The Reactor Rate Diagram introduced in NUKEFACT #6 stands alone as one of the most powerful tools available for promoting an understanding of reactor behavior, yet it is not found in conventional texts or as a commercial training resource. This essay, and future essays, will demonstrate the many valuable features and applications of the Reactor Rate Diagram, including the following:
This term was first identified as the "prompt neutron contribution" in NUKEFACT #5. Of course, the three rate curves shown will shift over the fuel cycle with the changing mix of fissile isotopes, typically U-235 and Pu-239. However, for the purpose of basic understanding of reactor behavior, the fuel cycle effects are a secondary matter to be dealt with later. Note also that a single reactivity rate of ±2x10-4 delta-rho/second is illustrated. This choice is arbitrary and perhaps somewhat large for certain commercial application, such as withdrawal of a single control rod. In fact, the Reactor Rate Diagram can include a number of ramp curves covering a range of reactivity rates. Since the ramp component is linear in rho-dot, a reactivity rate of ±1x10-4 delta-rho/second lies midway between the stable rate curve and the ramp curves shown.
The two contributors to reactor rate, as discussed in NUKEFACT #5, are clearly visible on the Reactor Rate Diagram. The stable rate curve represents the rate of power change due to an ongoing change in the delayed neutron source strength with time. If reactivity is constant, then this is the sole contributor to ongoing power change. The ramp curves represent the rate of power change due to the combined contributions of ongoing change in delayed neutron source strength and ongoing change in source multiplication with time. If reactivity is changing with time, as is frequently the operational case, then there are two contributors to reactor rate. The offset of the ramp curve from the stable rate depicts the contribution of ongoing source multiplication change to the total reactor rate.
To determine reactor rate from the Reactor Rate Diagram, the reactivity condition must be fully specified, i.e. both rho and rho-dot must be given. The reactor rate scale used is Startup Rate, simply because, being linear, it is easier to read than the nonlinear period scale. Reactor period, in seconds, can be obtained by using the relationship T = 26/SUR.
Example: given rho= +10x10-4 and rho-dot = +2x10-4 delta-rho/sec, find the reactor rate ..... Enter the Reactor Rate Diagram on the reactivity scale at rho = +10x10-4 and move upward to the ramp-out curve for rho-dot = +2x10-4 delta-rho/sec. Move horizontally to the Startup Rate scale and read SUR = +1.4 DPM. The reactor period is T = 26/1.4 = +18 seconds.
Reactor rate in this example is determined graphically with no calculation necessary, except for the conversion of startup rate to reactor period. One of the benefits of using the Reactor Rate Diagram is the minimization of distractive mathematical exercise, so as to allow more emphasis on the operational implications.
Once the student understands how typical points on the stable and transient rate curves are calculated, and the physical meaning of these curves, it serves no useful purpose to trudge through the mathematics for each new situation. The Reactor Rate Diagram provides precalculated rates for a wide range of off-critical reactivity conditions. It is an ideal tool for solving practical operational power transients. In addition, the Reactor Rate Diagram provides a visual overview that is far more meaningful than the rate equation by itself.