Early in your study of the reactor you were probably exposed to some form of a reactor rate curve for the Delayed-Critical region, albeit nothing as understandable and complete as the D-C Rate Diagram found in NUKEFACTs. Since, your reactor rate meter, like everyone else's, also functions in the Sub-Critical Region (i.e., the low power subcritical condition where non-fission source neutrons are significant), perhaps you noticed the lack of a rate curve for the S-C Region. Unless you have access to our manual, Basic Reactor Behavior, it is fairly certain that this non-trivial aspect of the reactor rate has been ignored in your training. This omission is especially curious considering that the rate equation that incorporates the non-fission neutron source has widespread recognition in U.S. nuclear plants. It is expressed as:
where: S-bar = S/(2.5x3.1x1010), watts
S = non-fission source strength, neutrons/second
P = fission power, watts
The S-bar/P term accounts for the non-fission neutron source contribution to reactor rate. This is the general equation for reactor rate. It applies to both the Sub-Critical Region and the Delayed-Critical Region of operation, from shutdown to full power. In the S-C Region the rate equation applies as shown. In the D-C Region the S-bar/P term can be omitted because non-fission source emissions are a negligible part of total neutron production.
It is the D-C form of the rate equation that is used to construct the Delayed-Critical Reactor Rate Diagrams illustrated in NUKEFACT #17. And the S-C form of the rate equation can be used in like manner to construct a Sub-Critical Reactor Rate Diagram. But what do we already know about reactor rate in the S-C Region? First, there is only one stable rate, namely SUR = 0 DPM or T = infinite seconds, as occurs at equilibrium subcritical multiplication. If the reactor is off-equilibrium, then power will move toward its equilibrium level at a decelerating transient rate. Thus, the stable rate curve in the S-C Region consists of a horizontal line at 0 DPM (infinite sec) that extends from shutdown reactivity to criticality. Also, we know that power responds to ramp action as a rho-dot term is introduced. As might be expected, the transient rate curves for ramp-out and ramp-in lie above and below, respectively, the S-C stable rate curve as on the D-C rate diagram. The PWR Rate Diagram uses Start-Up Rate, while the BWR Rate Diagram uses Reactor Period. For reference, both Diagrams first illustrated just the stable rate curve (the locus of rates for constant reactivity conditions, i.e. with rho-dot equal to zero).
The equivalent reactor rate diagram scaled for reactor period displays the same horizontal stable rate curve.Then, starting from the initial reactivity of -0.0300, a ramp-out to rho = -.0010 followed by ramp-in to the initial reactivity, using rho-dot = ±2x10-4 delta-rho/second, produces the following graphic:
The equivalent reactor rate diagram scaled for reactor period displays the same ramp sequence. Observe that the subcritical reactor rate increases in magnitude for SUR and shortens in time for reactor period as negative reactivity is reduced. This is an important indicator for the proximity of criticality during reactor startup. On termination of ramping, the reactor rate moves vertically to the stable rate curve as power reaches equilibrium multiplication. The initial curl on the ramp-in curve is caused by delayed neutron precursors realigning from a steady state mix to a decreasing power transient. Otherwise, the S-C ramp-out and ramp-in curves are near mirror images of each other.
In NUKEFACT #20 we further discuss the S-C Rate Diagram and combine the S-C and D-C Diagrams into a General Reactor Rate Diagram.
