While the control-rod insertion must be as quick as possible in order to be able to shut-down the reactor after an accident with minimum delay, the extraction speed must not be greater than that which is necessary for flexible operation. This is done in order to reduce the maximum rate of reactivity insertion in case of accidental withdrawal of a rod. Usually the maximum extraction speed is required to compensate the loss of reactivity due to 135Xe build-up after a power reduction, considering the control-rod pattern giving the minimum possible worth.

The problem is strictly related to the definition of the number of control rods which can be extracted at the same time from the core. The required rate of reactivity insertion can be given with one rod at a relatively high speed, or more rods at a lower speed. For safety reasons it is better to restrict to a minimum the number of rods being extracted at the same time, but the simultaneous movement of more than one rod may be necessary in order to avoid too high a speed for one single rod, and thus too strict mechanical requirements (high speed and high positioning accuracy).

The accuracy with which a position can be reached and the minimum possible movement determine the accuracy with which the critical point can be reached. These requirements are, of course, stricter for each rod if more rods are being operated simultaneously. The accuracy with which criticality can be attained determines the accuracy with which a constant reactor temperature can be assured. This is not an important problem as long as the temperature coefficient is sufficiently negative, but if the temperature coefficient is zero or positive a small inaccuracy in reaching the critical control-rod position can lead to strong temperature variations. In this case, if the critical position can only approximately be reached, the temperature can only be kept within the desired limits by a continuous movement of the control rods (making the reactor continuously slightly over — and then undercritical). Consequently this relates the positioning accuracy to the frequency of the control-rod movement.

It must also be considered that one or more rods can fail to enter the core. If control-rod mechanisms can be inspected during operation it must be assumed that the rods being inspected are not available for shut-down.

The reactor must be kept undercritical even without the missing rods, which must be assumed to be the most effective ones. The criticality of a reactor in which some control rods are locally missing is sometimes improperly called “local criticality”. The reactivity released by the extraction of these missing rods must, of course, be subtracted from the control-rod effectiveness.

If the region in which control rods fail to enter is sufficiently large and has a high k* (e. g. fresh fuel) it might be difficult or even impossible to keep the reactor undercritical simply adding more rods in the surrounding regions. This problem is strongly dependent on the к» of the region considered, so that it is usually only important in the cold unpoisoned condition. This means that if control rods fail to enter a region large enough for local criticality, the reactor can be shut down, but after cooling down and Xe decay it may start up again. The power would then automatically stabilize itself to the level whose temperature corresponds to criticality. In this normal case of negative tempera­ture coefficient local criticality is not an accident with serious consequences, but makes a normal reactor shut-down impossible. It must be noted that if we consider the region without rods as an independent critical reactor, this would have a very high leakage because of its small size, and consequently a large negative temperature coefficient.

The problem of avoiding local criticality poses a restriction on the permissible control-rod pattern. Calculations about local criticality are usually performed in R-в geometry. It is better to represent control rods as non-diffusion regions, at least in the vicinity of the region without rods, because the use of equivalent diffuse poisons calculated for an infinite lattice is questionable in this case. It is important to calculate the complete reactor (e. g. 360° in R-в geometry). A calculation on a 180° geometry with (for symmetry reason) twice as many missing rods does not necessarily give the double excess reactivity than a 360° calculation. The reason is that if there are two completely independent critical regions the reactor has the same kcf! as with only one critical region (two critical reactors are as critical as one critical reactor).