NUKEFACT #27

PROMPT JUMP IS NOT REACTOR RATE RESPONSE

last update July 4, 1997

Both the INPO Test Item Catalog and certain reactor vendor manuals assign a dual definition to "prompt jump", namely as the immediate response of reactor power to a step change in reactivity and also, as the response of reactor rate to a step change in reactivity. This is yet another example of mangled terminology in the subject area of reactor behavior, which does nothing but confuse the student and create unnecessary doubt and uncertainty in needed understanding. To compound the confusion, a prompt jump in power is also incorrectly identified as a step change in power.

"Prompt Jump" applies to the immediate response of reactor power to a step change in reactivity. The terminology derives, not because the response is immediate, or prompt, but rather from the fact that the power response is attributable to the prompt neutron behavior. This essay discusses the basics of prompt jump in power and applies the concept to operational situations.

First, consider the two basic modes of reactivity change, either by "ramp" (over an interval of time) or by "step" (instantaneous). Operational changes in fuel status, usually expressed in terms of reactivity change, always occur over some finite interval of time. Therefore, operational reactivity change is by ramp. The rate of change of reactivity with time is referred to as the "reactivity rate", or rho-dot, with units of delta-rho/second. A constant reactivity rate produces a reactivity variation that is linear with time. For a typical transient, reactivity is changed from a constant initial reactivity to a constant final reactivity. When plotted versus time, the linear reactivity change takes the form of a ramp:

RAMP CHANGE IN REACTIVITY

Several earlier NUKEFACTS have discussed reactivity ramp transients, as related to reactor rate behavior.

For a very rapid ramp, occurring within one second or less, the reactivity behavior with time can be approximated as a "step change" in reactivity. Here, the reactivity change is assumed to be instantaneous. When plotted versus time, the reactivity change takes the form of a squared-off step:

STEP CHANGE IN REACTIVITY

For a step change in reactivity, the power response produced by the prompt neutrons is so rapid as to be designated a "prompt jump". To indicate jump direction, convention is that a jump increase in power associated with a positive reactivity step delta-rho is a "prompt jump", while a jump decrease in power associated with a negative reactivity step delta-rho is a "prompt drop".

A prompt jump does not persist because both the source strength, non-fission neutrons plus delayed neutrons, and the fuel status, or final reactivity, are constant. The rapid incremental change in power, due to a change in source multiplication, to a momentary quasi-steady state, constitutes "prompt jump". Recall from NUKEFACT #4 that below prompt criticality, the reactor is always subcritical on prompt neutrons.

A simple equation exists that provides a good approximation of prompt jump. This equation can be derived from the General Equation for Source Multiplication given in NUKEFACT # 2. Let the initial power be defined as:

27.1

And with a constant neutron source, one that has yet to respond to a step change in reactivity, the power level after the prompt jump is:

27.2

Dividing P_j by P_i, the source terms cancel, giving the "prompt jump factor", PJF, as:

27.3

The prompt jump factor is the factor by which power undergoes immediate (but not instantaneous) change in response to a step change in reactivity. This power change occurs over several hundred prompt neutron lifetimes, through alteration of the prompt neutron population because of change in the source multiplication factor, 1/(beta - rho). But with the prompt neutron lifetime being of the order of 1x10^-4 seconds, this involves only a small fraction of one second. During this short interval, the delayed neutrons remain essentially at constant strength. For a step change from criticality, rho-i is zero and the prompt jump factor reduces to:

27.4

As a theoretical limit, the final reactivity, rho_f, must be less than prompt criticality. Operationally, the idealized step change in reactivity can be used with good approximation for any reactivity input completed in less than about 1 second. A reactor scram, or a control rod drop, can be considered to be a step change in reactivity. Of course, at Chernobyl, where a scram required 30 seconds, or more, for the control rods to reach the fully inserted position, this approximation was totally inappropriate.

