Coupling parameters for partially reflected reactors

For situations in which the standard point kinetic model does not adequately characterize the kinetic behavior of a reflected system, the Avery-Cohn differential equations can be used. However, these equations require that one determine the coupling parameters between the core and the reflector, f{sub cr} and f{sub rc}. The coupling parameter, f{sub cr}, represents the probability that a neutron in the core will leak into the reflector, and the coupling parameter, f{sub rc}, represents the probability that a neutron in the reflector will scatter back into the core. As discussed in Reference 3, these two coupling parameters can be calculated from the multiplication factor of the bare core, k{sub c}, the effective multiplication factor of the integral system, k{sub eff}, and the fraction of system neutrons absorbed in the core region, P{sub ca}. The methodology presented in Ref. 3 was described for a fully reflected system, but it is also applicable to some types of partially reflected systems. In particular, it is applicable to those systems where neutrons leaving any core surface not contiguous to the reflector have a zero probability of entering the reflector. In other words, these surfaces have a view factor of 0 to all reflector surfaces in the system. However, if the view factor between an unreflected core surface and a reflector surface is not zero, then the aforementioned methodology has to be modified. To calculate f{sub cr}, one must include an estimate of the single-pass probability that a neutron escapes from the core to infinity, f{sub ci}. This is accomplished by including a view factor(s) in the calculations that accounts for the fraction of neutrons that are not traveling on a line intersecting some portion of the reflector. This paper illustrates this modification by assuming the partially reflected system shown in Fig. 1c