When can I use the prompt jump approximation?

[dRic2]

I know that it is only an approximation to get an idea, but at times it works quite well (in class we solved the kinetics equation for a PWR reactor (point-reactor model) with MATLAB and then we plotted the solution along with the prompt jump approximation... It was very good).
But I did not fully understand when you can use it. It seems to me that the main conditions are:
1) very small mean generation time
2) I have a step of reactivity very far from 1$ (much smaller or bigger).

Any other constraints ? (Point-reactor model for kinetics equation must hold in the first place)

Thanks Ric

 

[rpp]

When you derive the prompt jump, the first approximation is that the precursor concentration does not change and you are calculating the change due to prompt neutrons. This is a valid approximation for times immediately after a transient because the prompt neutrons have a much shorter lifetime than the precursors.

The second approximation is that $\rho \ll \beta$ so that the following exponential is negligible.
$$ \exp \left( \frac{\rho-\beta}{\Lambda} t \right) \approx 0$$

Therefore, the equation is valid any time $$\rho \ll \beta$$. The reactivity can be positive or negative, but definitely cannot be greater than beta (i.e. must not be prompt critical or close to prompt critical.)

As an example, if you have a reactivity change of $0.1 and a lifetime of 10^-4, the exponential is exp(-58t), which is extremely small.

Your next question is "when can this be used?". The prompt jump approximation is mainly used to help you understand how the reactor operates, and also to interpret the behavior of a reactor. You can see the prompt jump occur when you pull rods in a small reactor, or scram in any reactor (usually large reactors change reactivity too slow to observe the prompt jump). As far as I know, it is not "used" in any calculations, it just helps explain the reactor behavior.

I hope this helps.

 

[dRic2]

Thank you very much! Very clear and helpful explanation!