and no lead radiation shielding for you.

My interested parties are informed that money and resources aren't a problem at all. I received a lot of money from interested parties, and my father, former Emperor, has already supplied me with a lot of iron and beryllium for making the "StarShell"

So, my honorable investors, I came to you to ask this question:

What are the problems with my design, and what should I do to fix them?

Heavy Elements: Elements with an atomic no. greater than Iron.

Answer 1

Let us first consider the temperature of a neutron star. They can be very hot indeed... this physics.SE answer suggests over a million Kelvin. Whilst they are quite small, this is still a considerable amount of radiated power... if we assume the shell of a neutron star is basically a black body (which is probably an OK assumption) we can use the Stefan-Boltzmann law to get radiated power which is $j^* = \sigma AT^4$ where $\sigma$ is the Stefan-Boltzmann constant, $A$ is the surface area of the neutron star (~1257km²) and $T$ is its temperature in Kelvin, which gives us about 0.186L_☉, where L_☉ is the the luminosity of the Sun.

If your shell had an outer radius of 500km (~310 miles) then it has a surface area of about $\pi$ million square km . If it were in thermal equilibrium, and absorbed all the radiated energy of the neutron star, it would have a black-body temperature of over 141000K. There ain't no way it is going to remain a solid at that temperature.

All is not lost though, because if you wait long enough radiative cooling will bring them down to a more hospitable temperature. A billion year old neutron star might have a surface temperature much like the Sun's (say, 5770K), giving a much more manageable luminosity of ~80PW. Your shell would therefore have an outer temperature of little over 800K... hot enough to glow cherry red, but not hot enough to melt.

However. Shells around things that gravitate are not stable! Any slight peturbation, and the bits of the shell that are further from the star feel less gravitational attraction, and the bits that are closer feel more, and so your shell then accelerates until the star hits the wall and then it is game over. A dense, multilayered Dyson Swarm would not have this particular failure mode.

I begin bombarding the neutron star with relativistic projectiles, to blow off massive chunks off the crust of the neutron star

Remember that unless you're firing a projectile in excess of the star's escape velocity, and for a neutron star with a typical mass of 1.4 solar masses, $v_e$ is going to be >0.64c. Accelerating any projectile to a greater speed than that is going to be intensely energy-consuming.

Lifting matter from the surface of that neutron star to an orbit at 100km altitude requires about 17.65 petajoules per kilo lifted (see specific orbital energy). Lifting matter from a 100km orbit to a 1000000km orbit takes another ~1 PJ per kilo.

The gas you're using to fuel your system also needs to be injected into a close orbit around your neutron star. Without knowing how your gas gets to the neutron star, I can't be more specific, but it needs to get ~1PJ/kg from somewhere.

If your energy collectors and projectile accelerators and debris-catching devices and mass conversion was 100% efficient (which of course it really won't be) then your neutron star radiates enough energy to produce 4kg of matter per second, equivalent to 345.6 tonnes per Earth day or a bit more than 126230 tonnes per year.

The plan is to turn my industry, called Hekaton into the cheapest source of heavy elements in the entire galaxy. Do not comply and no gold for you, do not comply and no lead radiation shielding for you.

Lets compare your 126kT a year to an asteroid in our own back yard... 16 Psyche. There's been a bit of brouhaha about it in recent years, as it appears to contain quite a lot of heavy metals and might be an interesting thing to mine. We have a good idea of the composition of metallic meteorites. and so with a bit of thought we can hazard a guess as to how much gold is in it. At ~2.29x10¹⁹kg, and with a gold fraction of somewhere between 0.0003 parts per million to 8.74 parts per million it'll have somewhere between 700 million and 200 billion tonnes of gold.

That means one asteroid has as much gold as the total output of your device could manage in thousands of years, and that's being pessimistic about the gold and optimistic about your device. And that's just gold! 16 Psyche also have all sorts of other interesting metals and minerals in it too.

One asteroid, in one solar system.

Back to the drawing board with you, I think.

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As a footnote though,

These free neutrons are then captured by the hydrogen/helium nuclei, which decay and form heavy metals, as the neutrons decay into protons.

I won't consider the physics of that here, but remember that if you have no shortage of iron then you should be transmuting iron rather than wasting loads of time and effort and energy and mass making more iron to transmute into heavier things.

If you have light element feedstocks, or you want to synthesize lighter elements you'd be better off just making giant fusion reactors and using the alpha process rather than mucking around with an artificial r-process. There are a few things that are hard to produce naturally (beryllium and lithium spring to mind) but not many.

For heavy-ish things, it may well be that regular neutron capture is an easier way to synthesize heavier elements... just putting bricks of feedstock around your fusion reactors and harvesting some of the neutron flux might work.

Where the r-process shines is the ability to ram stuff together before intermediate isotopes decay, making interesting superheavy elements (and maybe even stable transuranics, if they exist). Providing me with access to exotic elements that I cannot simply mine or synthesize myself is a much better prospect than offering me stuff I have a hojillion tonnes of just floating around for the taking.

Answer 2

These free neutrons are then captured by the hydrogen/helium nuclei, which decay and form heavy metals

to get heavy metals you don't need neutrons bombarding hydrogen or helium, you need to chain-wise fuse them into forming heavier nuclei.

Neutrons split the nuclei they hit, and hydrogen has nothing to split in, while helium can at best give you hydrogen and more neutron.

While using helium and hydrogen as basic "bricks" you can build up heavier nuclei.

Answer 3

Sadly, the only way to keep the shell around the star from melting and becoming a shiny blob of beryllium several hundred miles in diameter would be to put it so far away that the star is useless, and Hekaton goes bankrupt in a few weeks. A ring torus would work better, though it would still have to be far from the star. The rest of the stuff seems good to me though.

Answer 4

Once you can extract neutronium off the star, no need to do anything further to it, it will quickly decay into all kinds of heavy nuclei by itself. The neutrons tend to stick together by nuclear forces, they don't disperse immediately unless too hot. Astronomers actually observed this from collision of neutron stars, they detected gold and other elements in the ejected material.