Thorium vehicle will run 100 years on 8 grams of fuel

[PamW]

39. Criticality in non-operating - but NOT in melted.

johnd83,

In order to know what a reactor is going to do, and whether it is going to be critical or not; you need to know the neutron density function which tells you where the neutrons are and what they are doing, where they are going...

What is the dimensionality of this function; how many variables do you have to tell me before I can tell you how many neutrons there are doing whatever...

The dimensionality is 7. First you have to tell me the position and in 3-D that takes 3 variables, x, y, z. Then you need to tell me the direction which takes 2 vatriables, angles theta and phi ( just like a telescope; to define a direction you need right ascension and declination ). Then you need to tell me the energy of the neutrons you are interested in, and then the time you are interested in. That's a total of 7 variables. So it's a complicated function.

We can simplify this. First, we can say that we are interested in solutions where the reactions are self-sustaining and at constant power, i.e "critical". That leaves out the time variable; one solution for all time.

We were at this place in 1942, when an extremely clever physicist Enrico Fermi took the next step. He said consider an infinitely large mass of material. If the mass is infinite; then all points are the same, and all directions are the same. There can't be a dependency on x, y, z, theta, or phi. In this case, the equation that tells us the neutron distribution, the neutron transport equation is a function of a single variable E, the energy.

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

Note that if the mass is infinite there can be no loss due to neutrons leaking out of the core - the core is infinite. So a finite core has an additional neutron loss mechanism, namely leakage out of the core. Therefore, if a mixture of materials can not sustain crititicality in an infinite core, then it can't go critical in a finite geometry because that finite geometry has an additional loss mechanism.

So we come down to a neutrons transport equation in a single variable, the neutron energy, E. We solve that to determine if the mixture of materials can go critical.

If you go to the website of the nuclear data group at Brookhaven National Lab, you can plot the capture cross-section ( the propensity of a material to absorb neutrons parasitically ) for U-238 as a function of neutron energy. This is also the (n,gamma) cross-section because the impacted U-238 de-excites by emitting a gamma ray:

http://www.nndc.bnl.gov/sigma/index.jsp?as=238&lib=endfb7.1&nsub=10

Choose (n,gamma) plot from the list at right.

See all those "spikes" in the neutron cross section? They indicate that U-238 at energies from about 10 eV to 10,000 eV has a large propensity to capture a neutron parasitically, so it can't slow down to low energy and cause a fission. Neutrons are born in fissions at energies around 1 MeV to 2 MeV ( million electron volts ). The fission cross section of U-235 ( or U-233 ) is highest at low energies, so you need to slow neutrons down. The problem is how is the neutron going to slow down in the presence of U-238 which will be present in a homogeneous melted mixture like corium, and escape getting absorbed parasitically by the U-238 resonances as those peaks are called. The answer is: they CAN'T. You can show with mathematical certainty, not "assumptions" by solving the infinite medium transport equation that the mixture can NOT go critical. MATHEMATICAL CERTAINTY!!.

Since an infinite medium of corium can't go critical; then a finite mass of corium can't go critical.

But if that is the case; how does the reactor work to begin with.

When the reactor is intact, we don't have a mixture all melted together. We have a lattice - an array of rods surrounded by water.

Neutrons are born in fissions, which is in the fuel; so neutrons are born in the fuel rods. However, the fast newborn neutrons travel out of the rods and enter the water surrounding the rods. That's where they encounter the hydrogen atoms of the water. Neutrons slow down quite quickly in collisions with hydrogen atoms since the hydrogen nucleus, the proton, has about the same mass as the neutron.

Here's the important part. When the neutrons are slowing down through that energy range from 10 eV to 10,000 eV; they are in the water region. There's no U-238 in the water. That's the important part. There's no U-238 in the water So when the neutron has an energy in the resonance range of 10 eV to 10,000 eV and it would be susceptible to parasitic capture by U-238; there's no U-238 around. So the neutrons are not captured. They live on to slow to even lower energies that are in thermal equilibrium with the water at about 0.025 eV. Then the low energy or thermal neutron finds its way back into the fuel rod with the U-235 and U-238. However, now, it's energy is 0.025 eV and NOT in the "deadly" range of 10 eV to 10,000 eV. So U-238 "leaves the neutron alone"; and it can cause a fission on U-235. That's what keeps the reactor going.

That heterogeous lattice where there is separation between water moderator and parasitic resonance capture by U-238 is ALL IMPORTANT

If the rods are intact and unmelted; you have separation between water and U-238. If the U-238 is melted; then you have a mixture of U-238 and water.

Without that separation of water and U-238, the mathematics of the neutron transport equation MATHEMATICALLY PROVES there can't be a criticality.

That doesn't happen by accident; the reactor is DESIGNED that way. That is why power reactors use enrichments of 3% or 4%.

University research reactors use enrichments of 20%, and some used to go as high as >90% enrichment. We aren't worried about these low power reactors melting down. However, the big power reactors, we are worried about that. So the design decision is made to have low enrichments so that should there be a meltdown; the resulting corium can NOT sustain criticality.

As far as criticality accidents; yes there have been those accidents; but the core was NOT MELTED at the time of the accident. The core may have melted as a result of the accident; but was NOT melted during the criticality. Additionally, lots of those accidents were in nuclear weapons cores, and research reactors which don't have the low enrichment that power reactors do.

In terms of criticality accidents in US-style low enrichment power reactors; there have been NONE.

PamW