Ring of Control Rods in Two-group Model

The problem of determining the criticality condition and the flux distribution in the two-group model for a ring of gray rods has been considered by Avery. The method used is a generalization of the Nordheim-Scalettar approach and may be applied when either the rods or the reactor, or both, are multiplying media. 

If we choose M such pairs for the M rods, and add also a general solution 

it is convenient to use a series representation for each of the singular functions. Thus, as in (11.78), we write for rod m (refer to Fig. 11.11) 

Thus all terms in Eq. (11.96) vanish except those in the form Jatj, YuMt and and these appear with factor M, Equation (11.96) therefore reduces to 

Similar results can be obtained for the functions Ko(0dm) the substitution of these, along with (11.98), into the expression for the fast flux yields 

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