38 ms·

> So in principle if you just form a large enough ball of Pu-239, it would go critical Don't neutrons lose some energy as they transit through the material? Th

> So in principle if you just form a large enough ball of Pu-239, it would go critical Don't neutrons lose some energy as they transit through the material? That would make this bounded in some respect anyway.

Cerium 2y ago
As-in, the neutrons lose energy by hitting the material and creating more neutrons?
- pfannkuchen 2y ago
  No, as in, as the average distance a neutron-hitting nucleus travels before the collision increases, the average energy of the neutron at collision time decreases. Or so I imagine, that's what I'm asking. The scenario was that the size of the material can increase until you guarantee a sufficiently high rate of collision, and I'm asking whether neutrons really do not lose energy as they travel prior to collision (as the scenario seems to assume).
  - simonh 2y ago
    Why would the average distance a neutron has to travel to strike a nucleus increase? I suppose it does eventually, as the number of undecayed nuclei falls, but that wouldn’t be a significant effect until the criticality reaction had very significantly progressed. In other words the reaction can’t go on forever.
    - pfannkuchen 2y ago
      > Why would the average distance a neutron has to travel to strike a nucleus increase? Because if the problem is that neutrons are escaping the object before hitting a nucleus, and we are adding more nuclei so the likelihood that they hit something increases, the new collision candidates will be further away than the old ones. In other words, adding material to the edge of the object does not affect the per distance probability of collision. It only affects the overall probability of collision. Since the per distance probability does not change while the overall probability does, the probability increase must lie outside of the average path length of a neutron through the original object.
    - dumah 2y ago
      In the case we are considering, it doesn’t, but it could with other materials. Consider that the wavelength of the neutron is a function of its energy, and that the cross sections for interaction between nuclei and neutrons are strong and complex functions of energy. If the cross section for the interaction of interest gets smaller with decreasing energy, then it would be the case that the neutrons mean free path length would increase as energy decreased.
      - pfannkuchen 2y ago
        > In the case we are considering, it doesn’t, but it could with other materials. Sorry, I said something subtle and easy to miss and also made a confusing typo, writing too fast. "average distance a [nucleus-hitting neutron]" As in, as more material is added, the percent of neutrons that successfully collide and don't just fly out increases. But, for the class of nucleus-hitting neutrons, the average distance prior to collision increases. If the neutron loses energy as it travels, then as the average distance increases I suppose the probability of splitting the collidee nucleus decreases. So as the class increases in size, its rate of nucleus splitting may fall below the threshold, which bounds the useful size increase. Perhaps this doesn't occur until the object has grown in size way past the point of basically guaranteed criticality, I haven't done the math, just curious since GP's statement sounded as if neutrons do not lose energy across any distance and the object could therefore could be increased to an arbitrary size while maintaining the same qualitative per-iteration behavior, and I find that surprising.
        Tuna-Fish 2y ago
        > If the neutron loses energy as it travels Excluding collisions, it does not. As far as the neutron is considered, it's traveling through empty space, just as if it was in vacuum. > I suppose the probability of splitting the collidee nucleus decreases. In this regime, probability of splitting a nucleus goes up as energy decreases.
      - Tuna-Fish 2y ago
        In the regime that's interesting for pure fission devices, the opposite is true. The cross section increases as energy decreases. This is why moderators are a thing in nuclear reactors.
dontwearitout 2y ago
They certainly can, see https://en.wikipedia.org/wiki/Resonance_escape_probability https://en.wikipedia.org/wiki/Resonance_escape_probability. The all-important number in nuclear reactions is "k", the average number of child neutrons a single neutron will produce. The neutron population follows an equation something like N = exp((k - 1) * t). For k<1, you get exponential decay, and for k>1, you get exponential growth (until everything becomes a plasma and k changes). Check out https://en.wikipedia.org/wiki/Six_factor_formula https://en.wikipedia.org/wiki/Six_factor_formula.
- pfannkuchen 2y ago
  I think this is neutrons emitted from each collision. I’m interested in the energy of each neutron while it is in flight.
  - ridiculous_fish 2y ago
    It changes very little because there’s nothing to receive their kinetic energy. Neutrons lose energy by colliding with things of similar mass, such as hydrogen nuclei (often in water). If they collide with a heavy nucleus, such as plutonium, they just bounce off without losing speed. (Or fission or capture.) Think of billiards. The cue ball may slow or stop after hitting another ball, since they have similar masses. But hit the rail and it just bounces off, at the same speed, because the table is so much heavier. If there are no light nuclei in the environment, then the neutrons won’t slow down.
  - dontwearitout 2y ago
    The energy of neutrons isn't really analogous to the energy of atoms in chemical reactions, but absolutely affects the reaction dynamics. The "cross section", or interaction probability, is a strong function of neutron speed. In bombs the neutrons don't get a chance to slow down, but in reactors you try to reduce them to "room temperature" speeds using collisions with light, inert nuclei (the moderator). Here's a diagram showing the interaction probability vs. neutron speed for a few isotopes of uranium: https://tinyurl.com/u235-cross-section https://tinyurl.com/u235-cross-section

