Thermal nonleakage probability

Of the latter, some diffuse to outer surfaces and escape, but the fraction Fj remains in the reactor as thermal neutrons Fj is called the resonance-to-thermal nonleakage probability. Finally, the neutrons complete an energy cycle as et]m o PipP2 neutrons reach thermal energy per unit volume per unit time. The product P1P2 is the fission-to-thermal nonleakage probability, which we shall denote as F,h. 

We demonstrate the calculation of a temperature coefficient by considering the initial startup condition of the CP-5 and show how this coefficient may be used to predict the excess reacftivity (or multiplication) of the reactor at room temperature. Specifically, we compute the temperature coefficient of the hot clean reactor from the temperature derivatives of its thermal utilization, fast nonleakage probability, thermal nonleakage probability, and resonance-escape probability. The change in fc for a given change ST in temperature is then easily computed from the relation (6.142). 

The temperature coefficient of the thermal nonleakage probability is computed next. The appropriate relation is given in (6.165)... 

Equation (8.190), along with the determinant (8.188), may be regarded as the criticality requirements for this model. [Note that the last two factors on the left side of (8.190) give the fast and thermal nonleakage probabilities, respectively.] As in the bare-reactor calculation, (8.190) is solved for m (and X ) and the critical size (or concentration) obtained from the determinant. 

However, it seems clear that, in the case in which the unit-cell dimensions are small in comparison with the diffusion length, the form (1 H-would be a good approximation to the thermal nonleakage probability, and it would also be acceptable to use the general form L = D/S. Then, if we use... 

Turning now to the changes in neutron leakage induced by changes in reactor temperature, we note that the thermal nonleakage probability is given by equation (3.48) as... 

An infinite slab reactor of (extrapolated) thickness 1.5 m is composed of a uniform mixture of and graphite. Calculate (a) the ratio of carbon to atoms required for criticality and (b) the thermal nonleakage probability. 

L B thermal nonleakage probability ( 2) where L is the thermal diffusion length. 

The decrease in microscopic cross sections will increase L, and hence decrease the thermal nonleakage probability. 

We showed previously that the multiplication constant k for the finite medium could be written in the form (5.183) and identified the factor (1 + L B ) as the nonleakage probability for the neutrons based on the one-velocity approximation. In the case that the diffusion equation is used to describe the distribution of thermal neutrons in a reactor, this factor gives the nonleakage probability for the thermals. We demonstrate this relationship by applying two separate lines of reasoning According to our usual definition of the multiplication constant of a system, we can write... 

The quantities pth and g h in (9.84) denote the resonance-escape and fast nonleakage probabilities to thermal in the usual way [(4.260) and (6.79)). Penally, note that since the reactor described by (9.84) is not critical the multiplication constant will be different from unity and may be obtained from the relation... 

B. Density Coefficient A decrease in density decreases the macroscopic cross sections, which results in an increase of the mean free paths for absorption and scattering. The result is that the thermal diffusion length (L) and neutron age (t) increase. Because of the increase in L and T, the thermal and fast nonleakage probabilities are reduced. From Eq. (1) note that the reduced nonleakage probabilities decrease kg , which means that the reactivity effect is negative. A partial compensation for the effect of an increased L and t on the nonleakage if the core volume exp[Pg.193]

In this experiment the resonance escape probability in the core is determined through a foil measurement of the U cadmium ratio. A number of core parameters, such as thermal utilization and nonleakage probabilities, are required in this determination, and are calculated by the student with the aid of Appendix B. Two techniques for resolving the Np activity from the measured foil activity, which is due in part to and... 

---