For a given reactivity change, a step in reactivity produces the smallest change in power that can occur at termination of the reactivity change. The reason for this is that the resultant power change, the prompt jump, is due solely to the change in the source multiplication factor, 1/(beta - rho). The delayed neutron source does not respond immediately, remaining essentially constant. However, for a ramp reactivity change of the same magnitude, a reactivity change that occurs over an interval of time, the change in the source multiplication factor is identical to that for the step but is supplemented by the delayed neutron source strength which also exhibits change in the same direction as the source multipliction factor, making the total power change at the end of reactivity ramp larger than that of the step reactivity change. And, the slower the ramp, i.e. the smaller rho-dot, the larger the change in power at termination of the reactivity ramp.

Reactor power behavior with time, for a step-out in reactivity from criticality is shown in the following figure:

The power transient consists of two distinct parts. First, the power undergoes prompt jump as immediate response to the step-out in reactivity. Then, because the reactor is supercritical at the final reactivity condition, precursor production exceeds precursor decay, and the delayed neutron source strength begins to increase, resulting in a positive stable rate.

Note that the power response, even in this simplified illustration, does not take the form of a step. The reactivity change is in the form of a step. The transition between the prompt jump and upward sloping stable rate is a rounded corner as the delayed neutrons gradually begin to reflect the new reactivity situation. This rounding makes the prompt jump in power appear even less like a step.

EXAMPLE APPLICATIONS

1. A reactor is operating at 100% rated power when a scram occurs. If the control rods insert a delta-rho = -0.1000, what is the power level at the instant after the rod reaches the fully inserted position? Assume the time interval of rod travel is approximately one second and that the core beta = 0.0063.

   Answer: Since the scram is from a condition of criticality, Equation 27.4 applies. Substituting numerical values and solving for the prompt jump factor gives:

   
   
   Note that this 5.9% power at the end of a prompt drop is direct fission power. If the reactor has been at 100% for an extended period, then decay heat will be at 7% of rated power immediately following the scram. The fission power will decay more rapidly than the decay heat.

2. A reactor is operating at criticality, with power at 3x10^-8 amps on the Intermediate Range, when a single rod moves rapidly to the fully withdrawn position. If the control rod inserts a delta-rho = +0.0009, what is the power level at the instant after the rod reaches the fully withdrawn position? Assume the time interval of rod travel is approximately one second and that the core beta = 0.0057.
   
   
   Although this prompt jump in power appears to be a small change on the Intermediate Range, for a small positive delta-rho, it is 19% of the initial power level. If the initial power had been at 100% rated, then the prompt jump power would be 119% rated.

3. A reactor startup is interrupted as a single rod moves rapidly to the fully inserted position. If the initial reactivity is rho = -0.0200, the single rod delta-rho = -0.0078, and the equilibrium power level before the event was at 7x10⁵ cps on the Source Range, what is the power level at the instant after the single rod reaches the fully inserted positon? Assume the time interval of rod travel is approximately one second and that the core beta = 0.0062.
   
   

   Compare this PJF with that for a full scram in Example #1. Following the prompt drop, the reactor power will decay to a lower equilibrium level.

Prompt jump terminology defines a particular, and unique, form of power response. It applies specifically to power behavior associated with a step change in reactivity. There is a long standing, and simple, equation for defining the magnitude of prompt jump. The reactor rate during a promt jump in power reaches extremely large values because power is changing very rapidly. Reactor rate response during a prompt jump in power will spike upwards, or downwards, and then return immediately toward whatever stable or transient rate exists at constant final reactivity. This spike in reactor rate is NOT prompt jump.

In a future essay, we will show that for a rapid change in reactivity, the power at the end of the reactivity change can be calculated by either reactor rate or by prompt jump. The results will be nearly the same. Of course, the prompt jump equation is easier to use, when it applies. The point being that prompt jump is a limiting form of power behavior that is consistent with the concept of reactor rate. The concepts of reactor behavior hang together, if treated properly.

Prompt jump and prompt drop can be introduced, and practiced, in the class room on THE REACTOR TRAINER.