Point Kinetics for Linear Insertion of Reactivity

[a1234]

I want to use the point reactor kinetics equations to solve for the power as a function time when a reactivity of gamma*t is added to a reactor that is at equilibrium at time 0. I am also asked to consider the case where the transients are long-lived compared to the lifetime of prompt neutrons.

In solving for the reactor power, would the condition on the transients imply that the roots of the inhour equation would become more complicated (i.e. we cannot make the appropriate simplifications regarding the ratio of the reactivity to beta)? What other implications do the long-lived transients have in the solution?

 

[Astronuc]

I want to use the point reactor kinetics equations to solve for the power as a function time when a reactivity of gamma*t is added to a reactor that is at equilibrium at time 0. I am also asked to consider the case where the transients are long-lived compared to the lifetime of prompt neutrons.

In solving for the reactor power, would the condition on the transients imply that the roots of the inhour equation would become more complicated (i.e. we cannot make the appropriate simplifications regarding the ratio of the reactivity to beta)? What other implications do the long-lived transients have in the solution?

1. What text or reference is one using?

2. What does one mean by transient?

3. What is the lifetime of a prompt neutron?

4. Please write the point kinetics equations as you understand them.

5. What are the assumptions (and limitations) regarding the in-hour equation?

6. What does one mean by "we cannot make the appropriate simplifications regarding the ratio of the reactivity to beta"? The reactivity can be ρ < β, ρ = β, ρ < β; ρ < β is controlled, ρ > β essentially uncontrolled, and undesirable.

 

[raining Pete]

As an internet forum user, I am not an expert in reactor kinetics equations. However, based on my understanding, the condition on the transients would indeed make the roots of the inhour equation more complicated. This is because in the case of long-lived transients, the reactivity added to the reactor would have a significant impact on the power over an extended period of time, rather than a quick and short-lived effect.

This would mean that the ratio of reactivity to beta would not remain constant throughout the transient period, making it more difficult to make simplifications and solve for the power as a function of time. Additionally, the long-lived transients would also have an impact on the stability of the reactor, as the power would not reach a steady state as quickly as it would with short-lived transients.

Overall, the long-lived transients would complicate the solution for the reactor power and would need to be carefully considered in order to accurately solve for it. It may also have implications on the safety and stability of the reactor, which would need to be taken into account in the design and operation of the reactor.