Cerium 2y ago

As-in, the neutrons lose energy by hitting the material and creating more neutrons?

pfannkuchen 2y ago
No, as in, as the average distance a neutron-hitting nucleus travels before the collision increases, the average energy of the neutron at collision time decreases. Or so I imagine, that's what I'm asking. The scenario was that the size of the material can increase until you guarantee a sufficiently high rate of collision, and I'm asking whether neutrons really do not lose energy as they travel prior to collision (as the scenario seems to assume).
- simonh 2y ago
  Why would the average distance a neutron has to travel to strike a nucleus increase? I suppose it does eventually, as the number of undecayed nuclei falls, but that wouldn’t be a significant effect until the criticality reaction had very significantly progressed. In other words the reaction can’t go on forever.
  - pfannkuchen 2y ago
    > Why would the average distance a neutron has to travel to strike a nucleus increase? Because if the problem is that neutrons are escaping the object before hitting a nucleus, and we are adding more nuclei so the likelihood that they hit something increases, the new collision candidates will be further away than the old ones. In other words, adding material to the edge of the object does not affect the per distance probability of collision. It only affects the overall probability of collision. Since the per distance probability does not change while the overall probability does, the probability increase must lie outside of the average path length of a neutron through the original object.
  - dumah 2y ago
    In the case we are considering, it doesn’t, but it could with other materials. Consider that the wavelength of the neutron is a function of its energy, and that the cross sections for interaction between nuclei and neutrons are strong and complex functions of energy. If the cross section for the interaction of interest gets smaller with decreasing energy, then it would be the case that the neutrons mean free path length would increase as energy decreased.
    - pfannkuchen 2y ago
      > In the case we are considering, it doesn’t, but it could with other materials. Sorry, I said something subtle and easy to miss and also made a confusing typo, writing too fast. "average distance a [nucleus-hitting neutron]" As in, as more material is added, the percent of neutrons that successfully collide and don't just fly out increases. But, for the class of nucleus-hitting neutrons, the average distance prior to collision increases. If the neutron loses energy as it travels, then as the average distance increases I suppose the probability of splitting the collidee nucleus decreases. So as the class increases in size, its rate of nucleus splitting may fall below the threshold, which bounds the useful size increase. Perhaps this doesn't occur until the object has grown in size way past the point of basically guaranteed criticality, I haven't done the math, just curious since GP's statement sounded as if neutrons do not lose energy across any distance and the object could therefore could be increased to an arbitrary size while maintaining the same qualitative per-iteration behavior, and I find that surprising.
      - Tuna-Fish 2y ago
        > If the neutron loses energy as it travels Excluding collisions, it does not. As far as the neutron is considered, it's traveling through empty space, just as if it was in vacuum. > I suppose the probability of splitting the collidee nucleus decreases. In this regime, probability of splitting a nucleus goes up as energy decreases.
    - Tuna-Fish 2y ago
      In the regime that's interesting for pure fission devices, the opposite is true. The cross section increases as energy decreases. This is why moderators are a thing in nuclear reactors.

dontwearitout 2y ago

They certainly can, see https://en.wikipedia.org/wiki/Resonance_escape_probability https://en.wikipedia.org/wiki/Resonance_escape_probability. The all-important number in nuclear reactions is "k", the average number of child neutrons a single neutron will produce. The neutron population follows an equation something like N = exp((k - 1) * t). For k<1, you get exponential decay, and for k>1, you get exponential growth (until everything becomes a plasma and k changes). Check out https://en.wikipedia.org/wiki/Six_factor_formula https://en.wikipedia.org/wiki/Six_factor_formula.

pfannkuchen 2y ago
I think this is neutrons emitted from each collision. I’m interested in the energy of each neutron while it is in flight.
- ridiculous_fish 2y ago
  It changes very little because there’s nothing to receive their kinetic energy. Neutrons lose energy by colliding with things of similar mass, such as hydrogen nuclei (often in water). If they collide with a heavy nucleus, such as plutonium, they just bounce off without losing speed. (Or fission or capture.) Think of billiards. The cue ball may slow or stop after hitting another ball, since they have similar masses. But hit the rail and it just bounces off, at the same speed, because the table is so much heavier. If there are no light nuclei in the environment, then the neutrons won’t slow down.
- dontwearitout 2y ago
  The energy of neutrons isn't really analogous to the energy of atoms in chemical reactions, but absolutely affects the reaction dynamics. The "cross section", or interaction probability, is a strong function of neutron speed. In bombs the neutrons don't get a chance to slow down, but in reactors you try to reduce them to "room temperature" speeds using collisions with light, inert nuclei (the moderator). Here's a diagram showing the interaction probability vs. neutron speed for a few isotopes of uranium: https://tinyurl.com/u235-cross-section https://tinyurl.com/u235-cross-section