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.