Reactors with Spherical Symmetry Serber-Wilson Condition

3 Reactors with Spherical Symmetry Serber-Wilson Condition 

In this calculation, the continuity of net-current condition will be retained. This choice is made because the net current out of any region is proportional to the volume integral of the neutron density (or flux) over that region. Thus in computing the neutron leakage from a volume V having surface area Ay one might use a relation of the type 

In the present treatment we discard the condition that the flux be continuous at an interface, and select instead a relation of the integral type (as in the case of the net-current condition). The boundary conditions to be applied here in place of the continuity conditions (1) and (2) of (8.4) are as follows  

The method based on the Serber-Wilson condition is especially suited to the treatment of reactor systems which are spherically symmetric. We will develop the basic ideas involved in this method by analyzing, on the basis of the one-velocity model, the simple case of a spherical core surrounded by an infinite reflector. However, the method is generally applicable to finite systems, to multiregion configurations, and to multigroup (energy) calculations. These problems will not be discussed here. In order to demonstrate the effect on the criticality requirements of the 

Scrber-Wilson condition the critical radius of a spherical reactor with an infinite reflector will be computed for various core and reflector compositions, and the results will be compared with the computations based on the method of Sec. 8.2b (using the continuity-of-flux condition). 

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