Week 8: Nuclear fission (part 2) Flashcards
What is reactivity?
Another way of describing neutron multiplication. It is defined in terms of the multiplication factor as:
p = (k-1) / k
What units is reactivity measured in?
Reactivity is often measured in units of the delayed neutron fraction, with this unit being known as the dollar and 0.01$ being equal to one cent.
if k < 1, what does that say about the criticality and power of the reactor?
Criticality: Sub-critical
Power: Decreasing
if k = 1, what does that say about the criticality and power of the reactor?
Criticality: Critical
Power: Steady
if k > 1, what does that say about the criticality and power of the reactor?
Criticality: Super-critical
Power: Increasing
if k ~ 1.007, what does that say about the criticality and power of the reactor?
Criticality: Prompt critical
Power: Increasing extremely quickly
What is the neutron lifetime?
The duration of each generation.
l = tf + ts + tD
What is the process and typical value for tf?
Process: Fission
Time: 10^-14s
What is the process and typical value for ts?
Process: Slowing down
Time: ts «_space;tD
What is the process and typical value for tD?
Process: Diffusion
Time: ~ 0.1ms
Derive an equation for neutron population as a function of time.
(35)
What is the reactor period, Tp?
The time it takes for the power (or neutron population) to increase by a factor of e, and can be written as,
Tp = l / k-1 ~ l/p
Why are delayed neutrons needed for reactors?
If we consider only prompt neutrons in a reactor, the rate of change of neutrons is incredibly high and is uncontrollable by a mechanical system.
With delayed neutrons however, the production time is a lot longer, resulting in controllable circumstances.
What is prompt criticality?
If the reactivity rises to 1$ or more, the chain reaction is no longer reliant on the delayed neutrons and can proceed on prompt neutrons alone.
This is prompt criticality and will result in uncontrollable rates of power increase.
What are light water reactors?
LWRs use light water for both cooling and moderation.
Examples are pressurised water reactors and boiling water reactors.
What is the effect of an increase in temperature of an LWR?
When the water in an LWR increases in temperature, it expands.
This means that the neutrons are able to travel further through the moderator without interacting, so they do not slow down as well as they were previously.
If the water boils (“voids”), this effect will be even stronger.
How is an LWR self-stabilising?
An increase in temperature leads to a decrease in reactivity.
This leads to a decrease in power production.
This causes a decrease in temperature.
The reactor has negative feedback and is self-stabilising.
What is the ideal balance between moderator and fuel in an LWR?
The neutrons are being slowed down well, but can also easily find a fuel atom to continue the chain reaction.
What does under-moderated mean?
If the system is designed with a lower moderator to fuel ratio than the ideal balance.
What does over-moderated mean?
If the system is designed with a higher moderator to fuel ratio than the ideal balance.
How are water cooled reactors designed to achieve negative feedback?
Designed to be under-moderated.
How does feedback in a solid moderator reactor differ from that seen in a LWR?
Solid moderators do not expand with temperature as much as water, so negative feedback is not seen.
How do solid moderator reactors achieve negative reactivity?
Moderator temperature increases mean that neutrons reach thermal energies at higher values, resulting in smaller cross sections and some negative reactivity.
How does the resonance in the cross sections of solid moderator reactors, cause a feedback effect?
At higher temperatures, the resonances undergo Doppler broadening, which results in more neutron absorption in the resonance.
In low-enriched uranium fuels, this means more neutron are lost to U-238, resulting in negative reactivity.
