Prompt jump approximation

The prompt jump approximation. The neutron Equation (77) may be written as... 

A consequence of the prompt jump approximation is the sudden change of N following a sudden change of p. If p changes from pi to p2, then N changes from Ni to N2 where... 

In the numerical integrations of the one parameter Equations (77) and (78), numerical difficulties caused by the small value of Z can be avoided by the use of the prompt jump approximation which replaces the differential Equation (77) for N by the ordinary Equation (101). This reduction in the overall order of the system of equations must be accompanied by a changed set of initial conditions. Specifically, the initial conditions to be used are those which apply immediately following the prompt jump. Thus, in a problem where p changes suddenly, the calculation starts with the value of N following the prompt jump. If dpjdt changes suddenly, then the calculation... 

Some non-linear problems. Consider the problem of a sudden introduction of reactivity into a critical reactor with no source in which the feedback reactivity is proportional to the energy generated, as might be the case for a reactor with no cooling. Assuming that the reactivity is less than j8, the prompt jump approximation may be used, which in the one delay group approximation results in (compare Equation (106))... 

In a conventional point kinetics model, involving the concentration of xenon and the flux tending to bum it out, the problem is nonlinear. However, it seems reasonable to make the prompt jump approximation in which the neutron lifetime and the lifetime of the precursors are neglected in comparison with the periods of the iodine and xenon isotopes governing the problem. We can then regard the flux as a control variable that can be adjusted to different levels as required in an optimum program. 

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