Here, you can adjust the control rods in a simulated nuclear reactor and you can see how the power changes. Behind the scenes, this is running the real point kinetics equation.
Nuclear chain reactions are dynamic systems where one fissioning nucleus releases a number of neutrons that go on to fission other nuclei. If more neutrons are released than are consumed, the power increases and the reactor is called supercritical. If fewer neutrons are being generated, the reactor is subcritical and the power is decreasing.
A measure of this characteristic is called reactivity, which has special units called "dollars" or "cents". These units are unrelated to the financial terms and were invented in the Manhattan Project, when code-names and strange things were somewhat valued.
When nuclear fuel atoms split, they release most of their neutrons right away. These are called prompt neutrons. But, around half a percent of the neutrons are emitted by the delayed decay of some neutron-rich fission products. These are called delayed neutrons. While prompt neutrons can cause generations of the chain reaction to tick by very rapidly (microseconds), the delayed neutrons are released on the order of seconds and minutes. These delayed neutrons allow nuclear chain reactions to be controlled easily.
When you change the reactivity, you’ll see a rapid change proportional to the size of the reactivity change. This is the fast effect of the prompt neutrons. After that you will see the slower dynamics of the delayed neutrons kicking in. Try to bring the reactor up to 10,000 Watts and hold it steady there.
This kinetics simulator solves the point kinetics equation (PKE) on a webserver in the background. This is a very simple simulation and does not (yet) include any of the thermal feedback mechanisms inherent in any high-power chain reactor. Still, it can give you a feel for what it's like to operate a fission chain reaction. It uses 6 groups of delayed neutron precursors and directly integrates the PKE every time you update the slider.
You can read more about neutron kinetics here.
We limit reactivity insertions to below a dollar for now because the solver quickly runs into numerical troubles. We hope to enable this in the future.